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

Abstract

We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr = 0.7, a Rayleigh number Ra = 10 5 , and an aspect ratio Γ = 16 is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem et al., Phys. Rev. E 93, 063107 (2016), builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τ L and lengths λ L U of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, τ and λU , respectively. This trajectory-based clustering is found to work for times t τ ≈ τ L . Longer time periods t τ L require a change of the analysis method to a density-based trajectory clustering by means of timeaveraged Lagrangian pseudo-trajectories, which is applied in this context for the first time. A small coherent subset of the pseudo-trajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.

Lagrangian perspectives on turbulent superstructures in Rayleigh‐Bénard convection

“…1 (b)-(f)), similar to the superstructures obtained in the Eulerian frame of reference ( Fig. The characteristic time scale for these large-scale structures is found to be τ ≈ 20 T f [1], which is the average turnover time of a Lagrangian particle, where T f is the free-fall time unit. The characteristic time scale for these large-scale structures is found to be τ ≈ 20 T f [1], which is the average turnover time of a Lagrangian particle, where T f is the free-fall time unit.…”

“…A detailed Lagrangian study of Rayleigh-Bénard convection by means of trajectory clustering is carried out in [1]. A detailed Lagrangian study of Rayleigh-Bénard convection by means of trajectory clustering is carried out in [1].…”

Flow organisation in laterally unconfined Rayleigh–Bénard turbulence

“…It should additionally be noted that the present approach provides information on the typical turnover time scale of the superstructure in an averaged sense. This is different from Schneide et al (2018) who studied turnover times for individual fluid particles. Particles may linger for long times in either the core of the structures or within the boundary layers, leading to a very wide distribution of time scales in the latter case.…”

Pair dispersion in inhomogeneous turbulent thermal convection

“…Moreover, heat flux and particle dispersion were numerically studied by Schumacher and co-workers all along the decade. Among these previous studies, the pair dispersion was explored numerically in thermally-driven flows [29,30]. The Batchelor and Richardson-Obukhov regimes were observed.…”