  We introduce order parameter models for describing the dynamics of sand
ripple patterns under oscillatory flow. A crucial ingredient of these models is
the mass transport between adjacent ripples, which we obtain from detailed
numerical simulations for a range of ripple sizes. Using this mass transport
function, our models predict the existence of a stable band of wavenumbers
limited by secondary instabilities. Small ripples coarsen in our models and
this process leads to a sharply selected final wavenumber, in agreement with
experimental observations.
