  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.
