Lagrangian single-particle, multi-particle and topological analyses in turbulent Rayleigh-B\'enard convection

TL;DR

This study uses advanced Lagrangian analysis techniques on high-Rayleigh-number turbulent convection simulations to uncover detailed transport mechanisms, vortex structures, and dispersion behaviors beyond traditional global scaling laws.

Contribution

It introduces novel Lagrangian diagnostics and analysis methods to characterize turbulent convection, revealing detailed flow topologies and dispersion dynamics at high Rayleigh numbers.

Findings

Lagrangian heat fluxes can reach 500 times the mean, showing extreme intermittency.

Distinct topological signatures of vortices are identified in the Q-R invariant plane.

Dispersion exhibits temporally organized regimes, with short plume ejections and sustained Richardson-like scaling.

Abstract

We present three-dimensional direct numerical simulations of turbulent Rayleigh-B\'enard convection (RBC) in the Lagrangian frame of reference for Rayleigh numbers $10^5 \leq Ra \leq 10^{10}$ and a Prandtl number $Pr=0.7$ in a plane layer at an aspect ratio $L:L:H=4:4:1$ with a horizontal length $L$ and height $H$. We use particle accelerations, Lagrangian heat transfer, $Q$-$R$ invariant topology, Lagrangian particle pair dispersion, scale-dependent Lagrangian eddy viscosity, and principal-component analysis (PCA) of dense particle clouds to characterise convective transport along material trajectories. By computing particle accelerations at the integration time step and controlling spectral-element-method signatures, we obtain robust acceleration statistics and recover Heisenberg-Yaglom behaviour. Lagrangian heat transfer is extremely intermittent: individual massless Lagrangian particles can carry convective heat fluxes up to $500$ times the global Eulerian mean, although higher-order heat flux moments decrease toward Gaussian values with increasing $Ra$. The analysis of velocity gradient invariants in the $Q$-$R$ plane along trajectories identifies a distinct topological footprint of dust-devil-like convective vortices in the quadrant of $Q>0$, $R<0$, associated with vortex stretching, plume detachment, and intense localised heat transfer. Global unconditioned pair dispersion exhibits neither extended Richardson nor Bolgiano-Obukhov scaling plateaus. Rather, scale-dependent eddy viscosity and conditioned PCA of dense particle clouds reveal that buoyancy- and shear-driven dispersion are temporally organised: rapid plume-driven ejection produces a short $t^5$-like episode, followed by sustained Richardson-like $t^3$-scaling. Thus, Lagrangian topology and cloud geometry provide mechanism-resolving diagnostics for active-scalar turbulence beyond RBC-specific global scaling laws.