Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard Convection

Klünker, Anna; Schneide, Christiane; Froyland, Gary; Schumacher, Jörg; Padberg‐Gehle, Kathrin

doi:10.1007/978-3-030-51264-4_4

Cited by 2 publications

(2 citation statements)

References 48 publications

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“…To extract Lagrangian coherent sets from spectral properties of the diffusion map, we apply the recently developed sparse eigenbasis approximation (SEBA) [23]. The combination of these methods allows us to disentangle the contribution of the tracer trajectories that are trapped in Lagrangian coherent sets to the overall heat transfer in comparison to the rest, extending our recent Lagrangian studies of RBC [13][14][15] to the analysis of turbulent transport. Figure 1 illustrates these coherent sets in panel (a) in a perspective view and replots representative trajectories in panel (b).…”

Section: Introductionmentioning

confidence: 99%

Lagrangian heat transport in turbulent three-dimensional convection

et al. 2021

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Barriers to the turbulent transport of heat in a convection flow can be identified by Lagrangian trajectories that stay together for a long time and thus probe spatial regions in the bulk of the fluid flow that do not mix effectively with its surroundings. They form Lagrangian coherent sets which we investigate here in direct numerical simulations of three-dimensional Rayleigh-Bénard convection at three different Prandtl numbers. The analysis is based on 524, 288 massless Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by the diffusion map approach, which quantifies the connectivity of trajectory segments by a diffusion process on the data, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The diffusion kernel contains a cutoff that is based on the time-averaged distance between mutual Lagrangian tracers in a time window. The numerical simulations are performed in a cell at an aspect ratio Γ = 16, at fixed Rayleigh number Ra = 10 5 , and Prandtl numbers Pr = 0.1, 0.7 and 7. The combination of diffusion map and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the Lagrangian coherent sets contribute significantly less to the global turbulent heat transfer for all chosen Prandtl numbers as the trajectories in the spatial complement. This is realized by monitoring local Nusselt numbers, a dimensionless measure of heat transfer, along the tracer trajectories.

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Section: Introductionmentioning

confidence: 99%

Lagrangian heat transport in turbulent three-dimensional convection

et al. 2021

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“…Our technique is based on the zero diffusion limit established in Froyland and Kwok (2016); it uses Arnoldi iterations to compute eigenvectors of the transfer operator L without the need of storing the matrix associated to its finite dimensional approximation. We therefore do not rely on the construction of finite-element bases and our method can be considered as an alternative to those of (Froyland and Junge (2018); Klünker et al (2020)). Crucially the same number of particles is used to compute FTLEs, rigid sets, or coherent sets with a resolution identical to that of the input velocity field.…”

Section: Introductionmentioning

confidence: 99%

Rigid Sets and Coherent Sets in Realistic Ocean Flows

Feppon

Lermusiaux

2022

Preprint

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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 volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new “diffeomorphism-based” criterion to extract “rigid sets”, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.

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Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard Convection

Cited by 2 publications

References 48 publications

Lagrangian heat transport in turbulent three-dimensional convection

Lagrangian heat transport in turbulent three-dimensional convection

Rigid Sets and Coherent Sets in Realistic Ocean Flows

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