Classical chaotic dynamics of sound rays in 3-D inhomogeneous waveguide media

Abstract

The chaotic dynamics of sound rays in a near-bottom waveguide channel is studied on the basis of the Hamiltonian dynamics of nonparaxial rays in inhomogeneous moving media. The bottom is assumed to have a two-dimensional roughness. The mapping of the coordinates of the rays upon reflection from the rough bottom is derived through a solution of the corresponding ray equations in an unperturbed waveguide with a horizontal bottom. A numerical analysis of the mapping reveals that a chaotic instability of rays which start out at small angles from the horizontal develops at short distances from the source. Because of this instability, the path segments of a ray along the horizontal coordinates and the signal passage time along a ray are random functions of the angle at which the ray emerges from the source. Upon a further reflection of rays from the rough bottom, there is a diffusion of rays in a stochastic ring which forms in the plane of horizontal ray directions as a result of the overlap and intersection of resonance curves. A qualitative analysis of this effect is carried out. This effect leads to a nearly isotropic distribution of ray directions.