Non local Models for Envelope Waves in a Stratified Fluid

A new, nonlocal evolution equation similar to the nonlinear Schrödinger equation is derived for envelope waves in a continuously stratified fluid by means of a multiscale perturbation technique. This new equation governs propagation of quasi‐harmonic wave packets having length scales much longer than the depth of the density variations and much shorter than the total depth of fluid. Generalizations of the nonlocal evolution equation for a description of two‐dimensional wave modulations are also presented. The modulational stability of small‐amplitude waves is then investigated in the framework of the derived equations. It is shown that quasi‐harmonic waves with the scales under consideration are unstable with respect to oblique perturbations at certain angles.