Two-point cross correlations of turbulence and noise predictions: Analysis and simulation

This paper describes an analytical and computational study of the role of two-point cross correlations of turbulent fluctuations in the prediction of noise from turbulent flows. In the first part of the paper the relationship between noise prediction formulas based on a description of the turbulent statistics in both moving and fixed frames is given. It is shown that predictions of the far field spectral density and intensity are independent of the reference frame as long as the statistical descriptions in the two frames satisfy a certain criterion. By example, it is shown that this criterion is met if the correlations in the two reference frames are related by a simple coordinate transformation. In the second part of the paper, the effect of the choice of cross correlation function on the prediction formula developed by Tarn and Auriault is considered. It is shown that convective amplification effects are evident if forms consistent with those previously used in models based on the acoustic analogy are used. Finally, numerical simulations of the turbulence in a high speed jet are described. The turbulence database generated by the simulations is examined to extract the two-point cross correlations in both fixed and moving reference frames. Cross correlations of pressure, axial velocity and the convective derivative of pressure are presented.