Influence of container shape on scaling of turbulent fluctuations in convection

We perform large-eddy simulations of turbulent convection in a cubic cell for Rayleigh numbers, Ra, between 10(6) and 10(10) and the molecular Prandtl number, Pr=0.7. The simulations were carried out using a second-order-accurate finite-difference method in which subgrid-scale fluxes of momentum and heat were both parametrized using a Lagrangian and dynamic Smagorinsky model. The scaling of the root-mean-square fluctuations of density (temperature) and velocity measured in the cell center are in excellent agreement with the scaling measured in the laboratory experiments of Daya and Ecke [Phys. Rev. Lett. 87, 184501 (2001)] and differ substantially from that observed in cylindrical cells. We also observe the time-averaged spatial distributions of the local heat flux and density fluctuations, and find that they are strongly inhomogeneous in the horizontal midplane, with the largest density gradients occurring at the corners at the midheight, where hot and cold plumes mix in the form of strong counter-rotating eddies.