# A Geometric Heat-Flow Theory of Lagrangian Coherent Structures

@article{Karrasch2020AGH, title={A Geometric Heat-Flow Theory of Lagrangian Coherent Structures}, author={Daniel Karrasch and Johannes Keller}, journal={Journal of Nonlinear Science}, year={2020}, volume={30}, pages={1849-1888} }

We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection–diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or heat equation. By this coordinate transformation, the reversible effects of advection are separated from the irreversible joint effects of advection and diffusion. In this…

## 24 Citations

Lagrangian barriers to heat transport in turbulent three-dimensional convection.

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We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing…

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We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the…

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This work obtains explicit differential equations and a diagnostic scalar field that identify the most observable extremizers with pointwise uniform transport density in compressible flows and to diffusive concentration fields affected by sources or sinks, as well as by spontaneous decay.

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data

- Computer ScienceJ. Nonlinear Sci.
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It is argued that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport.

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Higher-order versions of these two numerical schemes for numerically computing the dynamic Laplace operator are considered and it is proved the numerically computed eigenvalues and eigenvectors converge to the true objects for both schemes under certain assumptions.

Lagrangian Transport Through Surfaces in Compressible Flows

- Computer ScienceSIAM J. Appl. Dyn. Syst.
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