Analytic investigation of chaos in a class of parabolic ray systems

It has 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. Analytical derivation of sufficient conditions for chaos in acoustic systems has been restricted to inherently discrete problems. This article reports a theoretical study of the existence of ray chaos in a class of continuous parabolic ray systems. This class of ray systems is indexed by a family of analytically prescribed double-channel sound-speed profiles perturbed by periodic range-dependent disturbances. The perturbed Hamiltonian ray systems are studied analytically via the Melnikov method. It is shown that, under certain conditions, ray trajectories of the systems are equivalent to trajectories of a classic chaotic system known as the horseshoe map when the perturbation is periodic and small. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior.