Dynamics of non-harmonic internal gravity wave packets in stratified media

TL;DR

This paper analyzes the evolution of non-harmonic internal gravity wave packets in stratified media using a modified geometrical optics method, accounting for slow parameter changes and local dispersive properties.

Contribution

It introduces a modified special-time ray method with non-integer asymptotic series to study wave packet dynamics in stratified media.

Findings

Wave phases are determined by numerically solving eikonal equations.

Amplitudes are derived from invariants conserved along rays.

The method captures local dispersive effects near special points.

Abstract

In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves has been analyzed. The concrete form of the wave packages can be expressed through some model functions and is defined by the local behavior of the dispersive curves of the separate modes near to the corresponding special points. The solution of this problem is possible with the help of the modified variant of the special-time ray method offered by the authors (the method of geometrical optics), the basic difference of which consists that the asymptotic representation of the solution may be found in the form the series of the non-integer degrees of some small parameter. At that the exponent depends on the concrete form of representation of this package. The obvious kind of the representation is determined from the principle of the localness and the asymptotic behavior of the solution in the stationary and the horizontally-homogeneous case. The phases of the wave packages are determined from the corresponding equations of the eikonal, which can be solved numerically on the characteristics (rays). Amplitudes of the wave packages are determined from the laws of conservation of the some invariants along the characteristics (rays).