Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form

Calculations are carried out of the shape of gravity and gravity–capillary waves on deep water in the presence of a thin sheet of uniform vorticity which models the effect of a wind drift layer. The dependence of the fluid speed at the wave crest is determined and compared for gravity waves with the theory of Banner & Phillips (1974). It is found that this theory underestimates the retardation due to drift and tendency to break. The retardation disappears when capillary forces are significant, but in this case it is found that there can be a significant alteration of the wave shape.