Harmonic Internal Waves in a Semi-Infinite Stratified Medium with Shear Flows

Abstract—The problem of constructing the solutions that describe harmonic internal gravity waves in a semi-infinite stratified medium with shear flow is considered. The model constant distribution of the Brunt–Väisälä frequency and the linear dependence of shear flow as functions of the depth are used and an analytical solution of the problem expressed in terms of the modified Bessel functions of the imaginary index is obtained. The analytical expressions for the dispersion relations are obtained using the Debye asymptotics of the modified Bessel function of the imaginary index and the phase characteristics of the wave fields are investigated. The wave characteristics of the excited fields are investigated as functions of the main parameters of the used stratification models, flows, and generation regimes.