Dynamical models for sand ripples beneath surface waves - art. no. 066308

We introduce order parameter models for describing the dynamics of sand rip ple patterns under oscillatory flow. A crucial ingredient of these models i s the mass transport between adjacent ripples, which we obtain from detaile d numerical simulations for a range of ripple sizes. Using this mass transp ort function, our models predict the existence of a stable band of wave num bers limited by secondary instabilities. Small ripples coarsen in our model s and this process leads to a sharply selected final wave number, in agreem ent with experimental observations.