NONLINEAR WIDE-ANGLE PARAXIAL ACOUSTIC PROPAGATION IN SHALLOW-WATER CHANNELS

A time-domain model that describes wide-angle paraxial propagation of acoustic pulses in shallow water is developed. This model incorporates weak nonlinear effects and depth variability in both ambient density and sound speed. Derivations of paraxial approximations are based on a n iterative approach, in which the wide-angle approximation is obtaine d by using a narrow-angle equation to approximate the second range der ivative in the two-way equation. Scaling arguments are used to obtain a more tractable simplification of the equation. The wide-angle equati on is solved numerically by splitting into components representing dis tinct physical processes and using a modified version of the time-doma in parabolic equation (TDPE) code [M. D. Collins, J. Acoust. Soc. Am. 84, 2114-2125 (1988)]. A high-order upwind flux-correction method is m odified to handle the nonlinear component. Numerical results are prese nted for adiabatic propagation in a shallow, isospeed channel. It is d emonstrated that nonlinear effects are significant, even at small rang es, if the peak source pressure is high enough. Both nonlinear and wid e-angle effects are illustrated, and their differences are discussed. (C) 1997 Acoustical Society of America.