Smirnov I. P., Virovlyansky A. L., Zaslavsky G. M.
Institute of Applied Physics, Russian Academy of Science, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.
Chaos. 2002 Sep;12(3):617-635. doi: 10.1063/1.1494250.
Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.
波导中的射线可被视为相应哈密顿系统的轨迹，在非均匀环境中该轨迹似乎是混沌的。从实验和实际角度来看，射线传播时间是一个重要特性，在某种程度上它涉及有关波导状况的信息。结果表明，在未受扰动的波导中，作为初始动量和传播距离函数的射线传播时间呈现出一种标度律。由该定律预测的射线传播时间的一些特性在具有混沌射线轨迹的周期性非均匀波导中仍然存在。作为例子，我们考虑了几个模型，特别关注了水下声波导。对于一个深海传播模型表明，即使在射线混沌的情况下，射线传播时间在很大程度上仍由射线端点的坐标和转折点的数量决定，即由射线路径的拓扑结构决定。我们展示了具有相同转折点数量的射线传播时间的接近程度如何在射线传播时间对起始动量和观测点深度的依赖关系中体现出来。已经表明，相同的效应与混沌射线和规则射线传播时间之间出现的间隙有关。讨论了射线传播时间中粘性的表现（在混沌轨迹中存在这样的部分，在这些部分中后者表现出几乎规则的行为）。（c）2002美国物理研究所。
