Allshouse Michael R, Peacock Thomas
Mechanical Engineering Department, Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA.
Chaos. 2015 Aug;25(8):087410. doi: 10.1063/1.4928210.
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.
虽然存在更严格、更复杂的用于识别基于拉格朗日的相干结构的方法，但有限时间李雅普诺夫指数（FTLE）场仍然是一种直观且流行的方法，可用于深入了解复杂的、随时间变化的二维流中的输运情况。鉴于其持久的吸引力，并为了支持良好的实践，我们首先研究离散化和噪声对两种计算FTLE场的数值方法的影响。然后提出了一种基于先前方法的实用方法，用于在二维流中提取和细化FTLE脊线。为了更好地确定FTLE脊线在流输运中的作用，我们采用了现有的分类方案，并全面探讨了对FTLE脊线所代表的变形类型进行分类时面临的挑战。作为一个实际演示，这些方法被应用于一个由数值模型生成的海洋表面速度场数据集。
