WikiROMS - User contributions [en]

INLET TEST CASE

2009-01-07T16:28:32Z

Etwomey:

<div class="title">Inlet Test Case</div>

This test case couples ROMS and [[SWAN]] directly using the Modeling Coupling Toolkit (MCT) library. To run this application the user needs to activate [[Options#INLET_TEST|INLET_TEST]]. It only can be run in distributed-memory (MPI) since the parallel threads are split to run both ROMS and SWAN at the same time. This test illustrates the
significance of wave-current coupling. This application and coupling methodology is described in [[Bibliography#WarnerJC_2008a|Warner ''et al.'' (2008)]].

This test case models and idealized tidal inlet system. The model domain is a 15x14 km rectangle with a uniform initial depth of 4 m. The model setup parameters are shown in the table below. The domain is separated into two regions: the seaward (top) and back-barrier (bottom) regions. The seaward region is open with radiation conditions on the western, northern and eastern edges. The back-barrier region is enclosed with four walls and is connected to the seaward region through a 2 km wide inlet. The model is forced by a tide and waves. An oscillating water level is imposed on the northern edge with a tidal amplitude of 1 m. Waves are also imposed on the northern edge with a height of 1 m, directed to the south with a period of 10s.

Files to run this test case can be downloaded [[media:Inlet_test_config.zip|here]].

Table 1. Important model parameters:
{| border="1" cellspacing="0" cellpadding="5" align="center"
!Model Parameter
!Variable
!Value
|-
|length, width, depth
|[[Variables#Xsize|Xsize]], [[Variables#Esize|Esize]], [[Variables#hmax|hmax]]
|15000 m, 14000 m, 4.0 m
|-
|number of grid spacings
|[[Variables#Lm|Lm]], [[Variables#Mm|Mm]], [[Variables#N|N]]
|75, 70, 10
|-
|bottom Roughness
|[[Variables#Zob|Zob]]
|0.015 m
|-
|time step
|[[Variables#dt|dt]]
|10 s
|-
|simulation steps
|[[Variables#ntimes|ntimes]]
|17280 steps (2 days)
|-
|morphology factor
|[[Variables#morph_fac|morph_fac]]
|10 (=20 day scaled simulation)
|-
|grain size
|[[Variables#Sd50|Sd50]]
|0.10 mm
|-
|settle velocity
|[[Variables#Wsed|Wsed]]
|11.0 mm s-1
|-
|erosion rate
|[[Variables#Erate|Erate]]
|5 x 10-3 kg m-2s-1
|-
|critical stress
|[[Variables#tau_cd|tau_cd]], [[Variables#tau_ce|tau_ce]]
|0.10 Nm-2
|-
|porosity
|[[Variables#poros|poros]]
|0.50
|-
|bed thickness
|[[Variables#bed|bed(:, :, :, ithck)]]
|10.0 m
|-
|northern edge tide
|A, Tt
|1.0 m, 12 h
|-
|northern edge wave height
|Hsig
|2 m
|-
|northern edge wave period
|T
|10 s
|-
|northern edge wave direction
|θ
|from 0° (from North)
|-
|}

Below we provide a brief example of the model output.

[[Image:Inlet_test_zeta_day0.5.png|thumb|850px|none|<center>Figure 1: ROMS output of free surface and barotropic currents at t=0.5 days.</center>]]

[[Image:Inlet_test_Hwave_day0.5.png|thumb|850px|none|<center>Figure 2: SWAN output of wave height (Hwave, m) and barotropic currents.]]

INLET TEST CASE

2009-01-07T16:24:48Z

Etwomey:

<div class="title">Inlet Test Case</div>

This test case couples ROMS and [[SWAN]] directly using the Modeling Coupling Toolkit (MCT) library. To run this application the user needs to activate [[Options#INLET_TEST|INLET_TEST]]. It only can be run in distributed-memory (MPI) since the parallel threads are split to run both ROMS and SWAN at the same time. This test illustrates the
significance of wave-current coupling. This application and coupling methodology is described in [[Bibliography#WarnerJC_2008a|Warner ''et al.'' (2008)]].

This test case models and idealized tidal inlet system. The model domain is a 15x14 km rectangle with a uniform initial depth of 4 m. The model setup parameters are shown in the table below. The domain is separated into two regions: the seaward (top) and back-barrier (bottom) regions. The seaward region is open with radiation conditions on the western, northern and eastern edges. The back-barrier region is enclosed with four walls and is connected to the seaward region through a 2 km wide inlet. The model is forced by a tide and waves. An oscillating water level is imposed on the northern edge with a tidal amplitude of 1 m. Waves are also imposed on the northern edge with a height of 1 m, directed to the south with a period of 10s.

Files to run this test case can be downloaded here: [[Image:Inlet_test_config.zip]].

Table 1. Important model parameters:
{| border="1" cellspacing="0" cellpadding="5" align="center"
!Model Parameter
!Variable
!Value
|-
|length, width, depth
|[[Variables#Xsize|Xsize]], [[Variables#Esize|Esize]], [[Variables#hmax|hmax]]
|15000 m, 14000 m, 4.0 m
|-
|number of grid spacings
|[[Variables#Lm|Lm]], [[Variables#Mm|Mm]], [[Variables#N|N]]
|75, 70, 10
|-
|bottom Roughness
|[[Variables#Zob|Zob]]
|0.015 m
|-
|time step
|[[Variables#dt|dt]]
|10 s
|-
|simulation steps
|[[Variables#ntimes|ntimes]]
|17280 steps (2 days)
|-
|morphology factor
|[[Variables#morph_fac|morph_fac]]
|10 (=20 day scaled simulation)
|-
|grain size
|[[Variables#Sd50|Sd50]]
|0.10 mm
|-
|settle velocity
|[[Variables#Wsed|Wsed]]
|11.0 mm s-1
|-
|erosion rate
|[[Variables#Erate|Erate]]
|5 x 10-3 kg m-2s-1
|-
|critical stress
|[[Variables#tau_cd|tau_cd]], [[Variables#tau_ce|tau_ce]]
|0.10 Nm-2
|-
|porosity
|[[Variables#poros|poros]]
|0.50
|-
|bed thickness
|[[Variables#bed|bed(:, :, :, ithck)]]
|10.0 m
|-
|northern edge tide
|A, Tt
|1.0 m, 12 h
|-
|northern edge wave height
|Hsig
|2 m
|-
|northern edge wave period
|T
|10 s
|-
|northern edge wave direction
|θ
|from 0° (from North)
|-
|}

Below we provide a brief example of the model output.

[[Image:Inlet_test_zeta_day0.5.png|thumb|850px|none|<center>Figure 1: ROMS output of free surface and barotropic currents at t=0.5 days.</center>]]

[[Image:Inlet_test_Hwave_day0.5.png|thumb|850px|none|<center>Figure 2: SWAN output of wave height (Hwave, m) and barotropic currents.]]

INLET TEST CASE

2009-01-07T16:03:41Z

Etwomey:

<div class="title">Inlet Test Case</div>

This test case couples ROMS and [[SWAN]] directly using the Modeling Coupling Toolkit (MCT) library. To run this application the user needs to activate [[Options#INLET_TEST|INLET_TEST]]. It only can be run in distributed-memory (MPI) since the parallel threads are split to run both ROMS and SWAN at the same time. This test illustrates the
significance of wave-current coupling. This application and coupling methodology is described in [[Bibliography#WarnerJC_2008a|Warner ''et al.'' (2008)]].

This test case models and idealized tidal inlet system. The model domain is a 15x14 km rectangle with a uniform initial depth of 4 m. The model setup parameters are shown in the table below. The domain is separated into two regions: the seaward (top) and back-barrier (bottom) regions. The seaward region is open with radiation conditions on the western, northern and eastern edges. The back-barrier region is enclosed with four walls and is connected to the seaward region through a 2 km wide inlet. The model is forced by a tide and waves. An oscillating water level is imposed on the northern edge with a tidal amplitude of 1 m. Waves are also imposed on the northern edge with a height of 1 m, directed to the south with a period of 10s.

Files to run this test case can be downloaded [[Inlet_test_config.zip|here]].

