Non-linear dynamics of underwater acoustics

The non-linear dynamic behavior of acoustic wave propagation in an underwat er sound channel, described by the Munk's classical sound speed profile per turbed by a single-mode internal wave, is studied using a parabolic ray the ory. The amplitude and wavelength of this single-mode wave are used as the branching parameters in bifurcation analysis. The phase plane trajectory of the ray-based system can be periodic, quasi-periodic, and unstable. The re gions of instability, located numerically via the bifurcation diagrams, are examined through a sequence of phase diagrams and Poincare maps. Charts sh owing the maximum uninterrupted propagation distance reveal instances of an omalous vertical scattering of sound energy. Floquet multipliers were used to investigate instability of periodic orbits. (C) 1999 Academic Press.