非周期流的拉格朗日描述：黑潮海流的个例研究
The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current
摘要：
本文回顾了几个最近开发的拉格朗日工具，并展示了它们的结合使用如何成功地获得一个详细的描述一般非周期性流动的纯平流运输事件。特别是，由于海洋运输过程的气候影响，我们说明了在黑潮电流的区域高度计数据集的二维应用程序，虽然所提出的技术是通用的，适用于任意时间依赖的非周期性流。描述非周期性时间依赖流中的运输的第一个挑战是获得其中可以识别最相关的动态特征的相图的表示。这种表示是通过使用全球拉格朗日描述符，例如，当应用到高度计数据集检索在海洋表面上的一个相图，其中相互关联的动力系统的几何形状是可见的。相图是必不可少的，因为它表明了哪些运输路线对整个流量起作用。一旦这些路线是粗略地认识到它是可能的，以完成一个详细的描述，通过直接计算的有限时间稳定和不稳定的特殊双曲线轨迹的流形，作为组织中心的流动。
英文摘要：
This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time dependent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.
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