According to ray theory, regions exist in an upward refracting atmosphere where no sound should be present. Experiments show, however, that appreciable sound levels penetrate these so-called shadow zones. Two mechanisms contribute to sound in the shadow zone: diffraction and turbulent scattering of sound. Diffractive effects can be pronounced at lower frequencies but are small at high frequencies. In the short wavelength limit then, scattering due to turbulence should be the predominant mechanism involved in producing the sound levels measured in shadow zones. No existing analytical method includes turbulence effects in the prediction of sound pressure levels in upward refractive shadow zones. In order to obtain quantitative average sound pressure level predictions, a numerical simulation of the effect of atmospheric turbulence on sound propagation is performed. The simulation is based on scattering from randomly distributed scattering centers (‘‘turbules’’). The scattering effect of each turbule is calculated with the help of the first Born approximation to scattering, using independently measured micrometeorological variables such as the variance 〈μ2〉 and correlation length L of the refractive index fluctuations. Sound pressure levels are computed for many realizations of a turbulent atmosphere. Predictions from the numerical simulation are compared with existing theories and experimental data.
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McBride et al. (1992) studied this question.