Turbulence effects on acoustic wave propagation over a smooth surface

Abstract

Turbulence produces fluctuations in the observed amplitude and phase of the direct and reflected waves whose sum constitutes the sound field p of an acoustic point source radiating above a smooth boundary. A perturbation approach is used to evaluate the corresponding long‐term average of the mean‐square pressure field p2. The result is energy conserving and is general enough to allow the insertion of an arbitrary refractive‐index correlation function. The effect of turbulence is shown to modify only the interference term of the resulting expression, and can be completely expressed in terms of a relatively simple function of the sum of the direct and reflected wave variances, the wave variance being the sum of the variances corresponding to the amplitude and phase fluctuations, and a quantity describing the lateral correlation between the direct and reflected waves. For certain cases, these results agree well with earlier work by other authors [G. A. Daigle, J. Acoust. Soc. Am. 68, 297–302 (1980)], however, fundamental differences in the propagation models yield significant discrepancies when more detailed comparisons are made.