Smirnov I P, Virovlyansky A L, Zaslavsky G M
Nizhny Novgorod State University, 23 Gagarina Prospekt, 603600 Nizhny Novgorod, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036221. doi: 10.1103/PhysRevE.64.036221. Epub 2001 Aug 29.
Chaotic ray dynamics in deep sea propagation models is considered using the approaches developed in the theory of dynamical chaos. It has been demonstrated that the mechanism of emergence of ray chaos due to overlapping of nonlinear ray-medium resonances should play an important role in long range sound propagation. Analytical estimations, supported by numerical simulations, show that for realistic values of spatial periods and sound speed fluctuation amplitudes associated with internal-wave-induced perturbations, the resonance overlapping causes stochastic instability of ray paths. The influence of the form of the smooth unperturbed sound speed profile on ray sensitivity to the perturbation is studied. Stability analysis has been conducted by constructing the Poincaré maps and examining depth differences of ray trajectories with close take-off angles. The properties of ray travel times, including fractal properties of the time front fine structures, under condition of ray chaos have been investigated. It has been shown that the coexistence of chaotic and regular rays, typical for dynamical chaos, leads to the appearance of gaps in ray travel time distributions, which are absent in unperturbed waveguides. This phenomenon has a prototype in theory of dynamical chaos called the stochastic particle acceleration. It has been shown that mesoscale inhomogeneities with greater spatial scales than that of internal waves, create irregular local waveguide channels in the vicinity of the axis (i.e., sound speed minimum) of the unperturbed waveguide. Near-axial rays propagating at small grazing angles, "jump" irregularly between these microchannels. This mechanism determines chaotic behavior of the near-axial rays.
利用动力混沌理论中发展起来的方法，研究了深海传播模型中的混沌射线动力学。结果表明，由于非线性射线-介质共振重叠而产生射线混沌的机制，在远距离声传播中应发挥重要作用。数值模拟支持的分析估计表明，对于与内波引起的扰动相关的空间周期和声速波动幅度的实际值，共振重叠会导致射线路径的随机不稳定性。研究了光滑无扰动声速剖面的形式对射线对扰动敏感性的影响。通过构建庞加莱映射并检查具有相近起飞角度的射线轨迹的深度差异，进行了稳定性分析。研究了射线传播时间的特性，包括在射线混沌条件下时间前沿精细结构的分形特性。结果表明，动力混沌中典型的混沌射线和规则射线共存，导致射线传播时间分布中出现间隙，而在无扰动波导中不存在这种间隙。这种现象在动力混沌理论中有一个原型，称为随机粒子加速。结果表明，空间尺度比内波大的中尺度不均匀性，在无扰动波导的轴（即声速最小值）附近产生不规则的局部波导通道。以小掠射角传播的近轴射线在这些微通道之间不规则地“跳跃”。这种机制决定了近轴射线的混沌行为。
