CALCULATION OF TURBULENCE EFFECTS IN AN UPWARD-REFRACTING ATMOSPHERE

The parabolic equation (PE) method is used together with a two-dimensional atmospheric turbulence model to calculate the effect of turbulence on sound propagation. Both a nonrefractive atmosphere and a refractive atmosphere are considered. The nonrefractive calculation serves as a test of the two-dimensional model for turbulence. For a nonrefractive atmosphere, good agreement is obtained with experiment and the theory of Daigle. The calculation with upward refraction is compared to the data of Weiner and Keast who observed that the relative sound-pressure level versus range follows a characteristic “step” function. The calculations, which contain no adjustable parameters, give reasonable agreement with the data. In particular, the shape of the step function is well predicted. In the geometric shadow region, the observed strong dependence on refraction strength and weak dependence on range, height, and frequency are also predicted. It is concluded that, for a receiver deep in a shadow zone and frequencies greater than a few hundred hertz, the measured sound-pressure level is due almost entirely to sound scattered into the shadow zone by atmospheric turbulence. Consequently, for upward refraction and frequencies above a few hundred hertz, turbulence must be included in long-range propagation calculations if one is to obtain useful predictions. © 1990, Acoustical Society of America. All rights reserved.