Estimates of the relevant turbulent scales for acoustic propagation in an upward refracting atmosphere

International audienceTurbulent fluctuations of temperature and velocity in the atmospheric boundary layer play a significant role on acoustic propagation, especially when an acoustic shadow zone is present. Spatial scales of turbulence span many orders of magnitude, and it has been recognized that some of them scatter acoustic energy more effectively. This selection of relevant turbulent scales depends on propagation geometry and acoustic frequency. The goal of this paper is to estimate the extent of the turbulence spectrum that contributes to acoustic scattering into a refractive shadow zone. The study is based on elements of wave propagation in random media theory on the one hand, and parabolic equation (PE) simulations on the other hand. To be representative of transportation and industrial noise conditions, PE simulations are performed in third octave bands between 50 Hz and 1600 Hz; the maximum propagation distance is 1 km. The turbulent fields are generated using a random Fourier modes technique. Theoretical tools are used to analyze the numerical results. Concerning small structures, an expression for the maximum cutoff turbulent wave number is obtained from the characteristics of the scattering cross-section. Concerning large structures, an estimate of the minimum cut-off turbulent wave number involving the Fresnel radius is found; it is based on the form of the variance of log-amplitude fluctuations in the Rytov approximation. This estimate is valid when the scattering is unsaturated, i.e. when the propagation distance and acoustic frequency are relatively small. The relations presented here may be used for modelling purposes and for experimental data analysis toknow if the measured turbulent spectra cover a wide enough range of spatial scales in a given configuration