# Detecting the birth and death of finite-time coherent sets

@inproceedings{Froyland2021DetectingTB, title={Detecting the birth and death of finite-time coherent sets}, author={Gary Froyland and P{\'e}ter Koltai}, year={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 vortices in the ocean and atmosphere, respec-tively. The boundaries of ﬁnite-time coherent sets are examples of Lagrangian coherent structures (LCSs). The selection of the time duration over which FTCS and LCS computations are made in practice is crucial to their success. If this time is longer than the…

## Figures from this paper

## 4 Citations

A patch in time saves nine: Methods for the identification of localised dynamical behaviour and lifespans of coherent structures

- Mathematics
- 2021

We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify…

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…

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows.

- PhysicsChaos
- 2022

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…

Definition, detection, and tracking of persistent structures in atmospheric flows

- Environmental Science
- 2021

in atmospheric flows Johannes von Lindheim,1 Abhishek Harikrishnan,2 Tom Dörffel,2 Rupert Klein,2 Péter Koltai,2 Natalia Mikula,3 Annette Müller,4 Peter Névir,4 George Pacey,4 Robert Polzin,2 and…

## References

SHOWING 1-10 OF 63 REFERENCES

Almost-Invariant and Finite-Time Coherent Sets: Directionality, Duration, and Diffusion

- Mathematics
- 2014

Regions in the phase space of a dynamical system that resist mixing over a finite-time duration are known as almost-invariant sets (for autonomous dynamics) or coherent sets (for nonautonomous or…

Robust FEM-Based Extraction of Finite-Time Coherent Sets Using Scattered, Sparse, and Incomplete Trajectories

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2018

Three FEM-based numerical methods are developed to efficiently approximate the dynamic Laplace operator, and a new dynamic isoperimetric problem using Dirichlet boundary conditions is introduced.

Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

- Mathematics
- 2005

Lagrangian based methods for coherent structure detection.

- Environmental ScienceChaos
- 2015

A review of four Lagrangian analytical methods for detecting coherent structures in fluid flow transport via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach.

A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems

- MathematicsJournal of Computational Dynamics
- 2020

This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these structures undergo fundamental structural changes, such as merging and splitting events.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures

- Mathematics
- 2015

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to…

Estimating long-term behavior of periodically driven flows without trajectory integration

- Mathematics
- 2015

Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation…

Linear response for the dynamic Laplacian and finite-time coherent sets

- MathematicsNonlinearity
- 2021

Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical…

Computation and Optimal Perturbation of Finite-Time Coherent Sets for Aperiodic Flows Without Trajectory Integration

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2020

This work considers the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold to compute coherent sets from an aperiodic time-dependent dynamical system and obtains explicit solutions for these optimization problems using Lagrange multipliers.