Modeling Wind Effects on Shallow Water Waves

Abstract

A mechanism for the growth of waves by wind is included in a time-domain Boussinesq-type model. To facilitate direct analysis of the effect of wind on nonlinear wave–wave interactions over a flat bottom, a set of three harmonic evolution equations is derived from the time-domain model. These equations simulate the evolution of the principal components of three-wave (triad) nonlinear interactions, now including the effect of wind. A case of wave recurrence, in which energy is cycled between three harmonics, shows that a following wind can increase energy exchange to higher harmonics owing to nonlinearity, whereas an opposing wind suppresses this interaction. The time-domain model is then used to simulate wave propagation over a planar slope in the presence of wind. It is shown that wave growth is assisted by onshore winds and hindered by offshore winds. In addition, wave skewness and asymmetry, which quantify wave shape, are also similarly affected by wind direction. The results also show that the skewness and asymmetry undergo cyclic oscillation during the shoaling process; the degree to which these statistics exhibit the effect of wind is thus spatially dependent and can likely explain earlier laboratory studies regarding the increased dependence of wave-shape statistics on wind speed in shallow water relative to that seen in deeper water.