In a previous paper [A. M. Whitman and M. J. Beran, Waves in Random Media 11, 1–11 (1999)] we discussed the scattering of acoustic waves by random sound‐speed fluctuations in a two‐dimensional channel and presented an asymptotic form for an acoustic pulse propagating in the channel. Here we include the three‐dimensional effect of transverse scattering. We find an asymptotic solution in which initially the two‐dimensional mode‐transfer effect is more important than the transverse scattering effect. However, for large enough propagation distances the transverse scattering dominates the pulse spread. Here we show the form of the pulse shape in both propagation ranges as well as the transition regime. We begin with a discussion of the physics of the problem and then present a mathematical discussion.

Pulse propagation of acoustic waves scattered in a three‐dimensional channel

In previous papers we discussed the scattering of acoustic waves by random sound-speed fluctuations in lossless two- and three-dimensional channels. Here we include the effect of bottom loss in a three-dimensional channel. The bottom loss is included by replacing the rigid bottom condition by one allowing for loss. We find an asymptotic solution for the angular distribution of the scattered acoustic energy and the characteristic propagation distance at which the asymptotic solution is valid. Beyond this characteristic distance the angular distribution saturates and is no longer dependent on the propagation distance. Before the mathematical development is given a simple physical argument is presented which shows why a saturation region is expected.

Thomas E Barnard

Papers

Propagation of acoustic waves scattered in a lossy three-dimensional channel