title: Computing Lagrangian coherent structures from their variational theory.
abstract: Using the recently developed variational theory of hyperbolic Lagrangian coherent structures (LCSs), we introduce a computational approach that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows. The curves are obtained as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor. This approach eliminates false positives and negatives in LCS detection by separating true exponential stretching from shear in a frame-independent fashion. Having an explicitly parametrized form for hyperbolic LCSs also allows for their further in-depth analysis and accurate advection as material lines. We illustrate these results on a kinematic model flow and on a direct numerical simulation of two-dimensional turbulence.
authors.affiliation: Department of Mathematics and Statistics, McGill University, 817 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Farazmand
authors.forename: George
authors.initials: G
authors.lastname: Haller
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D012212:Rheology / Q000379:methods*