FTLE (Finite Time Lyapunov Exponent) computation is one of the standard approaches to Lagrangian flow analysis. The main features of interest in FTLE fields are ridges that represent hyperbolic Lagrangian Coherent Structures. FTLE ridges tend to become sharp and crisp with increasing integration time, where the sharpness of the ridges is an indicator of the strength of separation. The additional consideration of uncertainty in flows leads to more blurred ridges in the FTLE fields. There are multiple causes for such blurred ridges: either the locations of the ridges are uncertain, or the strength of the ridges is uncertain, or there is low uncertainty but weak separation. Existing approaches for uncertain FTLE computation are unable to distinguish these different sources of uncertainty in the ridges. We introduce a new approach to define and visualize FTLE fields for flow ensembles. Before computing and comparing FTLE fields for the ensemble members, we compute optimal displacements of the domains to mutually align the ridges of the ensemble members as much as possible. We do so in a way that an explicit geometry extraction and alignment of the ridges is not necessary. The additional consideration of these displacements allows for a visual distinction between uncertainty in ridge location, ridge sharpness, and separation strength. We apply the approach to several synthetic and real ensemble data sets.

翻译：FTLE（有限时间李雅普诺夫指数）计算是拉格朗日流场分析的标准方法之一。FTLE场的主要特征在于代表双曲拉格朗日相干结构的脊线。随着积分时间的增加，FTLE脊线趋于锐化清晰，脊线的锐度表征流体分离的强度。在考虑流场不确定性时，FTLE场中会出现模糊脊线。此类模糊脊线由多种原因导致：脊线位置的不确定性、脊线强度不确定性、或者低不确定性但弱分离效应。现有不确定流场FTLE计算方法无法区分这些脊线不确定性的不同来源。我们提出一种面向流场集成定义与可视化FTLE场的新方法。在计算并比较各集成成员的FTLE场之前，我们通过最优位移域变换使各成员的脊线最大程度对齐。该方法无需显式提取脊线的几何特征及其对齐操作。通过额外考虑位移参数，可直观区分脊线位置不确定性、脊线锐度变化与分离强度差异。我们将该方法应用于多个合成数据集与实测流场集成数据。