TY - CHAP

T1 - Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

AU - Schumacher, Jörg

AU - Schneide, Christiane

AU - Pandey, Ambrish

AU - Padberg-Gehle, Kathrin

PY - 2018

Y1 - 2018

N2 - We analyse the formation of large-scale patterns in a turbulent convection flow in a horizontally extended square convection cell by Lagrangian particle trajectories in three-dimensional direct numerical simulations. These large-scale patterns, which are termed turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. The corresponding graph is built from the Lagrangian particle tracks. We demonstrate that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, agree with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τ L and lengths λUL of the superstructures are found to agree well with their Eulerian complements, τ and λU, respectively. The clustering works well for times t < τ. Longer times t > τ require density-based trajectory clustering using time-averaged Lagrangian pseudo-trajectories. A coherent subset of these trajectories is obtained which consists of those particles tracks that are trapped for long times in the core of the superstructure rolls and thus not subject to ongoing turbulent dispersion.

AB - We analyse the formation of large-scale patterns in a turbulent convection flow in a horizontally extended square convection cell by Lagrangian particle trajectories in three-dimensional direct numerical simulations. These large-scale patterns, which are termed turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. The corresponding graph is built from the Lagrangian particle tracks. We demonstrate that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, agree with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τ L and lengths λUL of the superstructures are found to agree well with their Eulerian complements, τ and λU, respectively. The clustering works well for times t < τ. Longer times t > τ require density-based trajectory clustering using time-averaged Lagrangian pseudo-trajectories. A coherent subset of these trajectories is obtained which consists of those particles tracks that are trapped for long times in the core of the superstructure rolls and thus not subject to ongoing turbulent dispersion.

KW - Mathematics

M3 - Published abstract in conference proceedings

T3 - Bulletin of the American Physical Society

BT - 71st Annual Meeting of the APS Division of Fluid Dynamics

PB - American Physical Society

CY - New York

ER -