Smirnov I P, Virovlyansky A L, Edelman M, Zaslavsky G M
Institute of Applied Physics, Russian Academy of Science, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026206. doi: 10.1103/PhysRevE.72.026206. Epub 2005 Aug 15.
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.
考虑了在具有周期性距离依赖性的深水声波导强理想化模型中的声波传播。研究了射线和波混沌现象如何影响由天气涡旋引起的折射率强中尺度不均匀性处的声散射。应用了动力和量子混沌理论中推导的方法。在研究波混沌特性时，我们将波场分解为类似于具有固定准能量的量子态的弗洛凯模式之和。数值结果表明，射线系统相图中的“稳定岛”在各个弗洛凯模式的粗粒化维格纳函数中显现出来。推导了一种微扰理论，该理论深入了解了模式 - 介质共振在弗洛凯模式形成中的作用。结果表明，存在导致射线和波混沌的弱内波诱导微扰会强烈增加单色波场对涡旋出现的敏感性。为了研究瞬态波场的敏感性，我们考虑了由涡旋引起的射线传播时间（即声脉冲通过各个射线路径到达接收器的到达时间）的变化。结果表明，即使在射线混沌条件下，这些变化也是相对可预测的。这一结果表明，通过使用脉冲信号，混沌射线运动的影响可能会部分受到抑制。然而，由大规模不均匀性引起的传播时间变化的相对可预测性并非射线混沌的普遍特性。通过考虑完美反射条形式的不均匀性，以数值方式说明了这一说法。
