Ray chaos in underwater acoustics in view of local instability

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Abstract
It has previously been shown that acoustic ray paths in range‐dependent oceanmodels exhibit chaotic behavior. The objective of this paper is to investigate the influence of sound‐speed profile and perturbation on the ray chaos. Considering that chaos results from the instability of nonlinear equations, the instability of Hamilton’s ray equations is analyzed by using linear stability analysis. An instability criterion is derived as follows: [C 0 2/C(z 0)4]{C(z 0)[∂2 C(z 0)/∂z 2] −3[∂C(z 0)/∂z]2}+∂2 g(z 0,r 0)/∂z 2<0, where C 0 is the reference sound speed,C is the sound speed,g is the range‐dependent perturbation in potential function, z is the depth, z 0 is the reference depth, and r 0 is the reference range. By analyzinginstability, it is inferred that (1) the instability criterion is a necessary condition for ray chaos; (2) ray chaos may be induced if the derivative ∂2 g/∂z 2 is negative and ‖∂2 g/∂z 2‖ is large; and (3) double‐channel propagation is more likely to exhibit chaotic behavior. These ideas are then illustrated numerically by using two simple models: Munk’s canonical sound‐speed profile and a double‐channel North Atlantic profile, with a periodically range‐dependent perturbation.

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