ON THE APPEARANCE OF CAUSTICS FOR PLANE SOUND-WAVE PROPAGATION IN MOVING RANDOM-MEDIA

In this paper we derive expressions for the probability densities for the appearance of the first caustic fora plane sound wave propagating in moving random media. Our approach generalizes the previous work by White et al and Klyatskin in the case of motionless media. It allows u s to calculate analytically the probability density functions for two- and three-dimensional media and to express these functions in terms o f the diffusion coefficient. Explicit equations are given for Gaussian and von Karman spectra of velocity fluctuations. If the random scalar or vectorial fluctuations of the medium have the same contribution to the refractive-index fluctuations, we demonstrate that in a moving me dium caustics appear at shorter distances than in a non-moving one. Th e two-dimensional version of the theory is tested by numerical simulat ions in the case of velocity fluctuations with Gaussian spectra. Numer ical results are in very good agreement with the theoretical predictio ns.