Numerische Untersuchung rotierender Rayleigh-Bénard-Konvektion ohne Ekman-Schichten

Abstract

This work deals with numerical studies of rotating Rayleigh-Bénard convection in a planar fluid layer. A spectral method is employed with periodic boundary conditions in the horizontal directions. Either stress free (for simulations without Ekman layers) or no slip boundary conditions (for simulations with Ekman layers) in the vertical direction are applied to compare both cases. The parameters of the simulations range between 10^3 and 10^8 for the Rayleigh number and between 10^-5 and 10^-2 for the Ekman number, respectively. The Prandtl number is 0.7 or 7. These simulations are compared to those without rotation (corresponding to an infinite Ekman number) if possible.The overall as well as the convective heat transport are studied, expressed in terms of the Nusselt number Nu and Nu-1, respectively. Especially for Nu-1 a universal plot is found for a combination of Reynolds, Prandtl and Ekman numbers. Three regimes become visible: A laminar regime close to the onset of convection, which is dominated by rotation, an intermediate regime and a turbulent regime, for which the heat transport approaches the nonrotating case. Looking at diffusivity-free numbers in the intermediate regime, one finds a power law which is independant of thermal diffusivity and kinematic viscosity. The power law"s exponent is identical for both boundary conditions.In addition, the structure of the flow is studied. For this purpose, the helicity of the velocity field is inspected. Fluid particles in convection rolls move up-/downwards vertically in the case without rotation. Rotation leads to helical paths. After averaging over horizontal planes, the helicity is positive in the lower half of the domain and negative in the upper half. With increasing Rayleigh number the influence of rotation decreases. This is best seen in the rms-value of the helicity. Above some value of a combination of Reynolds and Ekman numbers, this value is as small as in the nonrotating case. This is interpreted as the transition to the nonrotating state of the flow.