Turbulent convection and large scale circulation in a cube with rough horizontal surfaces.

Large-eddy simulations of thermal convection are presented and discussed for a cube with rough horizontal surfaces. Two types of roughness are considered: uniformly placed pyramids, and grooves aligned parallel to one set of sidewalls. The Rayleigh number is 10^{8}, the Prandtl number 0.7, and the aspect ratio 1, as in a previous study [N. Foroozani, J. J. Niemela, V. Armenio, and K. R. Sreenivasan, Phys. Rev. E 95, 033107 (2017)10.1103/PhysRevE.95.033107], except that the meshes here are finer. When the thermal boundary layers are sufficiently large relative to the characteristic roughness height, i.e., for hydrodynamically smooth conditions, the mean properties of the large scale circulation (LSC) are qualitatively similar to the case of smooth surfaces. In particular, the LSC is always aligned along one of the diagonals of the cube. When the boundaries are hydrodynamically rough, the same result holds true only for the case of pyramidal structures; for grooved surfaces, the LSC is forced to be parallel to the sidewalls on average, alternating rapidly between the two diagonals of the cube with a mean period of the order 10 turnover times. Our analysis suggests that the difference from the pyramidal case is due to the breaking of the horizontal x-z symmetry under conditions of hydrodynamical roughness, and the corresponding directional concentration of plume emission along the grooves, from which the LSC is generated, providing a strong restoring force. Furthermore, in this study we observed a small reduction in heat transport for both roughness configurations which is in good agreement with past studies.