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 variety of barotropic flows. It specifically identifies the Stokes drift velocity 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 dynamics of the mean Eulerian velocity, by coupling to the mean vorticity. If tracers 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. The theory may be used to study the dynamics of large scale erodible beds composed of loose sediment subjected to interacting storm- and tidal-driven flows. One such problem is the origin and evolution of certain shore-oblique sand ridges. An hypothesis is that they are generated by instabilities in the erodible bed due to the passage of steady currents. By applying the theory we show how such an hypothesis is modified when the unsteadiness assumption is lifted and when both waves and currents are present.