Table 1. Important model parameters:
{| border="1" cellspacing="0" cellpadding="5" align="center"
!Model Parameter
!Variable
!Value
|-
|length, width, depth
|[[Variables#Xsize|Xsize]], [[Variables#Esize|Esize]], [[Variables#hmax|hmax]]
|15000 m, 14000 m, 4.0 m
|-
|number of grid spacings
|[[Variables#Lm|Lm]], [[Variables#Mm|Mm]], [[Variables#N|N]]
|75, 70, 10
|-
|bottom Roughness
|[[Variables#Zob|Zob]]
|0.015 m
|-
|time step
|[[Variables#dt|dt]]
|10 s
|-
|simulation steps
|[[Variables#ntimes|ntimes]]
|17280 steps (2 days)
|-
|morphology factor
|[[Variables#morph_fac|morph_fac]]
|10 (=20 day scaled simulation)
|-
|grain size
|[[Variables#Sd50|Sd50]]
|0.10 mm
|-
|settle velocity
|[[Variables#Wsed|Wsed]]
|11.0 mm s-1
|-
|erosion rate
|[[Variables#Erate|Erate]]
|5 x 10-3 kg m-2s-1
|-
|critical stress
|[[Variables#tau_cd|tau_cd]], [[Variables#tau_ce|tau_ce]]
|0.10 Nm-2
|-
|porosity
|[[Variables#poros|poros]]
|0.50
|-
|bed thickness
|[[Variables#bed|bed(:, :, :, ithck)]]
|10.0 m
|-
|northern edge tide
|A, Tt
|1.0 m, 12 h
|-
|northern edge wave height
|Hsig
|2 m
|-
|northern edge wave period
|T
|10 s
|-
|northern edge wave direction
|θ
|from 0° (from North)
|-
|}

Below we provide a brief example of the model output.

[[Image:Inlet_test_zeta_day0.5.png|thumb|850px|none|<center>Figure 1: ROMS output of free surface and barotropic currents at t=0.5 days.</center>]]

[[Image:Inlet_test_Hwave_day0.5.png|thumb|850px|none|<center>Figure 2: SWAN output of wave height (Hwave, m) and barotropic currents.]]

File:Inlet test config.zip

2009-01-07T15:41:59Z

Etwomey:

Test Cases

2009-01-06T20:03:48Z

Etwomey:

<div class="title">ROMS/TOMS Test Cases</div>

ROMS is distributed with several idealized and realistic applications that can be used for testing, benchmarking, process-oriented studies, accuracy of numerical algorithms, learning and training, and ocean modeling experimentation. It also can be used to evaluate the efficiency, accuracy, and robustness of its numerical and physical algorithms against the solutions produced by other ocean modeling systems. Analytical or semi-analytical solutions exist for some of these test cases and few metrics/scores can be computed to assess model skill.

==Idealized Applications==

Currently, there are several idealized applications in ROMS to test its algorithms. Mostly all of these applications are initialized and forced with analytical expressions in [[Functionals]]. It is recommended to the beginner user to run some of them to gain experience and explore ROMS capabilities.

* '''Process-oriented Applications'''
** [[BASIN_CASE | Big Bad Basin]]
** [[CANYON_CASE | Coastal Form Stress Canyon Test]]
** [[GRAV_ADJ_CASE | Gravitational Adjustment Test]]
** [[KELVIN_CASE | Kelvin Wave Test]]
** [[LAB_CANYON_CASE | Lab Canyon Test, Polar Coordinates]]
** [[OVERFLOW_CASE | Gravitational/Overflow Test]]
** [[RIVERPLUME1_CASE | River Plume Test 1]]
** [[RIVERPLUME2_CASE | River plume Test 2 (Hyatt and Signell)]]
** [[SOLITON_CASE | Equatorial Rossby Wave Test]]
** [[UPWELLING_CASE | Wind-Driven Upwelling/Downwelling over a Periodic Channel]] (default)
** [[WEDDELL_CASE | Idealized Weddell Sea Shelf Application]]
** [[WINDBASIN_CASE | Linear Wind-driven Constant Coriolis Basin]]

* '''Algorithm Testing'''
** [[BIO_TOY_CASE | One-dimensional Biology Toy]]
** [[BL_TEST_CASE | Boundary Layers Test]]
** [[CHANNEL_NECK_CASE | Channel with a Constriction]]
** [[FLT_TEST_CASE | Float Tracking Test]]
** [[LMD_TEST_CASE | Vertical Mixing K-Profile Parameterization Test]]
** [[SEAMOUNT_CASE | Seamount Test]]

* '''Adjoint-based Applications'''
** [[A4DVAR_TOY_CASE | 4DVAR Data Assimilation Toy over a Periodic Channel]]
** [[DOUBLE_GYRE_CASE | Double-Gyre Test]]

* '''Sediment Applications'''
** [[ESTUARY_TEST_CASE | ESTUARY_TEST]]: options for estuary with sediment (suspended) transport test
** [[LAKE_SIGNELL_CASE | LAKE_SIGNELL]]: options for closed basin (lake) forced with wind
** [[SED_TEST1_CASE | SED_TEST1]]: options for suspended sediment in a test channel
** [[SED_TOY_CASE | SED_TOY]]: options for one-dimensional (vertical) sediment toy (empty)
** [[SHOREFACE_CASE | SHOREFACE]]: shore face planar beach test case (empty)
** [[TEST_CHAN_CASE | TEST_CHAN]]: options for sediment test channel case
** [[TEST_HEAD_CASE | TEST_HEAD]]: options for sediment test headland case

* '''Model Coupling'''
** [[COUPLING_TEST_CASE | COUPLING_TEST]]: options for atmosphere-ocean two-way coupling test
** [[INLET_TEST_CASE | INLET_TEST]]: options for inlet test case, waves-ocean (SWAN/ROMS) two-way coupling
** [[TEST_HEAD_CASE | TEST_HEAD]]: options for sediment test headland case

* '''Benchmarks'''
** [[BENCHMARK_CASE | Benchmark Tests, Idealized Southern Ocean]]

==Realistic Applications==

==Contributed Applications==

TEST HEAD CASE

2008-12-08T16:20:41Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

<wikitex>Coriolis $\textcolor{blue}{f}~ =~ 1.0~ e^{-4}$</wikitex>
No heating/cooling 
No wind 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u}~ =~ 0~ m^{3}$ 
$Salinity~ =~ 0$ 
$\textcolor{blue}{Temperature}~ =~ 20^{\circ}C$</wikitex> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
<wikitex>Bottom roughness $\textcolor{blue}{Z_{\circ}}~ =~ 0.015~ m$ 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity $\textcolor{blue}{u_{\circ}}~ =~ 0.5~ m/s$ 
Celerity $\textcolor{blue}{C}~=~ \sqrt{(\textcolor{blue}{g}\times 20.0)}$ 
Reference water level $\textcolor{blue}{\xi_{\circ}}~ =~\textcolor{blue}{u_{\circ}}/\sqrt{(\textcolor{blue}{g}/20)}$ 
Wave period $\textcolor{blue}{T}~ =~ 12$ hours (43200 seconds) 
Wave length $\textcolor{blue}{L}~ = \textcolor{blue}{C}\times \textcolor{blue}{T}$ 
Wave number $\textcolor{blue}{k}~ =~ (2\times\pi)/\textcolor{blue}{L}$</wikitex> 

<wikitex>For each point $y$ along the boundary at time $\textcolor{blue}{t}$:

Water level $\textcolor{blue}{\xi}~ =~\textcolor{blue}{\xi_{\circ}}\times exp(\textcolor{blue}{-f}\times y/\textcolor{blue}{C}) \times cos(\textcolor{blue}{k} \times (x - \textcolor{blue}{C} \times \textcolor{blue}{t}))$</wikitex> 

{{note}}'''Note:''' <wikitex>$x$ at western boundary is $\textcolor{blue}{-L}/2$ 
Depth-mean flow $\textcolor{blue}{}~ =~ \sqrt{(\textcolor{blue}{g}/20)} \times \textcolor{blue}{\xi}(y)$</wikitex> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

<wikitex>Gravitational acceleration $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant $\textcolor{blue}{\kappa}~=~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\textcolor{blue}{\nu}~ =~ 1e^{-6}~ m^{2}/s$</wikitex> 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-12-08T16:19:43Z

