A well posed acoustic analogy based on a moving acoustic medium

TL;DR

This paper develops a well-posed acoustic analogy based on a moving acoustic medium, deriving a linear convected wave equation for lossless gas flows that demonstrates stability and reciprocity, and applies it to vortex-cylinder collision sound generation.

Contribution

It introduces a new acoustic analogy grounded in a self-adjoint wave equation for lossless flows, enabling better analysis of sound generation in moving media.

Findings

The wave equation is self-adjoint and satisfies reciprocity.

A quadratic conservation law indicates flow stability.

Application to vortex-cylinder collision demonstrates practical relevance.

Abstract

For flows of a lossless gas, the stagnation enthalpy obeys a linear convected wave equation with coefficients which depend on the flow variables. This equation is self-adjoint and one has a reciprocity relation between source and observer. It fulfills for subsonic flow a quadratic conservation equation implying stability. It is taken as basis for an acoustic analogy and is applied to the sound generation by the collision of a convected vortex and a rigid cylinder.