Distinguished material surfaces and coherent structures in three-dimensional fluid flows
Distinguished material surfaces and coherent structures in three-dimensional fluid flows
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DOI：
10.1016/s0167-2789(00)00199-8
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发表时间：
2001-03-01
期刊：
影响因子：
4
通讯作者：
Haller, G
中科院分区：
文献类型：
--
作者：
Haller, G
我们证明了在三维非定常流中存在有限时间吸引和排斥物质表面和线的解析准则。最长寿的这种结构定义了拉格朗日意义上的相干结构。我们的存在性标准涉及的速度梯度张量沿沿着流体轨迹的不变量。相干结构的另一种方法，导致其表征为最大的有限时间李雅普诺夫指数场直接从粒子路径计算的本地最大化。这两种方法提供了有效的工具，提取区分拉格朗日结构的三维速度数据。我们说明了稳定和非稳定的ABC型流的结果。(C)2001 Elsevier Science B.V.保留所有权利。
We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in three-dimensional unsteady flows. The longest lived such structures define coherent structures in a Lagrangian sense. Our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories. An alternative approach to coherent structures is shown to lead to their characterization as local maximizers of the largest finite-time Lyapunov exponent field computed directly from particle paths. Both approaches provide effective tools for extracting distinguished Lagrangian structures from three-dimensional velocity data. We illustrate the results on steady and unsteady ABC-type flows. (C) 2001 Elsevier Science B.V. All rights reserved.