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.