Direct Simulation of Unsteady Capillary Gravity Waves on Deep Water

Fully nonlinear time evolution of periodic capillary gravity waves on an inviscid fluid of infinite depth is investigated numerically. The cases where the effect of surface tension is weaker than that of gravity are considered. It is found that the weakly resonant symmetric steady waves are unstable to two kinds of disturbances: the sidebands and the higher harmonics. Ripples are generated within a time of a few periods. They first appear at the point with the greatest slope on the forward face of the highest crest of the disturbed steady waves.