Wave Dynamics of Stratified Mediums with Variable Depth: Exact Solutions and Asymptotic Representations

Wave dynamics of stratified medium (ocean, atmosphere) is highly dependent on bottom topography. The exact analytical solution is obtained only if the water distribution density and bottom shape described by some model functions. When the characteristics of the medium and the boundaries are arbitrary and can be built only numerical solutions of such problems. However, numerical solutions are not qualitatively analyze the characteristics of the wave of the fields. The need for a qualitative analysis of the far field of internal waves arise in the study of internal waves remote methods by means of aerospace-parameter radar. Then the description and analysis of wave dynamics can be made only on the basis of the asymptotic models. In this paper uniform asymptotic forms of the far field of internal gravity waves which propagate in strati- fied medium with a smoothly varying bottom are constructed. The solution is proposed in terms of wave modes, propagating independently in the adiabatic approximation, and described as a power series of a small parameter characterizing the strati- fied medium. The effect of the space frequency “blockage” of the wave fields is characteristic of the real oceanic shelf. De- pending on the frequency characteristics of the wave field and bottom topography, far internal gravity waves are either local- ized in some limited spatial domain (captured waves) or propagated over long distance (progressive waves). The spatial do- main, where progressive waves propagate depends on ocean stratification and bottom topography.