Necessity of dimensional support for the reliable calculation of finite-time Lyapunov exponent fields from experimental data

摘要

Using Lagrangian techniques to find transport barriers in complex, aperiodic flows necessitates a careful consideration of the available dimensional support of the data being analyzed. To illustrate this, planar finite-time Lyapunov exponent (FTLE) fields are computed from experimentally collected velocity fields. The FTLE fields calculated using three-component, three-dimensional velocity information (3D FTLE) are compared with calculations using two-dimensional data, and considering only the in-plane velocities (2D FTLE). In some regions, where the vortex rotation axis is perpendicular to the plane of interest, the 2D FTLE may perform well. However, in regions where the vortex rotation axis is parallel to the plane of interest, whole structures are simply not captured by the 2D FTLE, compared with the 3D FTLE. A quantitative analysis of the error as it relates to Instantaneous Vorticity Deviation (IVD) core angle was conducted using experimental data collected in the wake of a bio-inspired pitching panel. Lack of proper dimensional support in experimental velocity fields can cause major errors in the resulting FTLE, but with fundamental understanding about the flow field of interest, such as local vortex orientation, some of the pitfalls may be avoided.