Steep, steady surface waves on water of finite depth with constant vorticity

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Abstract
Two-dimensional steady surface waves on a shearing flow are computed for the special case where the flow has uniform vorticity, i.e. in the absence of waves the velocity varies linearly with height. A boundary-integral method is used in the computation which is similar to that of Simmen & Saffman (1985) who describe such waves on deep water. Particular attention is given to the effects of finite depth with descriptions of waves of limiting steepness, waves with eddies beneath their crests and extremely high waves on high-speed flows.Many qualitative features of these waves are relevant to steep waves propagating in shallow water, or on a strong wind-induced drift current. An important practical point in the interpretation of wave measurements of wind driven waves is that mean kinetic energy and potential energy densities are unequal even for infinitesimal waves. This may mean that wave energy spectra deduced from surface-elevation measurements in the conventional way may sometimes be misleading.

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