Acoustic scattering from locally homogeneous turbulence

Abstract

From the basic equations of fluid dynamics, an equation is derived for acoustic scattering from the velocity and temperature fields of a drifting blob of air turbulence. With the aid of the Born approximation, the equation is then solved for scattering from the mean and turbulent portions of both fields, and the time autocorrelation and power spectral density of the received signal are calculated. The mean velocity and temperature fields, as well as the corresponding turbulence intensity distributions, are allowed to be spatially nonuniform. The turbulent fields are required to be only locally homogeneous and, because of the nonzero drift, locally stationary. It is shown that the common practice of representing antenna patterns by either truncating the flow or tapering the strength of the flow is, at least in the case of the transmitting pattern, not a bad approximation. Spectral broadening of the received signal due to convection of the small scattering eddies by macroeddies and by the mean flow is modeled, and the broadening by macroeddy convection is seen to render negligible the broadening which arises from the drift of the target flow through the antenna beam. The analysis reveals that only for target flows having a high degree of spatial uniformity and/or symmetry does the received positive-frequency power spectral density turn out to be symmetrical about a center frequency.