Domain
Bottom Sediment
Forcing
Initial Conditions
Boundary Conditions
Output
Physical Constants
Results

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 suspendedsediment. This case is based on Signell and Geyer (1991) Journal of Geophysical Research 96(C2): 25612575.
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.
Length (eastwest) l = 100,000 m
Width (northsouth) w =50,000 m
Depth h = 20 m
Bottom Sediment
Single grain size on bottom
Size (D_{50}) = 0.1 mm (sand)
Density ρ_{s} = 2650 kg /m³
Settling velocity = 0.5 mm/s
Critical shear stress τ_{c}= 0.05 N/m²
Bed thickness 0.005 m
Erosion rate 5 e5 kg /m² /s
Forcing
Coriolis f = 1.0 e4
No heating/cooling
No wind
Initial Conditions
u = 0 m³ /s
Salinity = 0 Temperature = 20° 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 z_{0} = 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 u_{0} = 0.5 m/s
Celerity C = sqrt(g * 20.0)
Reference water level ξ_{0} = u_{0}/sqrt(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 ξ = ξ_{0} * exp(f * y/C) * cos(k * (x  C * t))
*Note: x at western boundary is L/2
Depthmean flow <u> = sqrt(g/20) * ξ(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 = 1e6 m² /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
Solution to Test Case 4: Tidal Headland
