TITLE:
Contrast of Perspectives of Coherency
AUTHORS:
Tian Ma, Erik Bollt
KEYWORDS:
Shape Coherent Set, Coherent Pairs, Geodesic Transport Barrier, Finite-Time Stable and Unstable Foliations, Implicit Function Theorem, Continuation, Mixing, Transport
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
June
30,
2015
ABSTRACT:
Mixing and coherence are fundamental issues
at the heart of understanding fluid dynamics and other non-autonomous dynamical
systems. Recently the notion of coherence has come to a more rigorous footing,
in particular, within the studies of finite-time nonautonomous dynamical systems.
Here we recall “shape coherent sets” which is proven to correspond to slowly
evolving curvature, for which tangency of finite time stable foliations
(related to a “forward time” perspective) and finite time unstable foliations
(related to a “backwards time” perspective) serve a central role. We compare
and contrast this perspective to both the variational method of geodesics [17],
as well as the coherent pairs perspective [12] from transfer operators.