Water-wave instability induced by a drift layer

A simple water-wave instability induced by a shear flow is re-examined, using a cubic equation first derived by Stern & Adam (1973) for a piecewise constant vorticity model. The instability criteria and the growth rate are computed. It is found that this mechanism is effective only if the surface drift velocity exceeds the minimum wave speed for capillary–gravity waves, and only if the drift-layer thickness lies within a band which depends on the wavelength and the drift velocity