ANALYTIC INVESTIGATION OF CHAOS IN A CLASS OF PARABOLIC RAY SYSTEMS

It has been shown that acoustic ray paths in range-dependent ocean mod els exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. Analytical d erivation of sufficient conditions for chaos in acoustic systems has b een restricted to inherently discrete problems. This article reports a theoretical study of the existence of ray chaos in a class of continu ous parabolic ray systems. This class of ray systems is indexed by a f amily of analytically prescribed double-channel sound-speed profiles p erturbed by periodic range-dependent disturbances. The perturbed Hamil tonian ray systems are studied analytically via the Melnikov method. I t is shown that, under certain conditions, ray trajectories of the sys tems are equivalent to trajectories of a classic chaotic system known as the horseshoe map when the perturbation is periodic and small. Thes e conditions are sufficient for ray chaos and easily satisfied, thus e xplaining why double-channel propagation is very likely to exhibit cha otic behavior. (C) 1997 Acoustical Society of America.