Chaos-induced intensification of wave scattering

Sound-wave propagation in a strongly idealized model of the deep-water acoustic waveguide with a periodic range dependence is considered. It is investigated how the phenomenon of ray and wave chaos affects the sound scattering at a strong mesoscale inhomogeneity of the refractive index caused by the synoptic eddy. Methods derived in the theory of dynamical and quantum chaos are applied. When studying the properties of wave chaos we decompose the wave field into a sum of Floquet modes analogous to quantum states with fixed quasi-energies. It is demonstrated numerically that the "stable islands" from the phase portrait of the ray system reveal themselves in the coarse-grained Wigner functions of individual Floquet modes. A perturbation theory has been derived which gives an insight into the role of the mode-medium resonance in the formation of Floquet modes. It is shown that the presence of a weak internal-wave-induced perturbation giving rise to ray and wave chaos strongly increases the sensitivity of the monochromatic wave field to an appearance of the eddy. To investigate the sensitivity of the transient wave field we have considered variations of the ray travel times--arrival times of sound pulses coming to the receiver through individual ray paths--caused by the eddy. It turns out that even under conditions of ray chaos these variations are relatively predictable. This result suggests that the influence of chaotic-ray motion may be partially suppressed by using pulse signals. However, the relative predictability of travel time variations caused by a large-scale inhomogeneity is not a general property of the ray chaos. This statement is illustrated numerically by considering an inhomogeneity in the form of a perfectly reflecting bar.