Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.