Etwomey: /* Physical Constants */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

<wikitex>Coriolis $\textcolor{blue}{f}~ =~ 1.0~ e^{-4}$</wikitex>
No heating/cooling 
No wind 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u}~ =~ 0~ m^{3}$ 
Salinity = $0$ 
$\textcolor{blue}{T}~ =~ 20^{\circ}C$</wikitex> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
<wikitex>Bottom roughness $\textcolor{blue}{Z_{\circ}}~ =~ 0.015~ m$ 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity $\textcolor{blue}{u_{\circ}}~ =~ 0.5~ m/s$ 
Celerity $\textcolor{blue}{C}~=~ \sqrt{(\textcolor{blue}{g}\times 20.0)}$ 
Reference water level $\textcolor{blue}{\xi_{\circ}}~ =~\textcolor{blue}{u_{\circ}}/\sqrt{(\textcolor{blue}{g}/20)}$ 
Wave period $\textcolor{blue}{T}~ =~ 12$ hours (43200 seconds) 
Wave length $\textcolor{blue}{L}~ = \textcolor{blue}{C}\times \textcolor{blue}{T}$ 
Wave number $\textcolor{blue}{k}~ =~ (2\times\pi)/\textcolor{blue}{L}$</wikitex> 

<wikitex>For each point $y$ along the boundary at time $\textcolor{blue}{t}$:

Water level $\textcolor{blue}{\xi}~ =~\textcolor{blue}{\xi_{\circ}}\times exp(\textcolor{blue}{-f}\times y/\textcolor{blue}{C}) \times cos(\textcolor{blue}{k} \times (x - \textcolor{blue}{C} \times \textcolor{blue}{t}))$</wikitex> 

{{note}}'''Note:''' <wikitex>$x$ at western boundary is $\textcolor{blue}{-L}/2$ 
Depth-mean flow $\textcolor{blue}{}~ =~ \sqrt{(\textcolor{blue}{g}/20)} \times \textcolor{blue}{\xi}(y)$</wikitex> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

<wikitex>Gravitational acceleration $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant $\textcolor{blue}{\kappa}~=~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\textcolor{blue}{\nu}~ =~ 1e^{-6}~ m^{2}/s$</wikitex> 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-12-08T16:15:15Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

<wikitex>Coriolis $\textcolor{blue}{f}~ =~ 1.0~ e^{-4}$</wikitex>
No heating/cooling 
No wind 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u}~ =~ 0~ m^{3}$ 
Salinity = $0$ 
$\textcolor{blue}{T}~ =~ 20^{\circ}C$</wikitex> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
<wikitex>Bottom roughness $\textcolor{blue}{Z_{\circ}}~ =~ 0.015~ m$ 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity $\textcolor{blue}{u_{\circ}}~ =~ 0.5~ m/s$ 
Celerity $\textcolor{blue}{C}~=~ \sqrt{(\textcolor{blue}{g}\times 20.0)}$ 
Reference water level $\textcolor{blue}{\xi_{\circ}}~ =~\textcolor{blue}{u_{\circ}}/\sqrt{(\textcolor{blue}{g}/20)}$ 
Wave period $\textcolor{blue}{T}~ =~ 12$ hours (43200 seconds) 
Wave length $\textcolor{blue}{L}~ = \textcolor{blue}{C}\times \textcolor{blue}{T}$ 
Wave number $\textcolor{blue}{k}~ =~ (2\times\pi)/\textcolor{blue}{L}$</wikitex> 

<wikitex>For each point $y$ along the boundary at time $\textcolor{blue}{t}$:

Water level $\textcolor{blue}{\xi}~ =~\textcolor{blue}{\xi_{\circ}}\times exp(\textcolor{blue}{-f}\times y/\textcolor{blue}{C}) \times cos(\textcolor{blue}{k} \times (x - \textcolor{blue}{C} \times \textcolor{blue}{t}))$</wikitex> 

{{note}}'''Note:''' <wikitex>$x$ at western boundary is $\textcolor{blue}{-L}/2$ 
Depth-mean flow $\textcolor{blue}{}~ =~ \sqrt{(\textcolor{blue}{g}/20)} \times \textcolor{blue}{\xi}(y)$</wikitex> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant = 0.41 
Dynamic viscosity (and minimum diffusivity) ν = 1e-6 m2/s 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-12-08T15:41:11Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

<wikitex>Coriolis $\textcolor{blue}{f}~ =~ 1.0~ e^{-4}$</wikitex>
No heating/cooling 
No wind 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u}~ =~ 0~ m^{3}$ 
Salinity = $0$ 
$\textcolor{blue}{T}~ =~ 20^{\circ}C$</wikitex> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= &radic;(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level ζ = ζ0 * exp(-f * y/C) * cos(k * (x - C * t)) 

{{note}}'''Note:''' x at western boundary is -L/2 
Depth-mean flow &lang;u&rang; = √(g/20) * ζ(y) 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant = 0.41 
Dynamic viscosity (and minimum diffusivity) ν = 1e-6 m2/s 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-12-08T15:37:49Z

Etwomey: /* Forcing */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

<wikitex>Coriolis $\textcolor{blue}{f}~ =~ 1.0~ e^{-4}$</wikitex>
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= &radic;(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level ζ = ζ0 * exp(-f * y/C) * cos(k * (x - C * t)) 

{{note}}'''Note:''' x at western boundary is -L/2 
Depth-mean flow &lang;u&rang; = √(g/20) * ζ(y) 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant = 0.41 
Dynamic viscosity (and minimum diffusivity) ν = 1e-6 m2/s 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

SED TEST1 CASE

2008-12-08T15:05:28Z

Etwomey: /* Physical Constants */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
<wikitex>No rotation $(\textcolor{blue}{f}~=~0)$</wikitex> 
No wind 
No heating/cooling 

==Boundary Conditions==

<wikitex>Inflow maintained as steady flow, depth-mean flow $\textcolor{blue}{}~ =~ 1~ m/s$ 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness $\textcolor{blue}{Z_{0}}~=~ 0.005$</wikitex> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

<wikitex>Gravitational acceleration $\textcolor{blue}{g}~=~ 9.81~ m/s^{2}$ 
Von Karman's constant $\textcolor{blue}{\kappa}~=~ 0.41$ 
Water density $\textcolor{blue}{\rho_{w}}~=~ 998~ kg/m^{3}$ 
Dynamic viscosity (and minimum diffusivity) $\textcolor{blue}{\nu}~=~ 1e-6~ m^{2}/s$</wikitex> 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of 10 m3/s/m of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of 4x10-5 m/m.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

:{|border="1"
!
!∂η/∂x
!u*m2/s2
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-12-08T14:56:38Z

Etwomey: /* Boundary Conditions */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
<wikitex>No rotation $(\textcolor{blue}{f}~=~0)$</wikitex> 
No wind 
No heating/cooling 

==Boundary Conditions==

<wikitex>Inflow maintained as steady flow, depth-mean flow $\textcolor{blue}{}~ =~ 1~ m/s$ 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness $\textcolor{blue}{Z_{0}}~=~ 0.005$</wikitex> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ= 0.41 
Water density ρw= 998 kg/m3 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of 10 m3/s/m of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of 4x10-5 m/m.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

:{|border="1"
!
!∂η/∂x
!u*m2/s2
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-12-08T14:54:11Z

Etwomey: /* Forcing */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
<wikitex>No rotation $(\textcolor{blue}{f}~=~0)$</wikitex> 
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow &lang;u&rang; = 1 m/s 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.005 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ= 0.41 
Water density ρw= 998 kg/m3 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of 10 m3/s/m of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of 4x10-5 m/m.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

:{|border="1"
!
!∂η/∂x
!u*m2/s2
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

ESTUARY TEST CASE

2008-12-08T14:38:01Z

Etwomey: /* Initial Conditions */

<div class="title">Suspended Sediment Test in an Estuary</div>

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

[[Image:Test_case_2.gif|center]]

==Domain==

The domain is a long, narrow rectangular channel.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|1000 m
|-
|Depth
|align="center"|h
|10 m at western end, decreasing linearly to 5 at eastern end
|-
|Temperature
|align="center"|T
|10°C
|}

