Internal Gravity Waves in a Stratified Medium with Model Shear Flow Distributions

The problem of the field of internal gravity waves in a stratified medium of finite depth is considered for model distributions of background shear flows. The constant distribution of the buoyancy frequency and various linear dependences of background shear flow on the depth are used to solve the problem analytically. The dispersion relations expressed in terms of the modified Bessel function of imaginary index are obtained. In satisfying the Miles–Howard stability condition in the case of large Richardson numbers, the Debye asymptotics of the modified Bessel function of imaginary index are used to construct the analytical solutions. The properties of the dispersion relation are studied and the basic analytical characteristics of the dispersion curves are investigated as functions of the parameters of background shear flows. The phase patterns of the excited fields are calculated numerically for various wave generation models.