The Effect of Wind on Wave Shape in Shallow Water

Wave shape (e.g., wave skewness and asymmetry) impacts sediment transport, beach morphology, and ship safety. Wind can affect wave shape through changes in surface pressure; the authors previously investigated this effect on waves in intermediate and deep water. It was found that the impact of wind on wave shape was most pronounced when the depth ($kh$) became small. The present work examines the effect of wind on wave shape in shallow water using a multiple-scales analysis. Stokes-type waves propagating on a flat, shallow ($kh \ll 1$) bottom are subjected to various surface pressure profiles such as Jeffreys-type and generalized Miles-type. The effects of wind on wave skewness, asymmetry, and relative amplitude of the bound harmonic are investigated. Wave shape parameters are extracted and compared to existing experimental results and numerical simulations.