Time Correlations and the Frequency Spectrum of Sound Radiated by Turbulent Flows

Theories of turbulent time correlations are applied to compute frequency spectra of sound radiated by isotropic turbulence and by turbulent shear ows. The hypothesis that Eulerian time correlations are dominated by the sweeping action of the most energetic scales implies that the frequency spectrum of the sound radiated by isotropic turbulence scales as ! for low frequencies and as ! 4=3 for high frequencies. The sweeping hypothesis is applied to an approximate theory of jet noise. The high frequency noise again scales as ! , but the low frequency spectrum scales as !. In comparison, a classical theory of jet noise based on dimensional analysis gives ! 2 and ! scaling for these frequency ranges. It is shown that the ! 2 scaling is obtained by simplifying the description of turbulent time correlations. An approximate theory of the e ect of shear on turbulent time correlations is developed and applied to the frequency spectrum of sound radiated by shear turbulence. The predicted steepening of the shear dominated spectrum appears to be consistent with jet noise measurements. * This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the authors were in residence at the Institute for Computer Applications inScience and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001. i