Chaotic dynamical systems often exhibit islands of regular behavior (elliptic islands) interrupting the surrounding chaotic sea that is dominated by hyperbolicity. A fascinating example of such coherent behavior is vortex tubes in turbulent fluid flow. While elliptic and hyperbolic structures are well understood in steady and time-periodic systems, their treatment in fully unsteady flows remains a topic of current research.
We have developed methods (based on variational principles) for frame-invariant detection and quantification of these structures.
Polar rotation-based detection of vortices:
Variational theory of shearless LCS:
Computation of LCS: