Fourth order nonlinear evolution equations for gravity-capillary waves in the presence of a thin thermocline in deep water

Abstract

AbstractFor a three-dimensional gravity capillary wave packet in the presence of a thin thermocline in deep water two coupled nonlinear evolution equations correct to fourth order in wave steepness are obtained. Reducing these two equations to a single equation for oblique plane wave perturbation, the stability of a uniform gravity-capillary wave train is investigated. The stability and instability regions are identified. Expressions for the maximum growth rate of instability and the wavenumber at marginal stability are obtained. The results are shown graphically.