Wave-current interactions in coastal waters and their application to shore-connected bars

Abstract

A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside the surf zone. The theory provides a practical and useful model with which wave-current coupling may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long, infra-gravity waves and wave-averaged vortex forces for the low-frequency current and sea-level evolution equations. Analogous relations are derived for material tracers and density stratification that include phase-averaged, Stokes-drift advection, including by a vertical Stokes pseudo-velocity that is the incompressible companion to the horizontal Stokes velocity. This theory is used to study the effect of waves on the evolution of large-scale erodible beds. In particular, the formation of certain up-current rotated, shore-connected bars is investigated. It is hypothesized that these bars form due to an instability of the bottom topography in the presence of a storm driven flow. This hypothesis is reviewed in the light of the presence of both waves and currents. It is shown that waves can significantly affect the instability. The effects of different wave parameters are investigated. Steady flow and boundary condition assumptions are also examined.