A simplified model

Kubatko_Ocean_Modelling
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us to verify the underlying numerics of the model in a simplified setting by comparing it to

analytical solutions. Assume that the flow is unidirectional (say in the x directional only) and

quasi-steady with a rigid lid. With these assumptions, the flow velocity is given by:

(9)

ζ -z

where qf is a constant flow discharge and ζ is the elevation of the rigid lid measured from the bed

datum (see Fig. 1). Furthermore, assume that the sediment transport is given by Eq. (3) with A =

constant and n = 1. With these assumptions the sediment continuity equation can be written as:

∂z ∂ ⎛

qf ⎞

+ ⎜A

⎟=0

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∂t ∂x ⎝ ζ - z ⎠