Surface waves and currents in aquatic vegetation

Abstract

A multiscale asymptotic theory is formulated for surface gravity waves and currents in finite-depth water with a vegetation canopy that provides a drag force on both flows with known drag coefficients. It assumes that the density is uniform and the depth is uniform pro tem and that the wave frequency is fast compared to the current advective rate. It is a quasi-linear theory in which the wave dynamics is independent of current and drag to leading order but provides perturbative corrections, and in which wave nonlinear interactions are neglected while quadratic wave-averaged wave fluxes and quadratic wave-drag effects are retained. The primary surface wave is modified by drag and current interactions, and the wave-averaged current momentum balance includes a wave-augmented drag force and several vortex forces due to Earth's rotation, current vorticity, Stokes drift and drag-induced wave vorticity. The wave-averaged current equations derived here are a suitable basis for future large-eddy simulation and submesoscale circulation computational models.