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.
Highlights
Understanding and describing mixing and transport in two-dimensional fluid flows have been a classic problem in dynamical systems for decades
This suggests an implicit connection between the geodesic theory and the coherent pairs theory
The zero-angle curves are developed from the nonhyperbolic splitting of stable and unstable foliations by continuation methods that relate to the implicit function theorem
Summary
Understanding and describing mixing and transport in two-dimensional fluid flows have been a classic problem in dynamical systems for decades.
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