The geometry of sound rays in a wind

TL;DR

This paper explores the geometric principles underlying sound ray propagation in moving media, linking classical Riemannian geometry to Finsler geometry, and demonstrates how wind effects can be modeled using geometric mappings.

Contribution

It develops a comprehensive geometric framework for sound rays in moving media, bridging Riemannian and Finsler geometries with practical examples.

Findings

Sound rays in stratified atmospheres can be modeled as circles and straight lines.

Finsler geometry generalizes classical geometry for moving media.

Geometric mappings simplify understanding of sound propagation in wind.

Abstract

We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known as Finsler geometry is needed. We develop these geometries ab initio, with examples, and in particular show how sound rays in a stratified atmosphere with a wind can be mapped to a problem of circles and straight lines.