==Bottom Sediment==

Single grain size on bottom:

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|-
|Bed thickness
|align="center"|bed_thick
|1 mm
|}

==Forcing==

No Coriolis 
No wind 
No heating/cooling 

==Initial Conditions==

<wikitex>Salinity distribution from $\textcolor{green}{west\ end}=~35$ to $\textcolor{green}{east\ end}=~0$. (Vertically well mixed)</wikitex> 

==Boundary Conditions==
General:
<wikitex>:'''North and south sides''' = walls with no fluxes, no friction '''Bottom roughness''' $\textcolor{blue}{K_{s}}~ =~ 0.15~ m~(\textcolor{blue}{Z_{o}}~ =~ \textcolor{blue}{K_{s}}/30~ =~ 0.005~ m )$ '''Sediment flux''' = calculated by model '''Surface''' = free surface, no fluxes 

Flow, Western end, tidal:
:<wikitex>$\textcolor{blue}{q_{west}}~ =~ 4000~ m^{3}/s~ \times~ sin(\textcolor{blue}{\omega t})~ -~\textcolor{blue}{q_{east}}$ 
:$\textcolor{blue}{\omega}~ =~ 2\pi~ / \textcolor{blue}{T}$ 
:$\textcolor{blue}{T}~ =~ 12~ \times~ 3600~ seconds~ =~ model~ time~ step~,~ seconds~$ </wikitex>

Flow, Eastern end, constant riverine (varying depth):
:<wikitex>$\textcolor{blue}{q_{east}}~ =~ 400~ m^{3}/s$</wikitex> 

Salinity, western end:
:<wikitex>Radiation condition with nudging, $\textcolor{blue}{t_{nudge}}~ =~ 3~ hours $</wikitex> 
:<wikitex>Salinity at eastern end = $0$</wikitex> 

==Output (ASCII files suitable for plotting)==

<wikitex>At $\textcolor{blue}{t}~ =~ 10~ days~ (20~ tidal~ cycles)$:</wikitex> 
:Tidally averaged velocity field (average over last 2 tidal cycles) Bed profile Tidal-mean suspended sediment field 

==Physical Constants==
<wikitex>Gravitational acceleration: $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant: $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity): $\textcolor{blue}{\nu}~ =~ 1e-6~ m^{2}/s$</wikitex>

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Fig1.gif|center|frame|'''Figure 1.''' Initial salinity distribution for estuary simulations.]]

Model was initialized with a constant longitudinal salinity field as shown in '''Figure 1'''. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. '''Figure 2''' shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of [[Bibliography#MellorGL_1982a|Mellor/Yamada (1982)]], and the GLS closures are computed with the method of [[Bibliography#UmlaufL_2003a|Umlauf and Burchard (2003)]]. The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by [[Bibliography#BurchardH_2001a|Burchard (2001)]], a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

[[Image:Estuary_4panel_salt.gif|center|frame|'''Figure 2.''' Initial salinity distribution for estuary simulations.]]

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

[[Image:Estuary_4panel_sed.gif|center|frame|'''Figure 3.''' Suspended sediment concentration distribution after 9.9 days for the estuary simulations.]]

ESTUARY TEST CASE

2008-12-05T21:10:29Z

Etwomey: /* Boundary Conditions */

<div class="title">Suspended Sediment Test in an Estuary</div>

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

[[Image:Test_case_2.gif|center]]

==Domain==

The domain is a long, narrow rectangular channel.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|1000 m
|-
|Depth
|align="center"|h
|10 m at western end, decreasing linearly to 5 at eastern end
|-
|Temperature
|align="center"|T
|10°C
|}

==Bottom Sediment==

Single grain size on bottom:

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|-
|Bed thickness
|align="center"|bed_thick
|1 mm
|}

==Forcing==

No Coriolis 
No wind 
No heating/cooling 

==Initial Conditions==

Salinity distribution from west end = 35 to east end = 0. (Vertically well mixed) 

==Boundary Conditions==
General:
<wikitex>:'''North and south sides''' = walls with no fluxes, no friction '''Bottom roughness''' $\textcolor{blue}{K_{s}}~ =~ 0.15~ m~(\textcolor{blue}{Z_{o}}~ =~ \textcolor{blue}{K_{s}}/30~ =~ 0.005~ m )$ '''Sediment flux''' = calculated by model '''Surface''' = free surface, no fluxes 

Flow, Western end, tidal:
:<wikitex>$\textcolor{blue}{q_{west}}~ =~ 4000~ m^{3}/s~ \times~ sin(\textcolor{blue}{\omega t})~ -~\textcolor{blue}{q_{east}}$ 
:$\textcolor{blue}{\omega}~ =~ 2\pi~ / \textcolor{blue}{T}$ 
:$\textcolor{blue}{T}~ =~ 12~ \times~ 3600~ seconds~ =~ model~ time~ step~,~ seconds~$ </wikitex>

Flow, Eastern end, constant riverine (varying depth):
:<wikitex>$\textcolor{blue}{q_{east}}~ =~ 400~ m^{3}/s$</wikitex> 

Salinity, western end:
:<wikitex>Radiation condition with nudging, $\textcolor{blue}{t_{nudge}}~ =~ 3~ hours $</wikitex> 
:<wikitex>Salinity at eastern end = $0$</wikitex> 

==Output (ASCII files suitable for plotting)==

<wikitex>At $\textcolor{blue}{t}~ =~ 10~ days~ (20~ tidal~ cycles)$:</wikitex> 
:Tidally averaged velocity field (average over last 2 tidal cycles) Bed profile Tidal-mean suspended sediment field 

==Physical Constants==
<wikitex>Gravitational acceleration: $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant: $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity): $\textcolor{blue}{\nu}~ =~ 1e-6~ m^{2}/s$</wikitex>

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Fig1.gif|center|frame|'''Figure 1.''' Initial salinity distribution for estuary simulations.]]

Model was initialized with a constant longitudinal salinity field as shown in '''Figure 1'''. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. '''Figure 2''' shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of [[Bibliography#MellorGL_1982a|Mellor/Yamada (1982)]], and the GLS closures are computed with the method of [[Bibliography#UmlaufL_2003a|Umlauf and Burchard (2003)]]. The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by [[Bibliography#BurchardH_2001a|Burchard (2001)]], a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

[[Image:Estuary_4panel_salt.gif|center|frame|'''Figure 2.''' Initial salinity distribution for estuary simulations.]]

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

[[Image:Estuary_4panel_sed.gif|center|frame|'''Figure 3.''' Suspended sediment concentration distribution after 9.9 days for the estuary simulations.]]

ESTUARY TEST CASE

2008-12-05T21:09:22Z

Etwomey: /* Boundary Conditions */

<div class="title">Suspended Sediment Test in an Estuary</div>

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

[[Image:Test_case_2.gif|center]]

==Domain==

The domain is a long, narrow rectangular channel.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|1000 m
|-
|Depth
|align="center"|h
|10 m at western end, decreasing linearly to 5 at eastern end
|-
|Temperature
|align="center"|T
|10°C
|}

==Bottom Sediment==

Single grain size on bottom:

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|-
|Bed thickness
|align="center"|bed_thick
|1 mm
|}

==Forcing==

No Coriolis 
No wind 
No heating/cooling 

==Initial Conditions==

Salinity distribution from west end = 35 to east end = 0. (Vertically well mixed) 

==Boundary Conditions==
General:
<wikitex>:'''North and south sides''' = walls with no fluxes, no friction '''Bottom roughness''' $\textcolor{blue}{K_{s}}~ =~ 0.15~ m~(\textcolor{blue}{Z_{o}}~ =~ \textcolor{blue}{K_{s}}/30~ =~ 0.005~ m )$ '''Sediment flux''' = calculated by model '''Surface''' = free surface, no fluxes 

Flow, Western end, tidal:
<wikitex>$\textcolor{blue}{q_{west}}~ =~ 4000~ m^{3}/s~ \times~ sin(\textcolor{blue}{\omega t})~ -~\textcolor{blue}{q_{east}}$ 
$\textcolor{blue}{\omega}~ =~ 2\pi~ / \textcolor{blue}{T}$ $\textcolor{blue}{T}~ =~ 12~ \times~ 3600~ seconds~ =~ model~ time~ step~,~ seconds~$ </wikitex>

Flow, Eastern end, constant riverine (varying depth):
:<wikitex>$\textcolor{blue}{q_{east}}~ =~ 400~ m^{3}/s$</wikitex> 

Salinity, western end:
:<wikitex>Radiation condition with nudging, $\textcolor{blue}{t_{nudge}}~ =~ 3~ hours $</wikitex> 
:<wikitex>Salinity at eastern end = $0$</wikitex> 

==Output (ASCII files suitable for plotting)==

<wikitex>At $\textcolor{blue}{t}~ =~ 10~ days~ (20~ tidal~ cycles)$:</wikitex> 
:Tidally averaged velocity field (average over last 2 tidal cycles) Bed profile Tidal-mean suspended sediment field 

==Physical Constants==
<wikitex>Gravitational acceleration: $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant: $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity): $\textcolor{blue}{\nu}~ =~ 1e-6~ m^{2}/s$</wikitex>

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Fig1.gif|center|frame|'''Figure 1.''' Initial salinity distribution for estuary simulations.]]

