  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.
