Analytical Solutions to Problems of Wave Dynamics of Stratified Media with Variable Buoyancy Frequency

In this work, the analytical solutions are constructed that describe the Green function for the equation of internal gravity waves in a stratified medium with variable buoyancy frequency. An asymptotical method for constructing solutions is proposed using the method of geometric optics; the method applies explicit analytical solutions for a semi-infinite stratified medium with linear distribution of the square of the buoyancy frequency. It is shown that the proposed algorithm for building the asymptotic of the Green function can be generalized to the case of horizontally inhomogeneous stratified media, when the buoyancy frequency depends not only on the vertical coordinate, but also on the horizontal coordinates.