Internal Gravity Waves Generated by Non-Stationary Sources of Perturbations in a Stratified Ocean with Shear Currents

Abstract—The problem of constructing solutions that describe generation of internal gravity waves by a localized oscillating source of perturbations in stratified medium of finite depth with background shear flows is considered. Model representations of the buoyancy frequency and the distribution of shear flow over depth were used to construct analytical solutions in a linear approximation. Integral representation of the solution in the form of sums of wave modes was obtained under the Miles–Howard assumption, and an asymptotic representation of the solution for each mode was constructed using the stationary phase method. Results of calculations of dispersion relations and phase structures of wave fields for various modes of wave generation are presented. Spatial transformation of the phase structures of wave fields was studied depending on the frequency of oscillations of the source of perturbations and the main characteristics of shear flows.