Dynamics of Coherent Structures in Turbulent Rayleigh-Bénard Convection by Lagrangian Particle Tracking of Long-Lived Helium Filled Soap Bubbles

Abstract

We present spatially and temporally resolved velocity and acceleration measurements of turbulent Rayleigh-Bénard convection covering the complete volume of a cylindrical sample with aspect ratio one. Using the "Shake-The-Box" Lagrangian particle tracking algorithm, we were able to instantaneously track more than 500,000 particles in the complete sample volume (~ 1 m³), corresponding to mean inter-particle distances down to 5-8 Kolmogorov lengths. We used the data assimilation scheme "FlowFit" with continuity and Navier-Stokes-constraints to interpolate the scattered velocity and acceleration data via continuous 3D B-Splines on a cubic grid and to recover the smallest flow scales. The measurements were enabled by a dedicated bubble fluid solution, which we developed for generation of longlived helium filled soap bubbles, allowing for long-term optical flow measurements at large scales in gaseous fluids. We show Lagrangian and Eulerian visualizations of the large-scale circulation (LSC) as well as small scale structures, such as thermal plumes and turbulent background fluctuations and unveil the dynamics of their complex interplay. By employing principal component analysis in the rotating frame of the LSC, we are able to describe the characteristic dynamics of the LSC with the first three POD modes with an accuracy of 95% by using only 50% of the turbulent kinetic energy of the flow.