Dynamics of internal gravity waves in the ocean with shear flows

The problem of the harmonic internal gravity wave dynamics in a stratified ocean of finite depth with shear flows is solved. Stratification with constant distribution of the buoyancy frequency and various linear dependences of the shear flow on depth were used for the analytical solution of the problem. Dispersion dependences were obtained, which are expressed through a modified Bessel function of an imaginary index. The Debye asymptotics of the modified Bessel function of the imaginary index were used to construct analytical solutions under the Miles stability condition and large Richardson numbers. The asymptotic properties of the dispersion equation are studied. The main analytical properties of dispersion curves are investigated. The results of numerical calculations of the fields of phase structures of the generated internal gravity waves for various models of wave generation are presented.