Model was initialized with a constant longitudinal salinity field as shown in '''Figure 1'''. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. '''Figure 2''' shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of [[Bibliography#MellorGL_1982a|Mellor/Yamada (1982)]], and the GLS closures are computed with the method of [[Bibliography#UmlaufL_2003a|Umlauf and Burchard (2003)]]. The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by [[Bibliography#BurchardH_2001a|Burchard (2001)]], a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

[[Image:Estuary_4panel_salt.gif|center|frame|'''Figure 2.''' Initial salinity distribution for estuary simulations.]]

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

[[Image:Estuary_4panel_sed.gif|center|frame|'''Figure 3.''' Suspended sediment concentration distribution after 9.9 days for the estuary simulations.]]

ESTUARY TEST CASE

2008-12-05T20:45:41Z

Etwomey: /* Output (ASCII files suitable for plotting) */

<div class="title">Suspended Sediment Test in an Estuary</div>

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

[[Image:Test_case_2.gif|center]]

==Domain==

The domain is a long, narrow rectangular channel.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|1000 m
|-
|Depth
|align="center"|h
|10 m at western end, decreasing linearly to 5 at eastern end
|-
|Temperature
|align="center"|T
|10°C
|}

==Bottom Sediment==

Single grain size on bottom:

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|-
|Bed thickness
|align="center"|bed_thick
|1 mm
|}

==Forcing==

No Coriolis 
No wind 
No heating/cooling 

==Initial Conditions==

Salinity distribution from west end = 35 to east end = 0. (Vertically well mixed) 

==Boundary Conditions==
General:
:'''North and south sides''' = walls with no fluxes, no friction '''Bottom roughness''' Ks = 0.15 m  ( Zo = Ks/30 = 0.005 m ) '''Sediment flux''' = calculated by model '''Surface''' = free surface, no fluxes 

Flow, Western end, tidal:
:qwest = 4000 m3/s * ''sin''(ωt) - qeast ω = 2π / T T = 12 * 3600 seconds t = model time step, seconds

Flow, Eastern end, constant riverine (varying depth):
:qeast = 400 m3/s

Salinity, western end
:Radiation condition with nudging, tnudge = 3 hours 
Salinity at eastern end = 0 

==Output (ASCII files suitable for plotting)==

<wikitex>At $\textcolor{blue}{t}~ =~ 10~ days~ (20~ tidal~ cycles)$:</wikitex> 
:Tidally averaged velocity field (average over last 2 tidal cycles) Bed profile Tidal-mean suspended sediment field 

==Physical Constants==
<wikitex>Gravitational acceleration: $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant: $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity): $\textcolor{blue}{\nu}~ =~ 1e-6~ m^{2}/s$</wikitex>

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Fig1.gif|center|frame|'''Figure 1.''' Initial salinity distribution for estuary simulations.]]

Model was initialized with a constant longitudinal salinity field as shown in '''Figure 1'''. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. '''Figure 2''' shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of [[Bibliography#MellorGL_1982a|Mellor/Yamada (1982)]], and the GLS closures are computed with the method of [[Bibliography#UmlaufL_2003a|Umlauf and Burchard (2003)]]. The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by [[Bibliography#BurchardH_2001a|Burchard (2001)]], a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

[[Image:Estuary_4panel_salt.gif|center|frame|'''Figure 2.''' Initial salinity distribution for estuary simulations.]]

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

[[Image:Estuary_4panel_sed.gif|center|frame|'''Figure 3.''' Suspended sediment concentration distribution after 9.9 days for the estuary simulations.]]

ESTUARY TEST CASE

2008-12-05T20:43:42Z

Etwomey: /* Physical Constants */

<div class="title">Suspended Sediment Test in an Estuary</div>

This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

[[Image:Test_case_2.gif|center]]

==Domain==

The domain is a long, narrow rectangular channel.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|1000 m
|-
|Depth
|align="center"|h
|10 m at western end, decreasing linearly to 5 at eastern end
|-
|Temperature
|align="center"|T
|10°C
|}

==Bottom Sediment==

Single grain size on bottom:

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|-
|Bed thickness
|align="center"|bed_thick
|1 mm
|}

==Forcing==

No Coriolis 
No wind 
No heating/cooling 

==Initial Conditions==

Salinity distribution from west end = 35 to east end = 0. (Vertically well mixed) 

==Boundary Conditions==
General:
:'''North and south sides''' = walls with no fluxes, no friction '''Bottom roughness''' Ks = 0.15 m  ( Zo = Ks/30 = 0.005 m ) '''Sediment flux''' = calculated by model '''Surface''' = free surface, no fluxes 

Flow, Western end, tidal:
:qwest = 4000 m3/s * ''sin''(ωt) - qeast ω = 2π / T T = 12 * 3600 seconds t = model time step, seconds

Flow, Eastern end, constant riverine (varying depth):
:qeast = 400 m3/s

Salinity, western end
:Radiation condition with nudging, tnudge = 3 hours 
Salinity at eastern end = 0 

==Output (ASCII files suitable for plotting)==

At t = 10 days (20 tidal cycles): 
:Tidally averaged velocity field (average over last 2 tidal cycles) Bed profile Tidal-mean suspended sediment field 

==Physical Constants==
<wikitex>Gravitational acceleration: $\textcolor{blue}{g}~ =~ 9.81~ m/s^{2}$ 
Von Karman's constant: $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity): $\textcolor{blue}{\nu}~ =~ 1e-6~ m^{2}/s$</wikitex>

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Fig1.gif|center|frame|'''Figure 1.''' Initial salinity distribution for estuary simulations.]]

Model was initialized with a constant longitudinal salinity field as shown in '''Figure 1'''. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. '''Figure 2''' shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on the classical scheme of [[Bibliography#MellorGL_1982a|Mellor/Yamada (1982)]], and the GLS closures are computed with the method of [[Bibliography#UmlaufL_2003a|Umlauf and Burchard (2003)]]. The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions.

The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter (E3 = 1.8). As discussed by [[Bibliography#BurchardH_2001a|Burchard (2001)]], a value of c3 ~ 2.5 (E3 ~ 5.0) provides a more realistic simulation of a wind induced surface mixed layer test experiment.

[[Image:Estuary_4panel_salt.gif|center|frame|'''Figure 2.''' Initial salinity distribution for estuary simulations.]]

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. For the MY25 closure, this limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

[[Image:Estuary_4panel_sed.gif|center|frame|'''Figure 3.''' Suspended sediment concentration distribution after 9.9 days for the estuary simulations.]]

