Analytical Solutions of the Internal Gravity Wave Equation in a Stratified Medium with Shear Flows

Abstract

The problem of constructing internal gravity wave fields generated by an oscillating localized point source of disturbances in a stratified medium with an average shear flow is considered. A model distribution of shear flow over depth is considered, and an analytical solution of the problem is obtained in the form of a characteristic Green function expressed in terms of modified Bessel functions of imaginary index. Analytical expressions for the dispersion relations are obtained using Debye asymptotics of the modified Bessel functions. Integral representations of solutions are constructed. The wave characteristics of the excited fields are investigated depending on the basic parameters of the used stratification models, shear flows, and generation modes.