Occurrence of Caustics for High Frequency Acoustic Waves Propagating Through Turbulent Fields

Abstract

Theoretical investigations of wave propagation in random media usually rely on a statistical approach. The interaction between the wave and the medium is expressed in terms of a random refractive index related to the fluctuations of the medium, which has been introduced in the Helmholtz equation. The equations which govern the second and higher moments of the transmitted sound pressure field are then deduced. Using a closure hypothesis for the index fluctuation, solutions may be obtained either by some analytical developments or by numerical integration. It is only recently that studies have been reported that make use of computer generated fields to simulate wave propagation in random media. However they are still limited to scalar random fields. Moreover, in acoustics, the presence of velocity components introduces additional effects of wave convection which cannot be described a priori by such a simplified approach.

In this paper we describe a different technique, which does take into account fluctuations in velocity fields and avoids purely statistical theory and not well founded hypotheses. Assuming that the turbulent field is frozen during the transit time of the acoustic wave, the medium can be modelled by a sequence of independent realizations of a random field. Each realization of the field is generated by a superposition of a finite number of discrete random Fourier modes. The amplitude of these modes is chosen in order to obtain a pre-defined energy spectum. Isotropic fields with scalar or vectorial fluctuations can be obtained with roughly the same techniques. Then we consider the deterministic propagation of acoustic waves (in the geometrical approximation) through individual realizations of the simulated turbulent field. We integrate the equations of geometrical acoustics to describe the trajectories of rays as well as the evolution

The full text of this paper is to appear inTheoretical & Computational Fluid Dynamics