Acoustic Propagation Through Turbulence: the Turbule Ensemble Model and the Green's Function Parabolic Equation.

Acoustic propagation in the atmosphere is strongly affected by random velocity and temperature fluctuations resulting from turbulence. Furthermore, it is subject to refraction by gradual, large-scale vertical sound-speed gradients. These two phenomena are generally modeled using different techniques; the former by various scattering theories and the latter by fast field programs and parabolic equations, for example. These techniques tend to be mutually exclusive; scattering models do not account for the refraction, and the refractive models do not represent turbulent scattering. A common occurrence in outdoor sound propagation is the scattering from turbulence into a refractive shadow zone. Modeling of this phenomenon requires the combination of both a scattering model and a refractive model. A recent theory, the Turbule Ensemble Model (TEM), describes turbulent scattering from a random distribution of deterministic "turbules." The scattered field from these turbules is found from the first Born approximation to Monin's equation, describing acoustic propagation in a moving medium. The TEM can be linked to the statistical description of turbulence through the velocity and temperature spectra. To model turbulent scattering into a refractive shadow zone, the TEM is incorporated into the Green's Function Parabolic Equation (GFPE), a propagation model which numerically solves the reduced wave equation. The turbulent scattering is introduced as a distribution of secondary sources, using direction and beamwidth dependent Gaussian starting fields to simulate the turbulent scattered fields. An energy balance problem results from the three-dimensional nature of the turbulent scattered fields vs. the two-dimensional nature of the GFPE. This is treated by a technique of range-averaging the scattered energy. The model is compared with a random phase screen parabolic equation as well as measurements. Sensitivity of the model to several numerical parameters is discussed. The relative contributions of different turbule sizes and different ratios of velocity and temperature fluctuation strengths are examined.