Woods Hole Coastal and Marine Science Center

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Test Case 2


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This test case provides a fundamental check of the ability of a model to represent 1) mixing processes typical of estuarine conditions, 2) resuspension, advection, and deposition for suspended-sediment transport, 3) temporal dynamics of upper bed layer, and 4) interaction of suspended-sediment and the bed.

Figure showing the layout of test case 2, an estuary.


The domain is a long, narrow rectangular channel.
Length (east-west) l = 100,000 m
Width (north-south) w =1000 m
Depth h = 10 m at the western end, decreasing linearly to 5 m at the eastern end
Constant temperature, 10° C

Bottom Sediment

Single grain size on bottom:
Size (D50) = 0.15 mm (fine sand)
Density ρs = 2650 kg/m³
Settling velocity = 0.50 mm/s
Critical shear stress τc= 0.05 N/m²
Fractional bed concentration (1-porosity) = 0.90
Sediment layer thickness = 1 mm


No Coriolis
No wind
No heating/cooling

Initial Conditions

Salinity distribution from west end = 35 to east end = 0
(Vertically well mixed.)

Boundary Conditions

North and south sides = walls with no fluxes, no friction
Bottom roughness ks = 0.15 m (zo = Ks/30 = 0.005 m)
Sediment flux calculated by model
Surface = free surface, no fluxes

Flow, Western end, tidal
qwest = 4000 m³ /s * sin (ω t ) - qeast
ω = 2π/T
T = 12 * 3600, seconds
t = model time step, seconds
Flow, Eastern end, constant riverine (varying depth)
qeast = 400 m³ /s
Salinity, western end
Radiation condition with nudging, tnudge = 3 hours
Salinity at eastern end = 0

Output (ASCII files suitable for plotting)

At t = 10 days (20 tidal cycles):
Tidally averaged velocity field (average over last 2 tidal cycles)
Bed profile
Tidal-mean suspended sediment field

Physical Constants

Gravitational acceleration g = 9.81 m/s²
Von Karman's constant κ = 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 2: Estuary

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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