Experimental measurements of spatiotemporal-resolved energy dissipation rate in turbulent Rayleigh–Bénard convection: Properties of the velocity gradient tensor and energy dissipation rate surrogates

We report a home-made velocity gradient tensor resolved particle image velocimetry (VGTR-PIV) system which spatially and temporally resolves all nine components of the highly fluctuating velocity gradient tensor. We applied this technique in the paradigmatic turbulent Rayleigh–Bénard convection in a cylindrical cell at three representative positions, i.e., center, side and bottom regions. The Rayleigh number varied in the range Ra=2×10⁸-8×10⁹ and the Prandtl number was fixed at Pr=4.34. The measured full velocity gradient tensor allows us to directly access, for the first time, the time-resolved energy dissipation rate and enstrophy in turbulent thermal convection. The probability density functions of the velocity gradient follow the exponential distribution and overlap at different Ra in each region. The turbulence is the most isotropic in the center and the least isotropic in the bottom region. In the side and bottom regions, the flow field becomes more isotropic as Ra increases. Comparing to the fully-resolved energy dissipation rate, the pseudo dissipation provides the best estimate, the planar (two-dimensional) surrogate has a larger relative error, and the one-dimensional surrogate has the largest error.