A perturbation expansion and a multigrid technique are developed for simulating the fully-nonlinear unsteady-interaction of short waves riding on long gravity waves. Both numerical techniques are capable of simulating wave slopes near breaking and wavelength ratios greater than thirty, but the multigrid technique converges more rapidly and it is more efficient. The results of numerical simulations agree qualitatively with experimental measurements of ripple formation on the front face of a gravity-capillary wave.

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