Woods Hole Coastal and Marine Science Center

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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.


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


Coriolis f = 1.0 e-4
No heating/cooling
No wind

Initial Conditions

u = 0 m³ /s
Salinity = 0
Temperature = 20° C

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


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


Solution to Test Case 4: Tidal Headland

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These pages are for communication among a group of researchers studying experimental methods of modeling and visualizing natural systems using digital (numerical) techniques. The methods and models discussed are in preliminary, developmental, stages and may be incorrect. The pages will be changed or removed without warning. The U.S. Geological Survey makes no representation as to the accuracy, correctness, or utility of any data, model, model results, or technique associated with these pages.

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This page last modified on Monday, 05-Dec-2016 16:31:20 EST