a Scattering Center Based Numerical Simulation of Small Scale Atmospheric Turbulence.

A computer simulation of the effect of small scale turbulence on atmospheric sound propagation over a complex impedance boundary is developed. The atmosphere is broken up into spherically symmetric eddies characterized by a Gaussian profile for mu, the change from unity of the index of refraction. Each eddie is assigned a positive or negative sign randomly and is assumed to scatter sound impinging on it. Single scatter is assumed and a closed form of the first Born approximation for scattering is obtained, giving each eddie's contribution to the total fluctuation of the sound pressure at a receiver downrange. Because of its close relationship to the first Born approximation and its widespread use in the literature, the first Rytov approximation is also calculated. It is found that they give almost identical results for the frequencies and ranges involved in this manuscript, but that for higher frequencies only the first Rytov approximation agrees with the results of ray theory. The first Rytov approximation was then adopted and a numerical simulation was accomplished with the concept of a "realization", or snapshot of the turbulent medium. Each eddie's scatter contribution was added up for a particular configuration of eddies, giving that realization's total sound pressure fluctuation. The eddies were then given a random change in their Cartesian coordinates up to a predetermined maximum of one meter. The total sound pressure was calculated for this realization, and the process repeated 500 times. The predictions of the standard deviations of the amplitude fluctuations, amplitude probability distributions, and structure functions were then tested against experimental data. Two data runs with a horizontal source-receiver separation of 91 meters were used for comparison, using the same receiver in both cases. For one run the source was near the ground and for the other the source was placed on a 31 m tower. Good agreement was found whenever the average intensity of the fluctuations was well above the background noise level. Encouraged by these results, the numerical simulation was compared to data taken in a shadow zone caused by an upward refractive atmosphere. Again, there was good agreement with experiment. The advantages of the numerical simulation over the analytical approach are discussed, such as the calculation of any desired statistical quantity and also its geometrical flexibility. Future test cases are proposed and improvements suggested.