Acoustic scattering from a turbulent vortex

With the aid of the Born approximation, the time autocorrelation and power spectral density are calculated for the received acoustic signal scattered from velocity fluctuations in a turbulent aircraft trailing vortex. The turbulence is required to be globally stationary, but only locally homogeneous. The treatment includes the effects of spectral broadening due to convection of the scattering eddies by a spatially varying mean flow and by macroeddies. The 3 db bandwidth of the received signal is related to the scattering angle and the core Mach number of the vortex. A primary feature of the analysis is that it provides a method for inferring the radial intensity distribution of turbulence in a vortex. The analysis technique is also applicable to scattering from other turbulent flows where significant variations of turbulence level occur over distances on the order of the macroeddy size.