Difference between revisions of "TEST HEAD CASE"

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Single grain size on bottom: <br>
Single grain size on bottom: <br>


{| border = "1"
:{| border="1"
!Model Parameter
!Variable
!Value
|-
|Size
|Size
|<math>D_{50}</math>
|align="center"|<span class="blue">D<sub>50</sub></span>
|0.1 mm
|0.1 mm
|-
|-
|Density
|Density
|<math>\rho_{s}</math>
|align="center"|<span class="blue">&rho;<sub>s</sub></span>
|<math>2650 \,kg/m^{3}</math>
|2650 kg/m<sup>3</sup>
|-
|-
|Settling Velocity
|Settling Velocity
|<math>w_{s}</math>
|align="center"|<span class="blue">w<sub>s</sub></span>
|0.5 mm/s
|0.50 mm/s
|-
|-
|Critical Shear Stress
|Critical shear stress
|<math>\tau_{c}</math>
|align="center"|<span class="blue">&tau;<sub>c</sub></span>
|<math>0.05 \,N/m^{s}</math>
|0.05 N/m<sup>2</sup>
|-
|-
|Bed Thickness
|Bed thickness
|<math>bed\_thick</math>
|align="center"|<span class="blue">bed_thick</span>
|0.005 m
|0.005 m
|-
|-  
|Erosion Rate
|Erosion Rate
|<math>E_{0}</math>
|align="center"|<span class="blue">E<sub>0</sub></span>
|<math>5e-5 \,kg/m^{2}/s</math>
| 5e-5 kg/m<sup>2</sup>/s
|}
|}


==Forcing==
==Forcing==


Coriolis f = 1.0 e-4 <br>
Coriolis <math>\color{blue}{f}\color{black}{~ =~ 1.0~ e^{-4}}</math><br>
No heating/cooling <br>
No heating/cooling <br>
No wind <br>
No wind


==Initial Conditions==
==Initial Conditions==


<math>u \,= \,0 \,m^{3} /s</math><br>
<math>\color{blue}{u}\color{black}{~ =~ 0~ m^{3}}</math><br>
Salinity = 0 <br>
<math>Salinity~ =~ 0</math><br>
Temperature = <math>20_{o}C</math><br>
<math>\color{blue}{Temperature}\color{black}{~ =~ 20^{\circ}C}</math>


Bathymetry: <br>
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.<br>
: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.<br>


==Boundary Conditions==
==Boundary Conditions==
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North, south = walls with no fluxes, no friction<br>
North, south = walls with no fluxes, no friction<br>
South wall = parabolic headland shape<br>
South wall = parabolic headland shape<br>
Bottom roughness <math>Z_{0} \,= \,0.015 \,m</math><br>
Bottom roughness <math>\color{blue}{Z_{\circ}}\color{black}{~ =~ 0.015~ m}</math><br>


Flow and elevation at western boundary is imposed.<br>
Flow and elevation at western boundary is imposed.<br>
Flow on eastern boundary is open radiation condition, or water level based, or Kelvin wave solution.<br>
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>\color{blue}{u_{\circ}}\color{black}{~ =~ 0.5~ m/s}</math>
:Celerity <math>\color{blue}{C}\color{black}{~=~} \sqrt{\color{blue}{g}\color{black}{\times 20.0}}</math>
:Reference water level <math>\color{blue}{\xi_{\circ}}\color{black}{~ =~}\color{blue}{u_{\circ}}\color{black}{}/\sqrt{(\color{blue}{g}\color{black}{/20)}}</math>
:Wave period <math>\color{blue}{T}\color{black}{~ =~ 12}</math> hours (43200 seconds)
:Wave length <math>\color{blue}{L}\color{black}{~ = }\color{blue}{C}\color{black}{\times }\color{blue}{T}</math>
:Wave number <math>\color{blue}{k}\color{black}{~ =~ (2\times\pi)/}\color{blue}{L}</math>


Flow and elevation, eastern/western boundaries: <br>
For each point <math>y</math> along the boundary at time <math>\color{blue}{t}</math>:


Reference velocity <math>u_{0} \,= \,0.5 \,m/s</math><br>
Water level <math>\color{blue}{\xi}\color{black}{}~ =~\color{blue}{\xi_{\circ}}\color{black}{}\times exp(\color{blue}{-f}\color{black}{}\times y/\color{blue}{C}\color{black}{}) \times cos(\color{blue}{k}\color{black}{} \times (x - \color{blue}{C} \color{black}{} \times \color{blue}{t}\color{black}{}))</math>
Celerity <math>C \,= \sqrt{g * 20.0}</math><br>
Reference water level <math>\zeta_{0} \,= \,u_{0}/\sqrt{g/20}</math><br>
Wave period T = 12 hours (43200 seconds)<br>
Wave length L = C * T <br>
Wave number k = (2 * π)/L  <br>




For each point y along the boundary at time t:
{{note}}'''Note:''' <math>x</math> at western boundary is <math>\color{blue}{-L}\color{black}{}/2</math>


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


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


==Output (ASCII files suitable for plotting)==
==Output (ASCII files suitable for plotting)==
Line 110: Line 113:
==Physical Constants==
==Physical Constants==


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


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


==Results==
==Results==

Latest revision as of 16:10, 17 May 2016

Sediment Test Headland Case

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 Signell and Geyer (1991).

Test case 4.gif


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.

Model Parameter Variable Value
Length (east-west) l 100000 m
Width (north-south) w 50000 m
Depth h 20 m

Bottom Sediment

Single grain size on bottom:

Model Parameter Variable Value
Size D50 0.1 mm
Density ρs 2650 kg/m3
Settling Velocity ws 0.50 mm/s
Critical shear stress τc 0.05 N/m2
Bed thickness bed_thick 0.005 m
Erosion Rate E0 5e-5 kg/m2/s

Forcing

Coriolis
No heating/cooling
No wind

Initial Conditions



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

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
Celerity
Reference water level
Wave period hours (43200 seconds)
Wave length
Wave number

For each point along the boundary at time :

Water level


NoteNote: at western boundary is

Depth-mean flow

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
Von Karman's constant
Dynamic viscosity (and minimum diffusivity)

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

Results

Figure 1. Plan view of final bathymetric change.


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