Corner Circulation Scaling Laws of Turbulent Rayleigh-Bénard Convection in a Cubic Cell

Rayleigh-Bénard convection (RBC) in a cubic cell is studied at Prandtl number \(\textrm{Pr} = 6.9\) in the hard turbulent regime with Rayleigh numbers Ra \(\gg \) Pr \( \cdot 10^{6}\) . The predominant flow structure is the large-scale circulation oriented along one of the cell diagonals. Corner circulations can develop in the cell corners along both cell diagonals. Here, the scaling laws for the Reynolds number of the corner circulations are calculated analyzing two direct numerical simulations performed for two Rayleigh numbers \(\textrm{Ra}\in \{3 \cdot 10^{8},1 \cdot 10^{10}\}\) . Two scaling laws are found, one for each cell diagonal and the corner circulations along the same diagonal seem to obey the same scaling law. One of the scaling laws is similar to the results obtained for an two-dimensional (2D) RBC sample. The scaling laws are validated with a particle tracking velocimetry experiment of a cubic Rayleigh-Bénard convection cell filled with water ( \(\textrm{Pr}\approx 6.9\) ) at \(\textrm{Ra}\approx 1 \cdot 10^{10}\) .