Level set formulation of two-dimensional Lagrangian vortex detection methods

TL;DR

This paper introduces a level set method for detecting Lagrangian vortices in 2D unsteady flows, unifying different variational approaches and enabling efficient identification of multiple vortices.

Contribution

It presents a novel level set formulation that captures multiple vortex boundaries simultaneously, improving computational efficiency over previous methods.

Findings

Successfully identifies vortices based on different coherence principles.

Captures an unknown number of vortices at low computational cost.

Demonstrates effectiveness on several flow examples.

Abstract

We propose here the use of the variational level set methodology to capture Lagrangian vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches that seek material vortex boundaries as extremum solutions of variational problems. We demonstrate the performance of this technique for two different variational formulations built upon different notions of coherence. The first formulation uses an energy functional that penalizes the deviation of a closed material line from piecewise uniform stretching [Haller and Beron-Vera, J. Fluid Mech. 731, R4 (2013)]. The second energy function is derived for a graph-based approach to vortex boundary detection [Hadjighasem et al., Phys. Rev. E 93, 063107 (2016)]. Our level-set formulation captures an a priori unknown number of vortices simultaneously at relatively low computational cost. We illustrate the approach by identifying vortices from different coherence principles in several examples.