Wave-current interactions in shallow waters and shore-connected ridges

A formalism is developed for the interactions of waves and currents on long time scales. The resulting hydrodynamic equations are applicable to a vari ety of barotropic flows. It specifically identifies the Stokes drift veloci ty due to the gravity waves as the contributing effect of the waves to the general circulation. The Stokes drift plays a role on the long-time dynamic s of the mean Eulerian velocity, by coupling to the mean vorticity. If trac ers are present in the flow, this Stokes drift also affects the dynamics of the mean tracer field by modifying its advection due to currents alone. Th e theory may be used to study the dynamics of large scale erodible beds com posed of loose sediment subjected to interacting storm- and tidal-driven fl ows. One such problem is the origin and evolution of certain shore-oblique sand ridges. An hypothesis is that they are generated by instabilities in t he erodible bed due to the passage of steady currents. By applying the theo ry we show how such an hypothesis is modified when the unsteadiness assumpt ion is lifted and when both waves and currents are present. (C) 2001 Elsevi er Science Ltd. All rights reserved.