**Abstract:**

When a transverse plane wave propagates through a shallow-water channel with random sound-speed fluctuations, the waveforms at different transverse separations no longer correlate perfectly. The associated coherence falls as the in-line propagation distance and the transverse separation increase. In the (lossless) rigid-bottom case, when the waveforms are represented as a summation of normal modes, the multimodal coherence vector obeys a first-order matrix differential equation with in-line propagation distance as the independent variable. The scattering matrix in this differential equation is a function of transverse separation. As the in-line propagation distance approaches infinity, the coherence vector approaches a constant vector times a scalar Dirac delta function centered at zero transverse separation. If the bottom is absorptive rather than rigid, an additional diffusion term appears in the matrix partial differential equation governing the coherence. Diffusion along the transverse separation axis then prevents the creation of a Dirac delta function as the in-line propagation distance increases without limit. This diffusion occurs whenever the imaginary part of the horizontal wave-number component for a particular mode is nonzero. Some graphical outputs depicting the coherence propagation for an absorptive bottom are presented in this paper. [Work supported by ONR Code 321.]

ASA 133rd meeting - Penn State, June 1997