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Test Case 4

Headland with Tidal Flow

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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) Journal of Geophysical Research 96(C2): 2561-2575.

Figure of test case 4, a headland with tidal flow.

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 (east-west) l = 100,000 m
Width (north-south) w =50,000 m
Depth h = 20 m

Bottom Sediment

Single grain size on bottom
Size (D50) = 0.1 mm (sand)
Density ρs = 2650 kg /m³
Settling velocity = 0.5 mm/s
Critical shear stress τc= 0.05 N/m²
Bed thickness 0.005 m
Erosion rate 5 e-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 = 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 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 = sqrt(g * 20.0)
Reference water level ξ0 = u0/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 = ξ0 * exp(-f * y/C) * cos(k * (x - C * t))
*Note: x at western boundary is -L/2
Depth-mean 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 = 1e-6 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

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