On the generation of sound by supersonic turbulent shear layers

Abstract

A theory is proposed to describe the generation of sound by turbulence at high Mach numbers. The problem is formulated most conveniently in terms of the fluctuating pressure, and a convected wave equation (2.8) is derived to describe the generation and propagation of the pressure fluctuations.

The supersonic turbulent shear zone is examined in detail. It is found that, at supersonic speeds, sound is radiated as eddy Mach waves, and as the Mach number increase, this mechanism of generation becomes increasingly dominant. Attention is concentrated on the properties of the pressure fluctuations just outside the shear zone where the interactions among the weak shock waves have had little effect. An asymptotic solution for large M is derived by a Green's function technique, and it is found that radiation with given frequency n and weve-number K can be associated with a coresponding critical layer within the shear zone.

It is found that $(\overline {p - p_0})^2 $ increases approximately as $\rm {M}^{\frac {3} {2}}$ for M [Gt ] 1 contrasting with the M⁸ variation found by Lightill for M [Lt ] 1. The acoustic efficiency thus varies as $\rm {M}^-{\frac {3} {2}}$ for M [Gt ] 1, and as M⁵ for M [Lt ] 1, indicating a maximum acoustic efficiency for Mach numbers near one. The directional distribution of the radiation is discussed and the direction of maximum intensity is shown to move towards the perpendicular to the shear zone as M increases. The predictions of the theory are supported qualitatively by the few available experimental observations.