On the existence of nearly stable dynamics in long-range sound propagation through oceanic mesoscale structure

Abstract

A dynamical system, motivated by ocean acoustic pulse propagation in the horizontal plane along the sound channel axis, is constructed using a potential derived from an idealized mesoscale eddy field. This problem is known to exhibit chaotic behavior in that rays are exponentially sensitive to both their initial condition and the position and strength of the individual eddies. The measure of chaos for the system has been expressed by deriving a Lyapunov exponent which determines the mean growth rate for the envelope of one of the elements of the stability matrix [M. A. Wolfson and F. Tappert, J. Acoust. Soc. Am. (to be published, 1998)]. However, the individual stability matrix elements are seen to fluctuate wildly from one ray to another. It turns out that many rays exhibit absolute traces of the stability matrix with values of O(1) even at basin scale ranges. This implies that much of the dynamics involves only local rotations as the flow evolves in phase space. Estimates are presented for a range-dependent measure of this nearly stable dynamical feature. Its relation to tomographic inversions of some features of mesoscale eddy fields is discussed.