An investigation of sound ray dynamics in the ocean volume using an area preserving mapping

Abstract

An area preserving mapping which describes sound ray propagation in a simple range-dependent model of the ocean sound channel is derived and studied. The unbounded ocean model has a bilinear sound speed profile in which the vertical sound speed gradient above the sound channel axis varies sinusoidally in range. It is assumed that the scale of the range-dependent perturbation is small compared to a typical upper loop length of a ray. The explicit mapping which results gives successive iterates of range and upgoing ray angle at the sound channel axis, ( r n, θ n ) → ( r n+ 1 , θ n +1 . The degree of stochasticity of the mapping is governed by a single dimensionless parameter, ε — the strength of the range dependent perturbation. Iterates of the mapping indicate that some ray trajectories are chaotic (i.e., exhibit estreme sensitivity to initial conditions) for perturbations comparable in strength to those produced by internal waves in the ocean. The chaotic nature of these rays is confirmed by the calculation of positive Lyapunov exponents.