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Lagrangian coherent structures, transport and chaotic mixing in simple kinematic ocean models

机译:简单运动学海洋模型中的拉格朗日相干结构,输运和混沌混合

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Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent structures in a randomly fluctuating ocean-a jet-like current and an eddy. Advection of passive tracers in a periodically-driven flow consisting of a background stream and an eddy (the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere) is analyzed as an example of chaotic particle's scattering and transport. A numerical analysis reveals a non-attracting chaotic invariant set Λ that determines scattering and trapping of particles from the incoming flow. It is shown that both the trapping time for particles in the mixing region and the number of times their trajectories wind around the vortex have hierarchical fractal structure as functions of the initial particle's coordinates. Scattering functions are singular on a Cantor set of initial conditions, and this property should manifest itself by strong fluctuations of quantities measured in experiments. The Lagrangian structures in our numerical experiments are shown to be similar to those found in a recent laboratory dye experiment at Woods Hole. Transport and mixing of passive particles is studied in the kinematic model inspired by the interaction of a current (like the Gulf Stream or the Kuroshio) with an eddy in a noisy environment. We demonstrate a non-trivial phenomenon of noise-induced clustering of passive particles and propose a method to find such clusters in numerical experiments. These clusters are patches of advected particles which can move together in a random velocity field for comparatively long time. The clusters appear due to existence of regions of stability in the phase space which is the physical space in the advection problem.
机译:动力学系统的理论方法用于在由随机欧拉相干结构组成的简单运动学海洋模型中,对简单的运动海洋模型中的被动粒子(水质量,温度,盐度,污染物等)的传输和混合进行数值研究。 -像潮流和漩涡。作为一个混沌粒子的散射和传输的例子,分析了被动示踪剂在由背景流和涡流组成的周期性驱动流中的平流(该模型受海洋和大气山脉上的地形涡流现象的启发)。数值分析揭示了一个非吸引人的混沌不变集Λ,它确定了来自传入流的粒子的散射和捕获。结果表明,混合区域中粒子的捕获时间和轨迹围绕涡旋缠绕的次数均具有分层的分形结构,这是初始粒子坐标的函数。在Cantor初始条件集上,散射函数是奇异的,并且此特性应通过实验中测量的量的强烈波动来体现。我们的数值实验中的拉格朗日结构与最近在伍兹霍尔的实验室染料实验中发现的拉格朗日结构相似。在运动模型中研究了无源粒子的传输和混合,该模型是在嘈杂的环境中,由水流(如墨西哥湾流或黑潮)与涡流的相互作用所激发的。我们演示了噪声引起的无源粒子聚类的非平凡现象,并提出了一种在数值实验中找到此类聚类的方法。这些簇是平移粒子的斑块,它们可以在随机速度场中相对较长的时间一起移动。由于在对流问题中作为物理空间的相空间中存在稳定区域,因此出现了簇。

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