V. V. Bulatov, Yu. V. Vladimirov
The internal gravity waves fields in a stratified fluid layer of variable depth are considered. Assuming a linear slope bottom, the exact solutions are obtained using the Kantorovich—Lebedev transform which describe an individual wave mode and a full wave field of internal gravity waves. Individual wave mode is expressed in terms of the hypergeometric function, the full wave field is described by semi-logarithmic function. WKBJ-asymptotics are constructed both for individual wave mode and for a full wave field. For the parameters of the stratified medium, which is characteristic for a real ocean (Bay of Biscay), the results of numerical calculations of the wave fields of asymptotic formulas are presented. A comparison with the results of numerical simulation of the complete system of hydrodynamic equations describing the evolution of nonlinear wave disturbances over a non-uniform ocean bottom, and it is shown that the amplitude-phase structure of the wave field is described by obtained in the paper asymptotic formulas. Available measurements data also show that the wave pattern with a strong beam structure can be observed in a real ocean, especially in the study of the evolution of a package of internal gravity waves over a non-uniform ocean bottom. In particular, analytical, numerical and measurements data show that the width of the wave ray decreases when approaching the shore. Typical ray pattern of the internal gravity waves in a stratified fluid layer of variable depth have been obtained without using of WKBJtechnics.