Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase variance

Abstract

A numerical technique for simulating the behavior of an acoustic wave propagating through a turbulent medium is introduced. The technique involves two elements: the generation of 3-D, random, hypothetical, isotropic velocity fields in terms of a collection of discrete Fourier velocity modes; and the integration of the ray-trace equations to describe the trajectories of points tagging an acoustic wave front. The propagation times for these points to travel fixed distances through each of an ensemble of random velocity fields are recorded, and the variance of travel time (or acoustic phase) over the ensemble is calculated. In numerical ray-trace experiments through fields having average perturbation indices ≊0.01, acoustic travel-time variances are obtained that have a higher-order dependence on travel distance R than the classical Chernov prediction—a linear increase with R. The Chernov result is obtained, however, when the rays are confined to axial trajectories. Additional numerical experiments integrating the stochastic Helmholtz equation and its parabolic approximation yield time-variance estimates consistent with the ray-trace results. Predictions from these simulations are then applied to the laboratory experiments of Blanc-Benon and found to be in qualitative agreement. Finally, a set of 2-D travel-time experiments are presented to identify differences between source–receiver eigenray propagation and preassigned initial direction ray propagation.