The noise spectrum of isotropic turbulence

Abstract

Proudman’s solution for the noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers was reviewed by Lilley (1994) following the simulation of Sarkar and Hussaini (1993). It was suggested (Lilley, 1996) that the Lighthill–Proudman theory could be used for the prediction of the radiated acoustic power from turbulent free shear flows in the absence of shock waves. In this approximation the Lighthill ‘‘filter function’’ was used with distributions of the turbulent kinetic energy, the temperature fluctuations, and the turbulent length scale. The results were compared with experimental measurements. But the method (Lilley, 1996) was only concerned with the total acoustic power. Modifications to this theory are required for the estimation of the spectrum and directivity of the radiated sound. The frequency resolution in time-dependent RANS calculation (TRANS) is limited by the grid used. In most, the large scale structure of the turbulence is resolved and consequently the energy containing scales captured. But the high-frequency part of the spectrum is poorly defined. Present work discusses two models for the high-frequency spectral decay and some of the properties of the high-frequency spectrum in turbulent shear layers.