Discrete vortex modelling of oscillatory flow over ripples

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/lambda corresponding to the vortex ripple regime (D-0 is the wave orbital diameter and lambda 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/lambda (greater than or similar to 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/lambda (less than or similar to 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. (C) 2002 Elsevier Science Ltd. All rights reserved.