Lab. de Mecan. des Fluides et d'Acoust., URA-CNRS 263, BP 163, Ecole Centrale de Lyon, 69131 Ecully Cedex, France
A numerical simulation has been developed to investigate the random focusing for an acoustic plane wave propagating through scalar or vectorial turbulent fields. The turbulence is represented as a set of realizations of random fields (temperature or incompressible velocity) generated by a limited number of random Fourier modes [M. J. Karweit et al., J. Acoust. Soc. Am. 89, 52--62 (1991)]. Through each realization the propagation of a plane wave is considered in either the geometric or the parabolic approximation. Using the ray equations the ray trajectories and the location of the instantaneous caustics are computed. The acoustic pressure field and the intensity fluctuations are obtained by solving a wide-angle parabolic equation. Ensemble averaging is then performed to evaluate the probability distribution of the occurrence of caustics and the variance of acoustic intensity fluctuations. For 2-D and 3-D scalar simulations the results demonstrate that the position of caustics as well as the maximum peak in the scintillation index are governed by universal parameters related to the transverse spatial derivatives of the correlation function of the fluctuating components of the turbulent medium. Results will be given to generalize the definition of these universal parameters for sound propagation in random velocity fields.