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

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.