  In this paper we consider fundamental processes of the disturbance and
propagation of internal gravity waves in the ocean modeled as a vertically
stratified, horizontally non-uniform, and non-stationary medium. We develop
asymptotic methods for describing the wave dynamics by generalizing the
spatiotemporal ray-tracing method (a geometrical optics method). We present
analytical and numerical algorithms for calculating the internal gravity wave
fields using actual ocean parameters such as physical characteristics of the
sea water, topography of its floor, etc. We demonstrate that our mathematical
models can realistically describe the internal gravity wave dynamics in the
ocean. Our numerical and analytical results show that the internal gravity
waves have a significant impact on underwater objects in the ocean.
