# A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit

@inproceedings{Karrasch2021ALP, title={A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit}, author={Daniel Karrasch and Nathanael Schilling}, year={2021} }

We study mass preserving transport of passive tracers in the lowdiffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonomous diffusion equation is approximated by that of a time-averaged diffusion equation. We show that leading order asymptotics that hold for functions [Krol, 1991] extend to the dominant nontrivial singular value. This answers questions raised in [Karrasch & Keller, 2020]. The generator of the time-averaged diffusion…

## 4 Citations

Heat-content and diffusive leakage from material sets in the low-diffusivity limit

- MathematicsNonlinearity
- 2021

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…

Persistence and material coherence of a mesoscale ocean eddy

- Environmental SciencePhysical Review Fluids
- 2022

Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit…

Rigid Sets and Coherent Sets in Realistic Ocean Flows

- Mathematics
- 2022

Abstract. This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non…

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- Mathematics
- 2021

Finite-time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some ﬁnite period of time; physical manifestations include eddies and…

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