ДИНАМИКА ПАКЕТА ВОЛН НА ПОВЕРХНОСТИ НЕОДНОРОДНО ЗАВИХРЕННОЙ ЖИДКОСТИ (ЛАГРАНЖЕВО ОПИСАНИЕ)
The nonlinear Schrödinger (NLS) equation describing the propagation of inhomogeneous vertical wave packets in an infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulation instability criteria of the considered weakly vortical waves and potential Stokes waves on deep water coincide. The effect of vorticity manifests itself in the shift of the wave number. A special case of Gerstner waves is noted, for which the coefficient of the nonlinear term in the NSE is zero.