FTLE for Flow Ensembles by Optimal Domain Displacement

TL;DR

This paper introduces a novel method for analyzing flow ensembles by optimally displacing domains to better visualize and distinguish different sources of uncertainty in FTLE ridges, enhancing flow analysis accuracy.

Contribution

The paper presents a new approach that aligns FTLE ridges across ensemble members without explicit geometry extraction, enabling clearer uncertainty distinction.

Findings

Effective separation of uncertainty sources in FTLE ridges

Improved visualization of flow ensemble data

Applicability to synthetic and real datasets

Abstract

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.