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.
- Publication:
-
Chaos
- Pub Date:
- March 2012
- DOI:
- 10.1063/1.3690153
- Bibcode:
- 2012Chaos..22a3128F
- Keywords:
-
- differential equations;
- nonlinear dynamical systems;
- tensors;
- 05.45.-a;
- 02.10.Ud;
- 02.30.Hq;
- Nonlinear dynamics and chaos;
- Linear algebra;
- Ordinary differential equations