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 in a cylindrical sample with aspect ratio one. Using the "Shake-The-Box" Lagrangian Particle Tracking algorithm, we were able to instantaneously track more than 560,000 particles in the complete sample volume (~ 1 m³), corresponding to mean inter-particle distances of less than 8 volume averaged Kolmogorov lengths. We used the data assimilation scheme "FlowFit" with continuity and Navier-Stokes-constraints to regularize the scattered velocity and acceleration data via continuous 3D B-Splines on a cubic grid to recover the smallest flow scales. The measurements were enabled by a dedicated bubble fluid solution, which we developed for generation of long-lived helium filled soap bubbles, allowing for long-term optical flow measurements at large scales in gaseous media. We show visualizations of the Large-Scale Circulation (LSC) using iso-surfaces the Q-criterion, that allow a glance into the turbulent structure of the flow and to spot some of the dynamic features of the LSC. By employing Proper Orthogonal Decomposition (POD) in the rotating frame of the LSC, we are able to model the oscillatory dynamics of the LSC using just the first three POD modes with a standard deviation from the full data set of less than 5 % utilizing only ~50% of the turbulent kinetic energy.