Lighthill's theory of sound generation in a non-isothermal medium

TL;DR

This paper extends Lighthill's theory of sound generation to non-isothermal media, revealing how temperature gradients influence acoustic sources and wave propagation, including the emergence of monopole and dipole sources and the acoustic cutoff frequency.

Contribution

It introduces an analytical model incorporating temperature gradients into Lighthill's theory, showing their impact on acoustic source types and wave behavior.

Findings

Temperature gradients induce monopole and dipole acoustic sources.

Efficiency of monopole and dipole sources can surpass Lighthill's quadrupoles.

Wave propagation is altered by the acoustic cutoff frequency due to temperature gradients.

Abstract

Lighthill's theory of sound generation was developed to calculate acoustic radiation from a narrow region of turbulent flow embedded in an infinite homogeneous fluid. The theory is extended to include a simple model of non-isothermal medium that allows finding analytical solutions. The effects of one specific temperature gradient on the wave generation and propagation are studied. It is shown that that presence of the temperature gradient in the region of wave generation leads to monopole and dipole sources of acoustic emission, and that the efficiency of these two sources may be higher than Lighthill's quadrupoles. In addition, the wave propagation far from the source is different than in Lighthill's original work because of the presence of the acoustic cutoff frequency resulting from the temperature gradient.