Lagrangian heat transport in turbulent three-dimensional convection
| Autor: | Vieweg, Philipp P., Schneide, Christiane, Padberg-Gehle, Kathrin, Schumacher, Jörg |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Phys. Rev. Fluids 6, L041501 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevFluids.6.L041501 |
| Popis: | Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-B\'{e}nard 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. Comment: 8 pages, 5 figures |
| Databáze: | arXiv |
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