The synthesis of spatially correlated random pressure fields

The feasibility is considered of synthesizing a spatially correlated random pressure field having specified statistical properties. Of particular interest is the use of a near-field array of acoustic sources to synthesize a pressure field whose statistical properties are similar to either a diffuse acoustic sound field or to that generated by a turbulent boundary layer (TBL). A formulation based on least-squares filter design is presented. Initially, the more fundamental question is addressed of how many uncorrelated signal components are required to approximate the pressure field. A one-dimensional analysis suggests that two uncorrelated components per acoustic wavelength are required to approximate a diffuse pressure field. Similarly, for a TBL pressure field, about one uncorrelated component per correlation length is required in the spanwise direction and about two uncorrelated components per correlation length are required in the streamwise direction. These estimates are in good agreement with theoretical predictions for an infinite array, based on the Fourier transform of the spatial correlation function. When a full simulation is performed, including the acoustic effect of an appropriately positioned array of monopole sources, it is found that the number of acoustic sources required to reasonably approximate the diffuse or TBL pressure field is only slightly greater than the lower bound on this number, set by the number of uncorrelated components required. (c) 2005 Acoustical Society of America.