Contribution to the theory of waves in multi-dimensional linear dispersive media

TL;DR

This paper develops asymptotic solutions for linear waves in multi-dimensional dispersive media using the Reference Solution Approach, revealing anisotropic wave patterns influenced by source shape and dispersion effects.

Contribution

It introduces the RSA method for asymptotic wave solutions and demonstrates its effectiveness in capturing anisotropic wave behaviors in dispersive media.

Findings

Pronounced anisotropy in wave amplitudes and phases for elongated sources

Kelvin angles determine directions of anisotropy due to dispersion

RSA solutions agree well with exact solutions

Abstract

The asymptotic solutions for linear waves generated by oscillating source of elliptic shape in the motionless media is constructed with the recently developed Reference Solution Approach (RSA). Pronounced anisotropy of the solutions is found for elongated sources both for amplitudes and phases of the resulting wave pattern. The classic Kelvin angles of the ship wave patterns determine specific directions of this anisotropy, thus, demonstrating the role of wave dispersion. The analytical results within the RSA are shown to agree remarkably well with exact solutions of the linear wave problem.