Internal gravity waves dynamics in a stratified viscous medium with background shear flows under critical regimes generation

The paper considers the problem of propagation of linear internal gravity waves in a layer of viscous stratified medium of finite depth with horizontal background shear currents under critical wave generation conditions. In a flat formulation, new model physical formulations of problems in which critical conditions may arise are discussed, in particular, wave generation by periodic oscillations of the bottom. For arbitrary distributions of shear currents and buoyancy frequency satisfying the Miles–Howard conditions and natural regularity conditions, a model equation describing the main features of solutions near the critical level was proposed. For real parameters of stratified media, using the asymptotics of the model equation, estimates of the spatial scales on which it is necessary to take into account the viscosity of the medium were obtained.