ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

3aAO9. Analytical investigation of ray chaos in an underwater acoustic system.

Zhong-Yue Jiang

Todd Pitts

James F. Greenleaf

Biodynamics Res. Unit, Dept. of Physiology and Biophysics, Mayo Clinic and Foundation, Rochester, MN 55905

It has previously been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. The objective of this report is to study theoretically the existence of ray chaos in a parabolic ray system with an analytically prescribed sound-speed model consisting of a double-channel profile perturbed by a typical periodic range-dependent disturbance. The perturbed Hamiltonian ray system is studied analytically via Melnikov's method. It is shown that, under certain conditions, ray trajectories in some regions of the Poincare section are equivalent to trajectories of the horseshoe map no matter how small the corresponding perturbation is. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior. [Work supported by CA43920 NIH.]