Tidal velocity asymmetries and bedload transport in shallow embayments

Abstract

Tidally forced circulation can cause a net near-bed transport of sediment when the tidal velocity is asymmetric about a zero mean (flood or ebb dominant) and the transport rate is nonlinearly related to velocity. The relationship between elevation and velocity is elucidated here to enable one to determine from tide gauge data and sediment transport relations whether tidal asymmetry may cause net sediment transport. Tidal elevation and tidal velocity are related through the equations of motion of the fluid. If the estuary is shallow, the change in cross-sectional area of the channel with the tide is significant with respect to total area: the equations become nonlinear and an exact solution does not exist. A relationship between elevation and velocity in a nonlinear system is derived through the continuity equation and shown to be significantly different than the linear relation. Finite difference numerical solutions of the one dimensional, shallow water nonlinear equations are compared to the continuity relation and are in good agreement. The relationship between elevation asymmetry and ratio of flood-to-ebb bedload transport is calculated for both the linear relation between elevation and velocity and the nonlinear relation. Results show that the ratio of flood·to-ebb bedload transport as calculated from the nonlinear relation between elevation and velocity is similar to the flood-to-ebb ratio calculated from the linear relation.