A turbulence spectral model for sound propagation in the atmosphere that incorporates shear and buoyancy forcings

A three-dimensional model for turbulent velocity fluctuations in the atmospheric boundary layer is developed and used to calculate scattering of sound. The model, which is based on von Karman's spectrum, incorporates separate contributions from shear- and buoyancy-forced turbulence. New equations are derived from the model that predict the strength and diffraction parameters for scattering of sound as a function of height from the ground and atmospheric conditions. The need is demonstrated for retaining two distinct scattering length scales, one associated with scattering strength and the other with diffraction. These length scales are height dependent and vary substantially with the relative proportions of shear and buoyancy forcing. The turbulence model predicts that for forward-scattered waves the phase variance is much larger than the log-amplitude variance, a behavior borne out by experimental data. A new method for synthesizing random fields, based on empirical orthogonal functions, is developed to accommodate the height dependence of the turbulence model. The method is applied to numerical calculations of scattering into an acoustic shadow zone, yielding good agreement with previous measurements.