Ray chaos, travel time modulation, and sensitivity to the initial conditions

Abstract

Using a model of underwater acoustic waveguide with a periodic range dependence, travel times of chaotic rays at long-range sound propagation in the ocean are studied. It is shown that the travel time as a function of the initial momentum and propagation range in the unperturbed (range-independent) waveguide displays a scaling law. Some properties predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. Ray tracing has demonstrated that the coexistence of chaotic and regular rays causes an appearance of a gap in the timefront, representing ray arrivals in the time–depth plane. Besides the gap, a “focusing” of ray travel times has been found within a comparatively small temporal interval preceding the gap. In numerical simulation of a sound pulse propagation this phenomenon reveals itself in the appearance of a bright spot in the distribution of acoustic energy in the time–depth plane. It has been shown that the effect of focusing is a manifestation of the so-called stickiness, i.e., the presence of such parts of the chaotic trajectory where the latter exhibits an almost regular behavior.