Discrete vortex modelling of oscillatory flow over ripples

Abstract

Two discrete vortex models of oscillating flow above two-dimensional vortex ripples are presented. These are a simple inviscid model, which contains no diffusion of vorticity, and a cloud-in-cell (CIC) model with diffusion represented by random walk. For values of D 0/ λ corresponding to the vortex ripple regime ( D 0 is the wave orbital diameter and λ is the ripple wavelength), both models are shown to be capable of producing the time-varying vortex strengths, positions and bed stresses observed in oscillating-flow laboratory experiments. For relatively large values of D 0/ λ (≳3), the CIC model has the advantage of being able to represent the first stages of breakdown of vortices into more homogenous turbulence. For relatively low values of D 0/ λ (≲1), the inviscid model is shown to produce the expected tendency towards non-separating flow behaviour which is markedly different from that of classical flat-bed models particularly in respect of the bed friction.