The evolution of the bed or bottom surface elevation due to the transport of sediment as

bed load is governed by the so-called sediment continuity or Exner equation (see for example

Henderson, 1966):

∂*z*

+ ∇ ⋅ **q**b = 0

(1)

∂*t*

where *z *is the elevation of the bed relative to a datum located below the bed (*z *is positive

upwards) and **q**b is the bed load sediment transport function vector.

sediment transport is always in the direction of the flow velocity, **U **= (*u*, *v*) where *u *and *v *are the

velocity components of the flow in the *x *and *y *directions, respectively. Thus the vector **q**b is

computed as:

^

(2)

^

^

normalized flow velocity vector (i.e. **U **= **U U **). There are a number of empirical bed load

sediment transport functions available (e.g. Bagnold, Einstein, Meyer-Peter and Mueller, see for

example Sleath, 1984 for a thorough list), most of which can be transcribed in the following form:

)U

(3)

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