Variational approach to Lagrangian vortices in 3D unsteady flows

From a Lagrangian perspective, vortices can be viewed as material surfaces, i.e., as surfaces moving with the fluid. Lagrangian vortices are therefore directly linked to particle motion. Here, we use the objective (frame-invariant) approach of Lagrangian Coherent Structures (LCSs) to identify Lagrangian vortices as tubular, non-filamenting material surfaces (elliptic LCSs). By introducing a dual and autonomous dynamical system, we present a new method for constructing LCSs in three-dimensional unsteady flows. We illustrate the geometric significance of this approach with various examples.