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

Abstract

We present three-dimensional velocity gradient statistics from turbulent Rayleigh–Bénard convection experiments in a horizontally extended cell of aspect ratio 25, a paradigm for mesoscale convection with its organisation into large-scale patterns. The Rayleigh number ${\textit{Ra}}$ ranges from $3.7 \times 10^5$ to $4.8 \times 10^6$ , the Prandtl number ${\textit{Pr}}$ 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 ${\textit{Ra}} = 1 \times 10^6$ and ${\textit{Pr}} = 6.6$ . As expected, with increasing ${\textit{Ra}}$ , the flow in the bulk approaches isotropic conditions in the horizontal plane. The focus of our analysis is on non-Gaussian velocity gradient statistics. We demonstrate that statistical convergence of derivative moments up to the sixth order is achieved. 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 ${\textit{Ra}}$ at fixed height. Both indicate enhanced small-scale intermittency of the velocity field. We also determine derivative skewness and flatness. The PDFs of the derivatives with respect to the horizontal coordinates are found to be more symmetric than the ones with respect to the vertical coordinate. The conditional statistical analysis of the velocity derivatives with respect to up-/down-welling regions and the rest did not display significant difference, most probably due to the moderate Rayleigh numbers. Furthermore, doubly logarithmic plots of the PDFs of normalised 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, in comparison with those in the bulk.

Affiliated Institutions

• Technische Universität Ilmenau DE

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