Wind-Induced Changes to Wave Shape

Wave shape (eg. skewness and asymmetry) plays an important role in beach morphology evolution and microwave backscatter. Past experiments have demonstrated that wind forcing can change wave shape; however, most analyses that couple wind and waves are phase-averaged and cannot predict the wave shape. Here, a wind-induced surface pressure is prescribed and a multiple-scale analysis is used to obtain solutions for periodic progressive waves. In the absence of wind, solutions reduce to deep water Stokes waves with zero asymmetry. Jeffreys- and Miles-types forcings, as well as a generalized Miles-type forcing, are considered at various orders in the perturbation expansion. The Miles-type forcing gives zero asymmetry identically, while the Jeffreys-type and generalized Miles-type each produce asymmetry that depends on the non-dimensional growth rate.