Probing turbulent superstructures in Rayleigh-B\'{e}nard convection by Lagrangian trajectory clusters

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 $\Gamma=16$ 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 {\it et al.}, Phys. Rev. E {\bf 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 $\tau^L$ and lengths $\lambda_U^L$ of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, $\tau$ and $\lambda_U$, respectively. This trajectory-based clustering is found to work for times $t\lesssim \tau\approx\tau^L$. Longer time periods $t\gtrsim \tau^L$ require a change of the analysis method to a density-based trajectory clustering by means of time-averaged 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.Comment: 12 pages, 7 downsized figures, to appear in Phys. Rev. Fluid

Lagrangian analysis of long-term dynamics of turbulent superstructures

In Rayleigh-Bénard convection, turbulent superstructures are large-scale patterns of circulation rolls created by hot ascending and cold descending thermal plumes. The evolution of these large-scale patterns happens on very large time scales τ [1]. Spectral clustering applied to Lagrangian particle trajectories on time intervals smaller than τ can be used to create clusters displaying a structure similar to the patterns detected in the Eulerian frame of reference [2]. However, this technique is unfeasible for the analysis of the evolution of turbulent superstructures due to turbulent dispersion. Therefore, we test the application of concepts of evolutionary spectral clustering [3] on Lagrangian particle trajectories to analyze the long-term dynamics of turbulent superstructures in the Lagrangian frame of reference

Lagrangian heat transport in turbulent three-dimensional convection

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 figure

Lagrangian perspectives on turbulent superstructures in Rayleigh-Bénard convection

We analyze large‐scale patterns in three‐dimensional turbulent convection in a horizontally extended square convection cell by means of Lagrangian particle trajectories calculated in direct numerical simulations. Different Lagrangian computational methods, i.e. finite‐time Lyapunov exponents, spectral and density‐based clustering and transfer operator approaches, are used to detect these large‐scale structures, which are denoted as turbulent superstructures of convection

Lagrangian analysis of long‐term dynamics of turbulent superstructures

In Rayleigh-Bénard convection, turbulent superstructures are large-scale patterns of circulation rolls created by hot ascending and cold descending thermal plumes. The evolution of these large-scale patterns happens on very large time scales τ [1]. Spectral clustering applied to Lagrangian particle trajectories on time intervals smaller than τ can be used to create clusters displaying a structure similar to the patterns detected in the Eulerian frame of reference [2]. However, this technique is unfeasible for the analysis of the evolution of turbulent superstructures due to turbulent dispersion. Therefore, we test the application of concepts of evolutionary spectral clustering [3] on Lagrangian particle trajectories to analyze the long-term dynamics of turbulent superstructures in the Lagrangian frame of reference

Machine Learning Applications in Convective Turbulence

Turbulent convection flows are ubiquitous in natural systems such as in the atmosphere or in stellar interiors as well as in technological applications such as cooling or energy storage devices. Their physical complexity and vast number of degrees of freedom prevents often an access by direct numerical simulations that resolve all flow scales from the smallest to the largest plumes and vortices in the system and requires a simplified modelling of the flow itself and the resulting turbulent transport behaviour. The following article summarises some examples that aim at a reduction of the flow complexity and thus of the number of degrees of freedom of convective turbulence by machine learning approaches. We therefore apply unsupervised and supervised machine learning methods to direct numerical simulation data of a Rayleigh-Bénard convection flow which serves as a paradigm of the examples mentioned at the beginning

Collaborative work in NFDI

The non-profit association National Research Data Infrastructure (NFDI) promotes science and research through a National Research Data Infrastructure. Its aim is to develop and establish an overarching research data management (RDM) for Germany and to increase the efficiency of the entire German science system. After a two-and-a-half year build up phase, the process of adding new consortia, each representing a different data domain, has ended in March 2023. NFDI now has 26 disciplinary consortia (and one additional basic service collaboration). Now the full extent of cross-consortial interaction is beginning to show

White Paper: Umgang mit Zielen der BLV als Grundlage für die Strukturevaluation

In der Bund-Länder-Vereinbarung (BLV) zu Aufbau und Förderung einer Nationalen Forschungsdateninfrastruktur (NFDI) (im Folgenden BLV-NFDI) wird in §1 festgehalten, dass mit der Förderung "eine Etablierung und Fortentwicklung eines übergreifenden Forschungsdatenmanagements" und damit eine "Steigerung der Effizienz des gesamten Wissenschaftssystems verfolgt" wird. In der BLV-NFDI werden dazu sieben Ziele vorgegeben, die eine Verfeinerung dieser Hauptziele darstellen. Dieses White Paper formuliert das gemeinsame Verständnis der beteiligten Konsortien für die sieben in der BLV-NFDI vorgegebenen Ziele. Auf der Grundlage dieses Verständnisses hat die Task Force Evaluation und Reporting Vorschläge gemacht, wie das Erreichen der Ziele erfasst, beschrieben und gemessen werden kann

White Paper: Interim report reference

This White Paper sets out commonly agreed definitions on activities of consortia within NFDI. It aims to provide a common basis for reporting and reference regarding selected questions of cross-consortial relevance in DFG’s template for the Interim Reports. The questions were prioritised by an NFDI Task Force on Evaluation and Reporting (formerly Task Force Monitoring) as a result of discussing possible answers to the DFG template. In this process the need to agree on a generalizable meaning of terms commonly used in the context of NFDI, and reporting in particular, were identified from cross-consortial perspectives. Questions that showed the highest requirement on clarification are discussed in this White Paper. As NFDI evolves, the Task Force will likely propose further joint approaches for reporting in information infrastructures. While each of broad relevance, the questions addressed relate to substantially different aspects of consortia’s work. They are thus also structured slightly different