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 atmosp heric 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 ar e derived from the model that predict the strength and diffraction paramete rs for scattering of sound as a function of height from the ground and atmo spheric conditions. The need is demonstrated for retaining two distinct sca ttering length scales, one associated with scattering strength and the othe r with diffraction. These length scales are height dependent and vary subst antially with the relative proportions of shear and buoyancy forcing. The t urbulence model predicts that fur forward-scattered waves the phase varianc e is much larger than the log-amplitude variance, a behavior borne out by e xperimental data. A new method for synthesizing random fields, based on emp irical orthogonal functions, is developed to accommodate the height depende nce of the turbulence model. The method is applied to numerical calculation s of scattering into an acoustic shadow zone, yielding good agreement with previous measurements.