Three-dimensional velocity gradient statistics in a mesoscale convection laboratory experiment

Abstract

We present three-dimensional velocity gradient statistics from Rayleigh--B\'enard convection experiments in a horizontally extended cell of aspect ratio 25, a paradigm for mesoscale convection. The Rayleigh number $Ra$ ranges from $3.7 \times 10^5$ to $4.8 \times 10^6$, and the Prandtl number $Pr$ from 5 to 7.1. Spatio-temporally resolved volumetric data are reconstructed from moderately dense Lagrangian particle tracking measurements. All nine components of the velocity gradient tensor from the experiments show good agreement with those from direct numerical simulations, both conducted at $Ra = 1 \times 10^6$ and $Pr = 6.6$. The focus of our analysis is on non-Gaussian velocity gradient statistics. Specifically, we examine the probability density functions (PDFs) of components of the velocity gradient tensor, vorticity components, kinetic energy dissipation, and local enstrophy at different heights in the bottom half of the cell. The probability of high-amplitude derivatives increases from the bulk to the bottom plate. A similar trend is observed with increasing $Ra$ at fixed height. Both indicate enhanced small-scale intermittency of the velocity field. Furthermore, doubly-logarithmic plots of the PDFs of normalized energy dissipation and local enstrophy at all heights show that the left tails follow slopes of $3/2$ and $1/2$, respectively, in agreement with numerical results. In general, the left tails of the dissipation and local enstrophy distributions show higher probability values with increasing proximity towards the plate, compared to those in the bulk.