Calculated coherence and extinction of sound waves propagating through anisotropic, shear-induced turbulent velocity fluctuations

Abstract

Previous calculations of the coherence and extinction of sound waves propagating through turbulence have almost always used isotropic models for the turbulence. However, low-frequency sound waves are strongly affected by energy-subrange turbulence structure, which is anisotropic by nature. In this paper, coherence and extinction are calculated using several anisotropic models for turbulent velocity fluctuations in the neutral atmospheric shear layer. New anisotropic versions of the Gaussian and von Kármán models are developed. The Kristensen et al. spectral model [Boundary-Layer Meteorol. 47, 149–193 (1989)] and Mann’s rapid-distortion, constant shear model [J. Fluid Mech. 273, 141–168 (1994)] are also considered. The turbulence models all predict that the crosswind extinction distance is longer than the along-wind value, although they disagree as to the extent of the lengthening: depending on the model, the ratio of crosswind to along-wind extinction varies from 2.1 to 13. These results point to the need for good experiments. Similarly, coherence of the propagating wavefronts is predicted to persist over longer distances in the crosswind direction.