Braids of entangled particle trajectories

被引:64
作者
Thiffeault, Jean-Luc [1 ]
机构
[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
基金
美国国家科学基金会;
关键词
chaos; geophysical fluid dynamics; Lyapunov methods; oceanography; vortices; TOPOLOGICAL FLUID-MECHANICS; CHAOTIC ADVECTION; ENTROPY; DYNAMICS; MIXERS;
D O I
10.1063/1.3262494
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure single-particle dispersion coefficients, but this only uses one trajectory at a time, so much of the information on relative motion is lost. In some circumstances the trajectories happen to remain close long enough to measure finite-time Lyapunov exponents, but this is rare. We propose to use tools from braid theory and the topology of surface mappings to approximate the topological entropy of the underlying flow. The procedure uses all the trajectory data and is inherently global. The topological entropy is a measure of the entanglement of the trajectories, and converges to zero if they are not entangled in a complex manner (for instance, if the trajectories are all in a large vortex). We illustrate the techniques on some simple dynamical systems and on float data from the Labrador Sea. The method could eventually be used to identify Lagrangian coherent structures present in the flow.
引用
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页数:14
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