Acoustic Energy and Momentum in a Moving Medium

TL;DR

This paper establishes conservation laws for acoustic energy and momentum in moving media by drawing an analogy with scalar fields in gravitational backgrounds, linking wave dynamics with fluid flow properties.

Contribution

It introduces a systematic approach to derive wave energy and momentum conservation laws using tensor formalism and analogies with gravitational fields.

Findings

Acoustic energy conservation is derived from a mixed energy-momentum tensor.

Wave energy exchange with mean flow is explained via radiation stress tensor.

The approach unifies wave and flow energy conservation principles.

Abstract

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.