Difference between revisions of "TEST HEAD CASE"

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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 <span class="blue">Z<sub>0</sub></span> = 0.015 m<br>
<wikitex>Bottom roughness $\textcolor{blue}{Z_{\circ}}~ =~ 0.015~ m$<br>


Flow and elevation at western boundary is imposed.<br>
Flow and elevation at western boundary is imposed.<br>
Line 89: Line 89:
Flow and elevation, eastern/western boundaries: <br>
Flow and elevation, eastern/western boundaries: <br>


Reference velocity <span class="blue">u<sub>0</sub></span> = 0.5 m/s<br>
Reference velocity $\textcolor{blue}{u_{\circ}}~ =~ 0.5~ m/s$<br>
Celerity <span class="blue">C</span>= <span>&radic</span>;(<span class="blue">g</span> * 20.0)<br>
Celerity $\textcolor{blue}{C}~=~ \sqrt{(\textcolor{blue}{g}\times 20.0)}$<br>
Reference water level <span class="blue">&zeta;<sub>0</sub></span> = <span class="blue">u<sub>0</sub></span>/&radic;(<span class = "blue">g</span>/20)<br>
Reference water level $\textcolor{blue}{\xi_{\circ}}~ =~\textcolor{blue}{u_{\circ}}/\sqrt{(\textcolor{blue}{g}/20)}$<br>
Wave period T = 12 hours (43200 seconds)<br>
Wave period $\textcolor{blue}{T}~ =~ 12$ hours (43200 seconds)<br>
Wave length L = C * T <br>
Wave length $\textcolor{blue}{L}~ = \textcolor{blue}{C}\times \textcolor{blue}{T}$ <br>
Wave number k = (2 * π)/L <br>
Wave number $\textcolor{blue}{k}~ =~ (2\times\pi)/\textcolor{blue}{L}$</wikitex><br>




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


Water level <span class="blue">&zeta;</span> = <span class="blue">&zeta;<sub>0</sub></span> * exp(-f * y/C) * cos(k * (x - C * t))<br>
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><br>




{{note}}'''Note:''' x at western boundary is -L/2 <br>
{{note}}'''Note:''' <wikitex>$x$ at western boundary is $\textcolor{blue}{-L}/2$ <br>
Depth-mean flow <span class="blue">&lang;u&rang;</span> = <span>&radic;</span>(<span class = "blue">g</span>/20) * <span class="blue">&zeta;(y)</span><br>
Depth-mean flow $\textcolor{blue}{<u>}~ =~ \sqrt{(\textcolor{blue}{g}/20)} \times \textcolor{blue}{\xi}(y)$</wikitex><br>


Sediment flux calculated by model<br>
Sediment flux calculated by model<br>

Revision as of 16:15, 8 December 2008

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

<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>


NoteNote: <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

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.