TEST HEAD CASE

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).

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 $\color {blue}{f}\color {black}{~=~1.0~e^{-4}}$
No heating/cooling
No wind

Initial Conditions

$\color {blue}{u}\color {black}{~=~0~m^{3}}$
$Salinity~=~0$
$\color {blue}{Temperature}\color {black}{~=~20^{\circ }C}$

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 $\color {blue}{Z_{\circ }}\color {black}{~=~0.015~m}$

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 $\color {blue}{u_{\circ }}\color {black}{~=~0.5~m/s}$

Celerity $\color {blue}{C}\color {black}{~=~}{\sqrt {\color {blue}{g}\color {black}{\times 20.0}}}$

Reference water level $\color {blue}{\xi _{\circ }}\color {black}{~=~}\color {blue}{u_{\circ }}\color {black}{}/{\sqrt {(\color {blue}{g}\color {black}{/20)}}}$

Wave period $\color {blue}{T}\color {black}{~=~12}$ hours (43200 seconds)

Wave length $\color {blue}{L}\color {black}{~=}\color {blue}{C}\color {black}{\times }\color {blue}{T}$

Wave number $\color {blue}{k}\color {black}{~=~(2\times \pi )/}\color {blue}{L}$

For each point $y$ along the boundary at time $\color {blue}{t}$:

Water level $\color {blue}{\xi }\color {black}{}~=~\color {blue}{\xi _{\circ }}\color {black}{}\times exp(\color {blue}{-f}\color {black}{}\times y/\color {blue}{C}\color {black}{})\times cos(\color {blue}{k}\color {black}{}\times (x-\color {blue}{C}\color {black}{}\times \color {blue}{t}\color {black}{}))$

Note: $x$ at western boundary is $\color {blue}{-L}\color {black}{}/2$

Depth-mean flow $\color {blue}{<u>}\color {black}{}~=~{\sqrt {(\color {blue}{g}\color {black}{}/20)}}\times \color {blue}{\xi }\color {black}{}(y)$

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

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

Figure 1. Plan view of final bathymetric change.

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