Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-B\'enard convection flows

TL;DR

This paper introduces an evolutionary clustering method to analyze Lagrangian trajectories in turbulent convection flows, enabling detection of dynamic coherent sets and their role in heat transfer, with potential applications in natural flow studies.

Contribution

The study develops an evolutionary clustering approach that captures the dynamic evolution of coherent sets in turbulent flows, overcoming limitations of traditional static methods.

Findings

Identified long-term coherent sets that contribute minimally to heat transfer.

Detected splits and mergers of coherent sets through eigenvalue spectrum analysis.

Revealed pathways of convective heat transfer via Lagrangian trajectories.

Abstract

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allow individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows which are typically based on sparse information from drifters and probes.