Whitecapping

The work we describe addresses the process of whitecapping. We first argue that, when the winds are strong enough, the ocean surface must develop an alternative means to dissipate energy when its flux from large to small scales becomes too large. We then show that the resulting Phillips' spectrum, which holds at small or meter length scales, is dominated by sharp crested waves. We next idealize such a sea locally by a family of close to maximum amplitude Stokes waves and show, using highly accurate simulation algorithms based on a conformal map representation, that perturbed Stokes waves develop the universal feature of an overturning plunging jet. We analyze both the cases when surface tension is absent and present. In the latter case, we show the plunging jet is regularized by capillary waves that rapidly become nonlinear Crapper waves in whose trough pockets whitecaps may be spawned. We are careful not to claim this as the definitive mechanism for whitecaps because three-dimensional effects, although qualitatively discussed, are not included in the analysis.