Wind-induced changes to surface gravity wave shape in shallow water

Wave shape (e.g. wave skewness and asymmetry) impacts sediment transport, remote sensing and ship safety. Previous work showed that wind affects wave shape in intermediate and deep water. Here, we investigate the effect of wind on wave shape in shallow water through a wind-induced surface pressure for different wind speeds and directions to provide the first theoretical description of wind-induced shape changes. A multiple-scale analysis of long waves propagating over a shallow, flat bottom and forced by a Jeffreys-type surface pressure yields a forward or backward Korteweg–de Vries (KdV)–Burgers equation for the wave profile, depending on the wind direction. The evolution of a symmetric, solitary-wave initial condition is calculated numerically. The resulting wave grows (decays) for onshore (offshore) wind and becomes asymmetric, with the rear face showing the largest shape changes. The wave profile's deviation from a reference solitary wave is primarily a bound wave and trailing, dispersive, decaying tail. The onshore wind increases the wave's energy and skewness with time while decreasing the wave's asymmetry, with the opposite holding for offshore wind. The corresponding wind speeds are shown to be physically realistic, and the shape changes are explained as slow growth followed by rapid evolution according to the unforced KdV equation.