Lagrangian coherent structure identification using a Voronoi tessellation-based networking algorithm

Abstract

The quantification of Lagrangian coherent structures (LCS) has been investigated using an algorithm based on the tesselation of unstructured data points. The applicability of the algorithm in resolving an LCS was tested using a synthetically generated unsteady double-gyre flow and experimentally in a nominally two-dimensional free shear flow. The effects of two parameters on LCS identification were studied: the threshold track length used to quantify the LCS and resulting effective seeding density upon applying the threshold. At lower threshold track lengths, increases in the threshold track length resulted in finite-time Lyapunov exponent (FTLE) field convergence towards the expected LCS ridge of the double-gyre flow field at several effective seeding densities. However, at higher track lengths, further increases to the threshold track length failed to improve convergence at low effective seeding densities. The FTLE of the experimental data set was well-resolved using moderate threshold track lengths that achieved field convergence but maintained a sufficiently high seeding density. In contrast, the use of lower or higher track lengths produced an FTLE field characterized by an incoherent LCS ridge. From the analytical and experimental results, recommendations are made for future experiments for identifying LCS directly from unstructured data.