Numerical investigation of local Kolmogorov scales in turbulent Rayleigh-Bénard convection

Abstract

Highly resolved direct numerical simulations (DNS) of turbulent Rayleigh-Benard convection in a cylindrical container with aspect ratio unity and Prandtl number Pr=0.786 have been performed for Rayleigh numbers Ra up to 10e9. The key ingredient for setting up a DNS is a sufficiently fine grid allowing to resolve the the local Kolmogorov scales. Usually this is done by fulfilling different published criteria for resolving the boundary layers and the bulk flow. To analyse if these criteria hold, absolute values of the smallest Kolmogorov scales obtained in DNS as well as their scaling with Ra are compared to the corresponding predictions from the theory. The analysis reveals that the smallest scales occurring in the boundary layer are about two thirds of the estimated ones. Further their scaling differs considerably from the above mentioned estimate while the bulk criterion fits quite well.