Computation of finite-time Lyapunov exponents from time-resolved particle image velocimetry data
Computation of finite-time Lyapunov exponents from time-resolved particle image velocimetry data
复制标题
根据时间分辨粒子图像测速数据计算有限时间李亚普诺夫指数
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
P. Vlachos
中科院分区：
文献类型：
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作者：
Samuel G. Raben;S. Ross;P. Vlachos
摘要
这项工作提出了两种新方法，用于从用于粒子图像测速 (PIV) 或粒子跟踪测速 (PTV) 的噪声时空分辨实验测量图像数据计算有限时间李亚普诺夫指数 (FTLE)。这些新方法基于这样一个简单的认识：PIV 实验期间记录的粒子图像代表拉格朗日流示踪剂，其轨迹适合直接计算流图以及流图梯度和 FTLE 等相关量。我们表明，使用这个想法，我们可以通过使用直接路径流图（PFM）计算（其中固定时间段内的单个粒子路径线用于确定流图）或粒子跟踪流图编译（FMC）（其中瞬时跟踪结果用于估计流图的小快照，然后将其编译以描述完整的流图）来提高 FTLE 计算的可靠性和准确性。用于计算 FTLE 场的传统速度场积分 (VFI) 方法与这些新方法的比较表明，FMC 对于合成数据和实验数据都能产生更准确的 FTLE 场估计，尤其是在粒子数密度较低的情况下。这是因为 VFI 估计粒子运动，而 PTV 直接测量粒子运动，因此生成更准确的流图。总的来说，我们的结果表明，当应用于嘈杂的实验 PIV 数据时，VFI 并不总是一种可靠的方法。对于帧之间粒子损失最小的情况，PFM 也可以产生更好的结果，但由于原始流图的非结构化性质，最终场很容易出错。在比较匹配流的真实分界线的能力时，FMC 被证明是一种优越得多的方法。 FMC 的分界线与真实解有 80% 的重叠，而 PFM 的重叠度约为 25%，VFI 方法的重叠度仅为 1%。当颗粒播种量较低时，FMC 显示出显着的优势，这对于环境或生物流的应用尤其相关，在环境或生物流中添加种子颗粒并不总是可行，并且拉格朗日流结构的研究必须依赖于自然发生的流动示踪剂。
Abstract
This work presents two new methods for computing finite-time Lyapunov exponents (FTLEs) from noisy spatiotemporally resolved experimentally measured image data of the type used for particle image velocimetry (PIV) or particle tracking velocimetry (PTV). These new approaches are based on the simple insight that the particle images recorded during PIV experiments represent Lagrangian flow tracers whose trajectories lend themselves to the direct computation of flow maps, and related quantities such as flow map gradients and FTLEs. We show that using this idea we can improve the reliability and accuracy of FTLE calculation through the use of either direct pathline flow map (PFM) calculation, where individual particle pathlines over a fixed period of time are used to determine the flow map, or particle tracking flow map compilation (FMC), where instantaneous tracking results are used to estimate small snapshots of the flow map which are then compiled to describe the complete flow map. Comparisons of the traditional velocity field integration (VFI) method for computing FTLE fields with these new methods show that FMC produces significantly more accurate estimates of the FTLE field for both synthetic data and experimental data especially in cases where the particle number density is low. This is because the VFI estimates particle motion while PTV directly measures particle motion and therefore generates a more accurate flow map. Overall, our results suggest that VFI is not always a reliable approach when applied to noisy experimental PIV data. For cases where particle loss between frames is minimal, the PFM can also produce better results, but the final field is susceptible to error due to the unstructured nature of the raw flow maps. When comparing the ability to match the true separatrix of a flow, FMC is shown to be a far superior method. The separatrix from FMC has an 80 % overlap with the true solution as compared to approximately 25 % for the PFM and only 1 % for the VFI method. FMC shows a significant advantage when the particle seeding is low, which is particularly relevant for applications to environmental or biological flows where adding seed particles is not always practical, and investigation of Lagrangian flow structures must rely on naturally occurring flow tracers.