LAKE SIGNELL CASE

2008-12-05T20:26:15Z

Etwomey:

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>Wind speed = $ 13~ m/s~ (\textcolor{blue}{\tau}~ =~ 0.25~ Pa)$, blowing along the lake to the east</wikitex> 

'''Waves:'''

<wikitex>RMS wave height = $0.5~ m$ 
Period = $5~ seconds$ 
Direction: propagating in wind direction</wikitex> 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u} ~= ~0 ~m/s^{2}$ 
Salinity = $0$ 
$\textcolor{blue}{T} = 20^{\circ}~ C$ </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $\textcolor{blue}{Z_{0}}~=~ 0.015~ m$ in absence of waves 
Surface roughness $\textcolor{blue}{Z_{0S}}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind)</wikitex> 

==Physical Constants==

<wikitex>Gravitational acceleration $\textcolor{blue}{g}~ =~ 9.81~ ^{2}$ 
Von Karman's constant $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\textcolor{blue}{\nu}~= 1e-6 m^{2}/s$</wikitex> 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T20:24:59Z

Etwomey:

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>Wind speed = $ 13~ m/s~ (\textcolor{blue}{\tau}~ =~ 0.25~ Pa)$, blowing along the lake to the east</wikitex> 

'''Waves:'''

<wikitex>RMS wave height = $0.5~ m$ 
Period = $5~ seconds$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u} ~= ~0 ~m/s^{2}$ 
Salinity = $0$ 
$\textcolor{blue}{T} = 20^{\circ}~ C$ </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $\textcolor{blue}{Z_{0}}~=~ 0.015~ m$ in absence of waves 
Surface roughness $\textcolor{blue}{Z_{0S}}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind)</wikitex> 

==Physical Constants==

<wikitex>Gravitational acceleration $\textcolor{blue}{g}~ =~ 9.81~ ^{2}$ 
Von Karman's constant $\textcolor{blue}{\kappa}~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\textcolor{blue}{\nu}~= 1e-6 m^{2}/s$</wikitex> 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T20:15:29Z

Etwomey: /* Forcing */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>Wind speed = $ 13~ m/s~ (\textcolor{blue}{\tau}~ =~ 0.25~ Pa)$, blowing along the lake to the east</wikitex> 

'''Waves:'''

<wikitex>RMS wave height = $0.5~ m$ 
Period = $5~ seconds$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$\textcolor{blue}{u} ~= ~0 ~m/s^{2}$ 
Salinity = $0$ 
$\textcolor{blue}{T} = 20^{\circ}~ C$ </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $Z_{0}~=~ 0.015~ m$ in absence of waves 
Surface roughness $Z_{0S}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

<wikitex>Gravitational acceleration $g~ =~ 9.81~ ^{2}$ 
Von Karman's constant $\kappa~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\nu~= 1e-6 m^{2}/s$</wikitex> 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T18:31:48Z

Etwomey:

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>Wind speed = $ 13~ m/s~ (\tau~ =~ 0.25~ Pa)$, blowing along the lake to the east</wikitex> 

'''Waves:'''

<wikitex>RMS wave height = $0.5~ m$ 
Period = $5~ seconds$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$u ~= ~0 ~m/s^{2}$ 
Salinity = $0$ 
$T = 20^{\circ}~ C$ </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $Z_{0}~=~ 0.015~ m$ in absence of waves 
Surface roughness $Z_{0S}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

<wikitex>Gravitational acceleration $g~ =~ 9.81~ ^{2}$ 
Von Karman's constant $\kappa~ =~ 0.41$ 
Dynamic viscosity (and minimum diffusivity) $\nu~= 1e-6 m^{2}/s$</wikitex> 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T16:22:58Z

Etwomey: /* Forcing */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>Wind speed = $ 13~ m/s~ (\tau~ =~ 0.25~ Pa)$, blowing along the lake to the east</wikitex> 

'''Waves:'''

<wikitex>RMS wave height = $0.5~ m$ 
Period = $5~ seconds$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$$u ~= ~0 ~m/s^{2}$$ 
$$Salinity~ =~ 0$$ 
$$T~ =~ 20^{\circ}~ C </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $Z_{0}~=~ 0.015~ m$ in absence of waves 
Surface roughness $Z_{0S}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ = 0.41 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T16:20:30Z

Etwomey: /* Boundary Conditions */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>$$Wind~ speed~ =~ 13~ m/s~ (\tau~ =~ 0.25~ Pa), blowing~ along~ the~ lake~ to~ the~ east</wikitex> 

'''Waves:'''

<wikitex>$$RMS~ wave~ height~ =~ 0.5~ m$$ 
$$Period~ =~ 5~ seconds$$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$$u ~= ~0 ~m/s^{2}$$ 
$$Salinity~ =~ 0$$ 
$$T~ =~ 20^{\circ}~ C </wikitex> 

==Boundary Conditions==

<wikitex>North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness $Z_{0}~=~ 0.015~ m$ in absence of waves 
Surface roughness $Z_{0S}~ =~ 0.02~ m$ 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ = 0.41 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T16:09:45Z

Etwomey: /* Forcing */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

<wikitex>$$Wind~ speed~ =~ 13~ m/s~ (\tau~ =~ 0.25~ Pa), blowing~ along~ the~ lake~ to~ the~ east</wikitex> 

'''Waves:'''

<wikitex>$$RMS~ wave~ height~ =~ 0.5~ m$$ 
$$Period~ =~ 5~ seconds$$ 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$$u ~= ~0 ~m/s^{2}$$ 
$$Salinity~ =~ 0$$ 
$$T~ =~ 20^{\circ}~ C </wikitex> 

==Boundary Conditions==

North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.015 m in absence of waves 
Surface roughness Z0S = 0.02 m 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ = 0.41 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

LAKE SIGNELL CASE

2008-12-05T15:27:45Z

Etwomey: /* Initial Conditions */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

Wind speed = 13 m/s (τ = 0.25 Pa), blowing along the lake to the east 

'''Waves:'''

RMS wave height = 0.5 m 
Period = 5 seconds 
Direction: propagating in wind direction 

==Initial Conditions==

<wikitex>$$u ~= ~0 ~m/s^{2}$$ 
$$Salinity~ =~ 0$$ 
$$T~ =~ 20^{\circ}~ C </wikitex> 

==Boundary Conditions==

North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.015 m in absence of waves 
Surface roughness Z0S = 0.02 m 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ = 0.41 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]

TEST HEAD CASE

2008-04-24T13:31:02Z

Etwomey: /* Physical Constants */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= &radic;(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level ζ = ζ0 * exp(-f * y/C) * cos(k * (x - C * t)) 

{{note}}'''Note:''' x at western boundary is -L/2 
Depth-mean flow &lang;u&rang; = √(g/20) * ζ(y) 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant = 0.41 
Dynamic viscosity (and minimum diffusivity) ν = 1e-6 m2/s 

{{note}}'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-24T13:28:31Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= &radic;(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level ζ = ζ0 * exp(-f * y/C) * cos(k * (x - C * t)) 

{{note}}'''Note:''' x at western boundary is -L/2 
Depth-mean flow &lang;u&rang; = √(g/20) * ζ(y) 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-24T13:21:05Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= √(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level ζ = ζ0 * exp(-f * y/C) * cos(k * (x - C * t)) 

{{note}}'''Note:''' x at western boundary is -L/2 
Depth-mean flow &lang;u&rang; = √(g/20) * ζ(y) 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:13:40Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= √(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:13:25Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity u0 = 0.5 m/s 
Celerity C= √(g * 20.0) 
Reference water level ζ0 = u0/√(g/20) 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:09:35Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:09:24Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:08:49Z

Etwomey: /* Boundary Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3</s 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness Z0 = 0.015 m 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:07:19Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 m3</s 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:06:54Z

Etwomey: /* Initial Conditions */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

u = 0 \,m3</s 
Salinity = 0 
Temperature = 20oC 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:05:25Z

Etwomey: /* Forcing */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

<math>u \,= \,0 \,m^{3} /s</math> 
Salinity = 0 
Temperature = <math>20_{o}C</math> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T20:00:35Z

Etwomey: /* Bottom Sediment */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.50 mm/s
|-
|Critical shear stress
|align="center"|τc
|0.05 N/m2
|-
|Bed thickness
|align="center"|bed_thick
|0.005 m
|-
|Erosion Rate
|align="center"|E0
| 5e-5 kg/m2/s
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

<math>u \,= \,0 \,m^{3} /s</math> 
Salinity = 0 
Temperature = <math>20_{o}C</math> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T19:57:52Z

Etwomey: /* Domain */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20 m
|}

==Bottom Sediment==

Single grain size on bottom: 

