Coherence calculations for propagation through anisotropic, turbulent velocity fluctuations

Abstract

Previous treatments of the mutual coherence function (MCF, describing the coherence between the signals received by two sensors as a function of their spatial separation) have been based on isotropic turbulence models. However, acoustic waves propagating through the atmosphere are strongly affected by a large-scale turbulence structure, which is anisotropic by nature. In this paper, the MCF is calculated using several rigorous, anisotropic models for turbulent velocity fluctuations in the neutral atmospheric shear layer: a generalized Gaussian model; a generalized von Kármán model; the Kristensen et al. model [Bound. Layer Meteor. 47, 149–193 (1989)]; and Mann’s rapid-distortion, shear model [J. Fluid Mech. 273, 141–168 (1994)]. Although it is possible to obtain analytical results for the MCF for the isotropic Gaussian model and von Kármán models, one can no longer do so when these models are extended in a suitable fashion to the anisotropic case. However, it is not difficult to obtain numerical results. By comparing the anisotropic models to their isotropic versions, it is shown that anisotropy can significantly affect coherence, even when the spacing of the sensors is small (in comparison to the height from the ground).