Numerical investigation of the spatial resolution requirements for turbulent Rayleigh-Benard convection

Abstract

The key requirement for setting up a direct numerical simulation (DNS) is a sufficiently fine grid allowing to resolve locally all relevant micro-scales. In case of turbulent Rayleigh-Bénard convection (RBC) this is usually done by fulfilling different analytically derived criteria for the boundary layers and the bulk flow. In order to analyse if these requirements are sufficient, DNS of turbulent RBC in a cylindrical container with aspect ratio unity and Prandtl number Pr = 0.786 have been performed for Rayleigh numbers Ra up to 109. The micro-scales obtained in the DNS as well astheir scaling with Ra are compared with the corresponding theoretical predictions. The analysis reveals that the smallest scales, occurring close to the wall, are about half of the estimated ones. Furthermore, their scaling differs slightly from the estimations while the criterion for the bulk flow fits quite well.