Two-point correlations of sound pressure in the far-field of a jet: theory

Abstract

A large body of careful experimental measurement of two-point jet noise correlation have been carried out and are reported in a companion paper by Lucio Maestrello. The result were not altogether as expected and motivated the present effort to bring theory to bear. The model of jet noise generation is that of Ribner (1963, 1964, 1969), which is development of the Lighthill for malism. It postulates isotropic turbulence superimposed on a specified mean shear flow, with assumed space-time velocity correlations. The particular vehicle is the Proudman format, which is extended from the 1969 work (mean square pressure) to display the two-point space-time correlations of pressure. Here, again, the self-noise (from turbulence alone) is accompanied by shear noise (from turbulence-mean flow interaction), with distinct and different contributions. The shape of polar plots of correlation derives from two main factors: (1) the derivatives of the constituent quadrupoles and (2) the noncompactness of the source region which allows differences in travel time to the two microphones. Comparisons are made with the results of Maestrello's measurements.