{| border = "1"
|Size
|<math>D_{50}</math>
|0.1 mm
|-
|Density
|<math>\rho_{s}</math>
|<math>2650 \,kg/m^{3}</math>
|-
|Settling Velocity
|<math>w_{s}</math>
|0.5 mm/s
|-
|Critical Shear Stress
|<math>\tau_{c}</math>
|<math>0.05 \,N/m^{s}</math>
|-
|Bed Thickness
|<math>bed\_thick</math>
|0.005 m
|-
|Erosion Rate
|<math>E_{0}</math>
|<math>5e-5 \,kg/m^{2}/s</math>
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

<math>u \,= \,0 \,m^{3} /s</math> 
Salinity = 0 
Temperature = <math>20_{o}C</math> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T19:57:43Z

Etwomey: /* Domain */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20
|}

==Bottom Sediment==

Single grain size on bottom: 

{| border = "1"
|Size
|<math>D_{50}</math>
|0.1 mm
|-
|Density
|<math>\rho_{s}</math>
|<math>2650 \,kg/m^{3}</math>
|-
|Settling Velocity
|<math>w_{s}</math>
|0.5 mm/s
|-
|Critical Shear Stress
|<math>\tau_{c}</math>
|<math>0.05 \,N/m^{s}</math>
|-
|Bed Thickness
|<math>bed\_thick</math>
|0.005 m
|-
|Erosion Rate
|<math>E_{0}</math>
|<math>5e-5 \,kg/m^{2}/s</math>
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

<math>u \,= \,0 \,m^{3} /s</math> 
Salinity = 0 
Temperature = <math>20_{o}C</math> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

TEST HEAD CASE

2008-04-15T19:57:18Z

Etwomey: /* Domain */

<div class="title">Sediment Test Headland Case</div>

This test case checks the ability of a model to represent 1) simplified alongshore transport, 2) implementation of open boundary conditions, and 3) resuspension, transport, and deposition of suspended-sediment. This case is based on [[Bibliography#SignellRP_1992a|Signell and Geyer (1991)]].

[[Image:Test_case_4.gif|center]]

==Domain==

The model domain is open at the east and west ends, has a straight wall at the north end, and a parabolic headland along the south wall.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|100000 m
|-
|Width (north-south)
|align="center"|w
|50000 m
|-
|Depth
|align="center"|h
|20
:}

==Bottom Sediment==

Single grain size on bottom: 

{| border = "1"
|Size
|<math>D_{50}</math>
|0.1 mm
|-
|Density
|<math>\rho_{s}</math>
|<math>2650 \,kg/m^{3}</math>
|-
|Settling Velocity
|<math>w_{s}</math>
|0.5 mm/s
|-
|Critical Shear Stress
|<math>\tau_{c}</math>
|<math>0.05 \,N/m^{s}</math>
|-
|Bed Thickness
|<math>bed\_thick</math>
|0.005 m
|-
|Erosion Rate
|<math>E_{0}</math>
|<math>5e-5 \,kg/m^{2}/s</math>
|}

==Forcing==

Coriolis f = 1.0 e-4 
No heating/cooling 
No wind 

==Initial Conditions==

<math>u \,= \,0 \,m^{3} /s</math> 
Salinity = 0 
Temperature = <math>20_{o}C</math> 

Bathymetry: 
Depths increase linearly (slope = 0.0067) from a minimum depth of 2 m at all alongshore points from the southern land boundary offshore to a maximum depth of 20 m at a point 3 km offshore. Offshore of 3 km there is a constant depth of 20 m. 

==Boundary Conditions==

North, south = walls with no fluxes, no friction 
South wall = parabolic headland shape 
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math> 

Flow and elevation at western boundary is imposed. 
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution. 

Flow and elevation, eastern/western boundaries: 

Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math> 
Celerity <math>C \,= \sqrt{g * 20.0}</math> 
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math> 
Wave period T = 12 hours (43200 seconds) 
Wave length L = C * T 
Wave number k = (2 * π)/L 

For each point y along the boundary at time t:

Water level <math>\zeta \,= \,\zeta_{0} * exp(-f * y/C) * cos(k * (x - C * t))</math> 
'''Note:''' x at western boundary is -L/2 
Depth-mean flow <math> \,= \,\sqrt{g/20} * \zeta(y)</math> 

Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Output (ASCII files suitable for plotting)==

After 10 days : 
Bed thickness 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 \,m/s^{2}</math> 
Von Karman's constant ? = 0.41 
Dynamic viscosity (and minimum diffusivity) <math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' 

If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used. 

==Results==

[[Image:Test_case4_fig1.gif|center|frame|'''Figure 1.''' Plan view of final bathymetric change.]]

Simulations were conducted for 3.0 days. Final bed thickness is shown in Figure 1.

SED TEST1 CASE

2008-04-15T19:38:14Z

Etwomey: /* Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>. */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation (f=0)
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow &lang;u&rang; = 1 m/s 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.005 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ= 0.41 
Water density ρw= 998 kg/m3 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of 10 m3/s/m of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of 4x10-5 m/m.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

:{|border="1"
!
!∂η/∂x
!u*m2/s2
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T17:31:33Z

Etwomey: /* Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width. */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation (f=0)
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow &lang;u&rang; = 1 m/s 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.005 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ= 0.41 
Water density ρw= 998 kg/m3 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of 10 m3/s/m of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T17:29:51Z

Etwomey: /* Physical Constants */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation (f=0)
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow &lang;u&rang; = 1 m/s 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.005 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ= 0.41 
Water density ρw= 998 kg/m3 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T17:26:34Z

Etwomey: /* Boundary Conditions */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation (f=0)
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow &lang;u&rang; = 1 m/s 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.005 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 m/s^{2}</math> 
Von Karman's constant <math>\kappa \,= \,0.41</math> 
Water density <math>\rho_{w} \,= \,998 kg/m^{3}</math> 
Dynamic viscosity (and minimum diffusivity)<math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T17:23:17Z

Etwomey: /* Forcing */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation (f=0)
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow <math> = 1 \,m/s </math> 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness <math>Z_{0} = 0.005</math> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 m/s^{2}</math> 
Von Karman's constant <math>\kappa \,= \,0.41</math> 
Water density <math>\rho_{w} \,= \,998 kg/m^{3}</math> 
Dynamic viscosity (and minimum diffusivity)<math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T17:22:44Z

Etwomey: /* Bottom Sediment */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

:{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|align="center"|D50
|0.15 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|w;s
|0.001 m/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Porosity
|align="center"|φ
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation <math>(f=0)</math> 
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow <math> = 1 \,m/s </math> 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness <math>Z_{0} = 0.005</math> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 m/s^{2}</math> 
Von Karman's constant <math>\kappa \,= \,0.41</math> 
Water density <math>\rho_{w} \,= \,998 kg/m^{3}</math> 
Dynamic viscosity (and minimum diffusivity)<math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T16:55:28Z

Etwomey: /* Domain */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l
|10000 m
|-
|Width
|align="center"|w
|1000 m
|-
|Temperature
|align="center"|T
|20o C
|}

==Bottom Sediment==

{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|<math>D_{50}</math>
|0.15 mm
|-
|Density
|<math>\rho_{s}</math>
|<math>2650 \,kg/m^{3}</math>
|-
|Settling Velocity
|<math>w_{s}</math>
|0.001 m/s
|-
|Critical Shear Stress
|<math>\tau_{c}</math>
|<math>0.05 \,N/m^{2}</math>
|-
|Porosity
|<math>\phi</math>
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation <math>(f=0)</math> 
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow <math> = 1 \,m/s </math> 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness <math>Z_{0} = 0.005</math> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 m/s^{2}</math> 
Von Karman's constant <math>\kappa \,= \,0.41</math> 
Water density <math>\rho_{w} \,= \,998 kg/m^{3}</math> 
Dynamic viscosity (and minimum diffusivity)<math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

SED TEST1 CASE

2008-04-15T16:54:39Z

Etwomey: /* Domain */

<div class="title">Suspended Sediment Test in Channel</div>

This case provides a fundamental check of the ability of a model to 1) represent a simple flow, 2) flux material from the bed, and 3) develop a suspended-sediment profile.

[[Image:Test_case_1.gif|center]]

==Domain==

The model domain is a long, narrow rectangular box, with a flat bottom.

