Lagrangian heat transport in turbulent three-dimensional convection

Abstract

Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $\Gamma =16$, Rayleigh number $Ra=10^5$, and Prandtl numbers $Pr=0.1,0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian 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 detected CS contribute by a third less to the global turbulent heat transport for all investigated $Pr$ compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.

8 pages, 5 figures

References in corpus (4)

• Coherent structure coloring: identification of coherent structures from sparse data using graph theory
• A review on turbulent and vortical flow analyses via complex networks
• Lagrangian studies in convective turbulence
• Lagrangian dispersion and heat transport in convective turbulence

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