Transient almost-invariant sets reveal convective heat transfer patterns in plane-layer Rayleigh-B\'enard convection

Aleksandar Badza; Gary Froyland; Roshan J. Samuel; Jörg Schumacher

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arXiv · 2510.05590

Transient almost-invariant sets reveal convective heat transfer patterns in plane-layer Rayleigh-B\'enard convection

Aleksandar Badza·Gary Froyland·Roshan J. Samuel·Jörg Schumacher

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Abstract

Horizontally extended plane-layer convection flows are characterized by characteristic patterns of turbulent heat transfer due to the convective fluid motion consisting of a nearly-regular ridge network where hot fluid rises and cold fluid sinks. Here, we analyse this transport behavior by the so-called inflated generator framework, which identifies quasi-stationary families of almost-invariant sets, derived from leading inflated generator eigenvectors. We demonstrate the effectiveness of this data-driven analysis framework in three-dimensional turbulent flow, by extracting transient characteristic heat transfer patterns as families of almost-invariant sets subject to a transient evolution, which contribute least to the convective heat transfer.

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Aleksandar Badza, Gary Froyland, Roshan J. Samuel, Jörg Schumacher. 2025-10-07. Transient almost-invariant sets reveal convective heat transfer patterns in plane-layer Rayleigh-B\'enard convection. https://arxiv.org/abs/2510.05590

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