The monography is devoted to the research of the processes of disturbance and propagation of the internal gravity waves within the vertically stratified horizontally non-uniform and non-stationary mediums, to development of the asymptotic methods being by the generalization of the space-time ray-tracing method (the method of the geometrical optics), to research of the critical phenomena at generation and propagations of the internal gravity waves, and also to development of non-spectral methods of the analysis of the full-scale measurements of the internal gravity waves in the ocean. The monography is intended for the specialists in the field of hydrodynamics, oceanology and the mathematical modeling of geophysical processes.

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