Dynamics of a Wave Packet on the Surface of an Inhomogeneously Vortical Fluid (Lagrangian Description)
A nonlinear Schrцdinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously
vortical 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 modulational instability criteria for the weakly vortical waves and potential Stokes waves on
deep water coincide. The effect of vorticity manifests itself in a shift of the wavenumber of high-frequency filling.
A special case of Gerstner waves with a zero coefficient at the nonlinear term in the NSE is noted.