Scattering of sound by atmospheric turbulence: A numerical simulation above a complex impedance boundary

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A computer simulation of the effect of small-scale turbulence on atmospheric sound propagation over a complex impedance boundary is developed. The atmospheric turbulence is modeled as an ensemble of spherically symmetric eddies with Gaussian refractive profiles. Single scatter is assumed and a closed form of the first Born approximation for scattering is obtained, giving each eddy’s contribution to the total fluctuation of the sound pressure at a receiver downrange. The numerical simulation is accomplished by repeated calculations for many ‘‘realizations,’’ or snapshots of the turbulent medium. Each eddy’s scatter contribution is added up coherently for a particular configuration of eddies, yielding that realization’s total sound pressure. The eddies are then given a random change in their coordinates. The total sound pressure is calculated for this realization, and the process repeated. Better agreement with the analytical results of Karavainikov [Akust. Zh. 3, 175–186 (1957)] for an unbounded medium is obtained at the higher frequencies with the use of the first Rytov approximation to scattering. A complex impedance boundary is added and the predictions of the standard deviations of the amplitude fluctuations, amplitude probability distributions, and structure functions are then tested against experimental data. Good agreement is found whenever the average sound pressure level was well above the background noise level.