Statistical Description of Ray Chaos in an Underwater Acoustic Waveguide

Abstract

An approximate analytical approach is developed to describe the chaotic behavior of ray trajectories in a deep-water acoustic waveguide up to three to five thousands of kilometers in length. The ray dynamics is investigated using the Hamiltonian formalism expressed in terms of the canonical action-angle variables. A realistic waveguide model is used, with refractive-index fluctuations due to the random field of internal waves. The Fokker-Planck equation is obtained for the action variable, and it is shown that the range dependence of this variable can be approximated by the Wiener random process, which represents the simplest model of diffusion. Formulas are derived for calculating the probability density of the coordinate and other ray characteristics. An approximate expression is found for the smoothed field intensity of a point source. For illustrating and testing the formulas obtained, their predictions are compared with the results of numerical solutions of ray equations and the results of field calculations by the parabolic equation method.