The frequency spectrum of sound radiated by isotropic turbulence

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.