Adaptation

The sediment transport functions predict the equilibrium sediment concentrations at each cross section. These methods are based on the assumption that sediment concentration in transport has adjusted to the local hydraulic conditions. The concentrations, particularly for deposition of finer sediments, however, may not be in equilibrium due to the time required for the sediment concentrations to adjust to a new equilibrium when settling velocities are low. The turbulent diffusion equation developed by Dobbins (1944) describes this effect, but its solution requires a two dimensional model.

A simpler method is applied in 1D Sediment Transport Solver, therefore, to simulate the adaptation effect: an equation was fitted to the results from a two-dimensional non-equilibrium sediment transport model based on the turbulent diffusion equation.

The form of the equation is an exponential decay function that describes the adjustment of concentrations from the concentrations upstream. The rate of adjustment depends on shear velocities and settling velocities. The equation used in 1D Sediment Transport Solver to calculate the adjusted downstream concentration, Cis:

                     (10)

Where

X_k+1 = downstream equilibrium transport concentration

C_k = sediment concentration at upstream section

                                                 (11)

                              (12)

V_s= settling velocity (for sand sizes this is computed from sediment diameters, using the relationship given by Soulsby, 1997)

h = flow depth

V = mean flow velocity

V_*= shear velocity

While the equation can have a significant impact for cohesive sediments, it has little impact for medium sands or coarser material.