The frequency spectrum of sound radiated by isotropic turbulence

The theory of turbulent time correlations is applied to compute the frequen cy spectrum of sound radiated by isotropic turbulence. Assuming the quasi-n ormality of the fourth-order velocity correlation generated by Lighthill's theory, it is argued that the frequency distribution of radiated acoustic e nergy is determined by the Eulerian space-time correlation function. The fr equency spectrum of the sound radiated by isotropic turbulence is found to scale as omega(-4/3) at high frequencies. Dimensional analysis based on Kol mogorov scaling predicts the dependence omega(-7/2) instead. The discrepanc y is explained by the dependence of Eulerian time correlations on an additi onal dimensional parameter: the sweeping velocity of the most energetic sca les of motion. (C) 2000 Elsevier Science B.V. All rights reserved.