Calculation of turbulence effects in an upward refracting atmosphere

Abstract

In an upward refracting atmosphere, measured values of excess attenuation (50–500 Hz) seldom exceed 20 to 30 dB at a range of 1 km. Calculations of excess attenuation for a steady (nonturbulent) atmosphere predict a deep shadow zone with much higher excess attenuation. This paper investigates the contribution of atmospheric turbulence to decreasing the predicted excess attenuation. Since no convenient analytical method presently exists which can simultaneously account for turbulence, upward refraction, and a finite-impedance ground surface, a parabolic equation method is used to numerically simulate sound propagation. As an initial test, the calculation is compared to Daigle's theoretical and experimental results for a homogeneous atmosphere [J. Acoust. Soc. Am. 65, 45–49 (1979)]. For a test with upward refraction, the calculation is compared to the experimental results of Wiener and Keast [J. Acoust. Soc. Am. 31, 724–733 (1959)].