Sediment Transport 1

Sediment Transport

Overview

For sand transport, the wash-load (i.e. sediment transport which does not contribute to the bed-material) can be assumed to be zero, and therefore, the total-load transport is equal to the sum of the bed- and the suspended-load transports: $q_{tk*}=q_{sk*}+q_{bk*}$.

There are currently three sediment transport models available in CMS:

(1) Equilibrium total load

(2) Equilibrium bed load plus non-equilibrium suspended load, and

(3) Non-equilibrium total-load.

The first two models are single-size sediment transport models and are only available with the explicit time-stepping schemes. The third is multiple-sized sediment transport model and is available with both the explicit and implicit time-stepping schemes.

Equilibrium Total-load Transport Model

In this model, both the bed load and suspended load are assumed to be in equilibrium. The bed change is solved using a simple mass balance equation known as the Exner equation.

${\frac {\rho _{s}(1-\rho _{m}^{'})}{f_{morph}}}{\frac {\partial z_{b}}{\partial t}}={\frac {\partial q_{t*j}}{\partial x_{j}}}+{\frac {\partial }{\partial x_{j}}}\left(D_{s}\mid q_{t*}\mid {\frac {\partial z_{b}}{\partial x_{j}}}\right)$ (2-42)

for $j=1,2;k=1,2,.....,N$ , where N is the number of sediment size classes and

t = time [s]

h = total water depth [m]

$x_{j}$ =Cartesian coordinate in the j^th direction [m]

$q_{t*}$ = equilibrium total-load transport rate [kg/m/s]

$z_{b}$ = bed elevation with respect to the vertical datum [m]

$p_{m}^{'}$ = bed porosity [-]

$f_{morph}$ = morphologic acceleration factor [-]

$\rho _{s}$ = sediment density [~2650 kg/m³ for quartz sediment]

$D_{s}$ = empirical bed-slope coefficient (constant) [-]