Spatially and temporally resolved measurements of turbulent Rayleigh-Bénard convection by Lagrangian particle tracking of long-lived helium-filled soap bubbles

Abstract

Rayleigh-Bénard convection (RBC), where a fluid is heated from below and cooled from above, is a prevalent model system to study the fundamentals of thermal convection. Typical for the turbulent RBC system is the occurrence of a large-scale circulation (LSC), which develops by self-organization of thermal plumes, erupted from the thermal boundary layers. In cylindrical samples of aspect ratios close to unity with a high degree of symmetry, the LSC reveals complex short- and long-term dynamics, which has been studied extensively in the past. Direct volumetric measurements of the LSC, however, allowing for a direct insight into the underlying turbulent processes are still rare. To bridge this gap, we performed Lagrangian Particle Tracking (LPT) by using a multi-camera setup, long-lasting, helium-filled soap bubbles and high-power LED arrays. With the "Shake-The-Box" Lagrangian particle tracking algorithm, we were able to instantaneously track up to 560,000 particles in the complete sample volume (~ 1 m³), corresponding to mean inter-particle distances down to 6-8 Kolmogorov lengths. We used the data assimilation scheme ‘FlowFit’, which involves continuity and Navier-Stokesconstraints, to map the scattered velocity and acceleration data on cubic grids, herewith recovering the smallest flow scales. Lagrangian and Eulerian visualizations reveal the dynamics of the large-scale circulation and its interplay with small scale structures, such as thermal plumes and turbulent background fluctuations. As a result, the complex time-dependent behavior of the LSC comprising azimuthal rotations, torsional oscillation and sloshing can be extracted from the data. Further, we found more seldom dynamic events, such as spontaneous reorientations of the LSC in the data from long-term measurements.