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length
|align="center"|l</spand>
|10000 m
|-
|Width
|align="center"|w</spand>
|1000 m
|-
|Temperature
|align="center"|T
|20o C</math>
|}

==Bottom Sediment==

{| border="1"
!Model Parameter
! Variable
! Value
|-
|Size
|<math>D_{50}</math>
|0.15 mm
|-
|Density
|<math>\rho_{s}</math>
|<math>2650 \,kg/m^{3}</math>
|-
|Settling Velocity
|<math>w_{s}</math>
|0.001 m/s
|-
|Critical Shear Stress
|<math>\tau_{c}</math>
|<math>0.05 \,N/m^{2}</math>
|-
|Porosity
|<math>\phi</math>
|0.90
|}

An infinite supply of sediment (not erosion, no armoring) is used.

==Forcing==

Inflow boundary condition only 
No rotation <math>(f=0)</math> 
No wind 
No heating/cooling 

==Boundary Conditions==

Inflow maintained as steady flow, depth-mean flow <math> = 1 \,m/s </math> 
Outflow = open 
Sides = walls with no fluxes, no friction 
Bottom roughness <math>Z_{0} = 0.005</math> 
Sediment flux calculated by model 
Surface = free surface, no fluxes 

==Channel Initial Conditions==

Channel initial conditions:
The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.

—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.

For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
MY25 = Mellor Yamada Level 2.5 Closure, parabolic wall proximity function
KKLpara = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a parabolic wall proximity function
KKLmin = Generic Length Scale parameterized as Mellor Yamada Level 2.5 with a linear wall proximity function (minimum distance to each surface)
KE = Generic Length Scale parameterized as k-epsilon closure
KW88 = Generic Length Scale parameterized as k-omega closure
ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

Kz = k u* z (1 - z/D)
where Kz = vertical eddy viscosity, m²/s
z = height above the bottom, m
D = depth of flow, m, = 10 m
and u* = friction velocity which was calculated according to the logarithmic profile.

[[Image:Equation_ustar.gif|center]]

where k = 0.41 and u = 1.0 m/s.

Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

[[Image:Jw_eq_1_E.gif|center]]

where E = erosive flux, kg/m²/s
Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4
por_1 = 1-porosity = 0.6
τw = shear stress exerted by the water, = ρ Cd V |V|
ρ= fluid density, kg/m³, = 998 kg/m³
V = magnitude of velocity = sqrt(u² + v²), m/s
τc = critical shear stress for erosion, = 0.05 N/m²
The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

==Analysis Data==

Velocity profile at x = 8000 m 
Suspended sediment profile at x = 8000 m 
Time series of net rate of sediment flux from bed and/or concentration at specified levels 

==Physical Constants==

Gravitational acceleration <math>g \,= \,9.81 m/s^{2}</math> 
Von Karman's constant <math>\kappa \,= \,0.41</math> 
Water density <math>\rho_{w} \,= \,998 kg/m^{3}</math> 
Dynamic viscosity (and minimum diffusivity)<math>\nu \,= \,1e-6 \,m^{2}/s</math> 

'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

===Results for Simulation 1: Constant flow of <math>10 \,m^{3}/s/m</math> of width.===

[[Image:Sed_test1.gif|center|frame|Figure 1. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 1.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara. This is to be expected because there are no buoyancy terms (see test case 2 - estuary case, for differences that arise due to the length scale limitations imposed by the 2 methods). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for the MY25 (and KKLpara) method has a lower value near the bed that is compensated for by a larger water surface slope (not shown).

===Results for Simulation 2: Constant bed slope and water surface slope of<math>4x10^{-5} \,m/m</math>.===

[[Image:Test_chan.gif|center|frame|Figure 2. Vertical profiles of velocity, eddy viscosity, eddy diffusivity, turbulent kinetic energy, dissipation, and suspended-sediment concentration (SSC) for simulation 2.]]

For all of the vertical profiles, the solutions for MY25 are consistent with the solutions of GLS as KKLpara (as for simulation 1). Typically, the vertical profiles from the KW88 method agree most closely with the analytical solution. The turbulent kinetic energy for all simulations are now consistent because the stress is the same for each closure.

{|border="1"
!
!<math>\partial\eta\backslash\partial x</math>
!<math> u^{*} (m^{2}\backslash s^{2})</math>
|-
|calculated
|4.00e-5
|0.0625
|-
|ANA
|4.21e-5
|0.0643
|-
|<math>\kappa-\varepsilon</math>
|3.98e-5
|0.0626
|-
|MY25
|3.00e-5
|0.0544
|}

LAKE SIGNELL CASE

2008-04-15T16:51:33Z

Etwomey: /* Physical Constants */

<div class="title">Lake Signell Sediment Test Case</div>

This case provides a fundamental check of the ability of a model to represent 1) wind driven transport in a closed basin, 2) wave-current influences on bottom friction and sediment resuspension, 3) flux of two grain sizes from the bed, and 4) resuspension, transport, and deposition of suspended-sediment. Lake Signell derives its name from the paper by [[Bibliography#SignellRP_1990a|Signell et al. (1990)]].

[[Image:Test_case_3.gif|center]]

==Domain==

The domain is an enclosed basin, rectangular in plan view, with a sloping bottom. 

:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Length (east-west)
|align="center"|l
|50000 m
|-
|Width (north-south)
|align="center"|w
|10000 m
|-
|Depth
|align="center"|h
|18 m at the northern end, decreasing linearly to 2 m at the southern end
|}

==Bottom Sediment==

:{| border="1"
|Size
|align="center"|D50
|0.1 mm
|-
|Density
|align="center"|ρs
|2650 kg/m3
|-
|Settling Velocity
|align="center"|ws
|0.1 mm/s
|-
|Critical Shear Stress
|align="center"|τc
|0.05 N/m2
|-
|Bed Thickness
|align="center"|bed_thick
|0.005 mm
|-
|Erosion Rate
|align="center"|E0
|5e-5 kg/m2/s
|}

==Forcing==

No Coriolis 
No heating/cooling 

'''Wind:'''

Wind speed = 13 m/s (τ = 0.25 Pa), blowing along the lake to the east 

'''Waves:'''

RMS wave height = 0.5 m 
Period = 5 seconds 
Direction: propagating in wind direction 

==Initial Conditions==

u = 0 m/s2 
Salinity = 0 
T = 20o C 

==Boundary Conditions==

North, south, east, and west sides = walls with no fluxes, no friction 
Bottom roughness Z0= 0.015 m in absence of waves 
Surface roughness Z0S = 0.02 m 
Sediment flux calculated by model 
Surface = free surface, no fluxes of heat or salt (momentum fluxes associated with wind) 

==Physical Constants==

Gravitational acceleration g = 9.81 m/s2 
Von Karman's constant κ = 0.41 
Dynamic viscosity (and minimum diffusivity) ν= 1e-6 m2/s 

{{note}}'''Note:'''
If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

==Results==

[[Image:Test_case3_fig1.gif|center|frame| '''Figure 1.''' Model bathymetry.]]

Model bathymetry has a sloping bottom as shown in figure 1. Simulations were conducted for 3.0 days. For this simulation, the bottom orbital velocities, wave period, and direction were obtained from a steady-state solution of the model SWAN. For the hydrodynamic simulation, the wave field results from SWAN were increased from 0 to their maximum values with a hyperbolic tangent function that reached maximum value at 10 hours. The surface stress was held constant until a total of 40 hours have elapsed, when the stress was decreased hyperbolically for 10 hours. The simulation continued until all sediment had settled from the water column.

Cross sectional plot of velocity contours at x = 25 km is shown in figure 2, at maximum wind stress. A downwind surface flow of near 32 cm/s is observed in the shallow region, with a compensating upwind flow at depth of 24 cm/s. Figure 3 shows the final bathymetric change. The majority of the sediment was transport from the southwest corner towards the northeast corner, due to the counter clockwise circulation from the westerly wind stress.

[[Image:Test_case3_fig2.gif|center|frame|'''Figure 2.''' Along channel velocity contours (cm/s) at x = 25 km. Positive velocity is out of the page (downwind flow), negative into the page (upwind flow).]]

[[Image:Test_case3_fig3.gif|center|frame|'''Figure 3.''' Plan view of final bathymetric change.]]