Rigid Lid

ζ

Bed Datum

Fig. 1: Definition sketch for Exner's model

For purposes of verifying our numerical scheme, we use a simplified mathematical model

that essentially uncouples the sediment continuity equation from the hydrodynamics. This allows

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 *q*f 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 * ∂ ⎛

+ ⎜*A*

⎟=0

(10)

∂*t * ∂*x *⎝ ζ - *z *⎠

8

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