where A is a given function and n is a given positive constant both of which are specific to the
particular sediment transport formula. Note that A is typically a function of the flow velocity, U,
the total height of the water column, H = ζ - z (where ζ is the water surface elevation relative to
the same datum as the bed), and a number of constants that are based on sediment properties such
as sediment type and grain size and data fitting procedures. The constant n is typically in the
range of 1 ≤ n ≤ 3 .
In our model, we will make use of a new bed load formula developed by Camenen and
Larson (2005), though the numerical model to be described will be general enough to allow the
use of any sediment transport formula provided it is a function of H and a monotonically
increasing function of U.
Camenen and Larson develop new bed load sediment transport
formulas for transport due to currents, waves, and combined waves and currents. Their formulas
were shown to provide the best agreement with the data sets that were compiled compared to a
number of previously proposed formulas (Camenen and Larson, 2005).
In this paper, we only consider the Camenen and Larson bed load sediment transport
formula due to currents which is given by (in dimensional form SI units):
qb = Cτ c exp ⎜ -4.5 cr ⎟
where τc is the shear stress at the bottom due to the current, τcr is the critical shear stress, and C is
a constant given by:
g ρ ( ρs - ρ )