Department of Mechanical Engineering, McGill University, 817 Sherbrooke Ave. West, Montreal, Quebec H3A 2K6, Canada.
Chaos. 2011 Jun;21(2):023115. doi: 10.1063/1.3579597.
We point out that local minimizing curves, or troughs, of the smallest finite-time Lyapunov exponent (FTLE) field computed over a time interval [t(0), t] and graphed over trajectory positions at time t mark attracting Lagrangian coherent structures (LCSs) at t. For two-dimensional area-preserving flows, we conclude that computing the largest forward-time FTLE field by itself is sufficient for locating both repelling LCSs at t(0) and attracting LCSs at t. We illustrate our results on analytic examples, as well as on a two-dimensional experimental velocity field measured near a swimming jellyfish.
我们指出，在[t(0), t]时间段内计算得到的最小有限时间 Lyapunov 指数（FTLE）场的局部最小曲线（或波谷），并在 t 时刻的轨迹位置上绘制，标志着在 t 时刻吸引拉格朗日相干结构（LCS）。对于二维保面积流，我们得出结论，仅计算最大向前时间 FTLE 场就足以定位 t(0)处的排斥 LCS 和 t 处的吸引 LCS。我们在分析示例以及在测量游泳水母附近的二维实验速度场的示例上展示了我们的结果。
