Wave Dynamics of Stratified Media with Variable Shear Flows

Abstract

In this work, internal gravity waves are considered that propagate in a stratified medium of finite depth with variable background shear flows. In the linear formulation, using the Fourier method, the author constructed the Green function of the corresponding equation of internal gravity waves. The asymptotic of the Green function in the far zone expressed through the square of the Airy function is studied. It is shown that, for real distributions of buoyancy frequency and shear flow vector, the wave zone is bounded by two closed curves: head and rear fronts. In the case when the components of shear velocity vector less vary over the vertical, the head wave front is a circle expanding with a maximum group velocity of the separate wave mode without flows and shifted by the flow with a velocity equal to the average value of the shear velocity vector taken with some weight.