# The frequency spectrum of sound radiated by isotropic turbulence

## Abstract

The theory of turbulent time correlations is applied to compute the frequency spectrum of sound radiated by isotropic turbulence. Assuming the quasi-normality of the fourth-order velocity correlation generated by Lighthill's theory, it is argued that the frequency distribution of radiated acoustic energy is determined by the Eulerian space-time correlation function. The frequency spectrum of the sound radiated by isotropic turbulence is found to scale as ω(-4/3) at high frequencies. Dimensional analysis based on Kolmogorov scaling predicts the dependence ω(-7/2) instead. The discrepancy is explained by the dependence of Eulerian time correlations on an additional dimensional parameter: the sweeping velocity of the most energetic scales of motion. (C) 2000 Elsevier Science B.V.