Rotation and non-Oberbeck-Boussinesq effects in turbulent Rayleigh-Bénard convection

Abstract

In this thesis different aspects of turbulent Rayleigh-Bénard convection have been studied that go beyond of what the majority of recent investigations focuses on. The two main concerns here, were the influence of rotation and the influence of non-Oberbeck-Boussinesq (NOB) effects, and their combination. In addition also the impact of the Prandtl number was considered. Thus, the objective was to get us closer to the understanding of the turbulent convective flow behaviour in nature. With this in mind, three-dimensional direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection were performed. Firstly, rotating Rayleigh–Bénard convection of a fluid with a Prandtl number of Pr = 0.8 confined in a slender cylindrical cell with an aspect ratio of 0.5 was studied under perfect Oberbeck-Boussinesq (OB) conditions. Based on this data, I proposed a new method to universally capture regime transitions using the decomposition of the velocity field into toroidal and poloidal parts. A good agreement with other common methods is found, having, however, several advantages over them: It captures all the transitions. It works independent of the Prandtl number and the aspect ratio. It is based on a global quantity, and, thus, is very robust. Secondly, the influence of temperature-dependent material properties on Rayleigh- Bénard convection was investigated in three different liquids, ranging from a very small Prandtl number for mercury with Pr = 0.0232, over a moderate one for water with Pr = 4.38, to a very large one for glycerol with Pr = 2547.9. A series of three-dimensional DNS was conducted in a cylindrical cell with a unity aspect ratio. Simulations were performed under OB conditions for all three liquids and furthermore, various NOB conditions, i.e. temperature differences, were studied on the examples of water and glycerol. For that purpose, I implemented temperature-dependent material properties into a finite volume DNS code, by prescribing polynomial functions (up to seventh order in the case of glycerol and up to third order in the case of water) for the viscosity, the heat conductivity and the density. The DNS revealed that NOB effects lead to a breakdown of the top-bottom symmetry typical for OB simulations. The observed NOB effects include, but are not limited to, different thermal and viscous boundary layer thicknesses, asymmetric plume dynamics and an increase of the centre temperature. Their intensity strongly depends on the particular fluid. Finally, rotating Rayleigh-Bénard convection was studied both under OB and under NOB conditions on the example of water. Rotation applied to NOB thermal convection reduces the central temperature enhancement. Under NOB conditions the top (bottom) thermal and viscous boundary layers become equal for a slightly larger (smaller) inverse Rossby number than in the OB case. Moreover, for rapid rotation the thermal bottom boundary layers become thicker than the top ones. The Nusselt number normalized by that in the non-rotating case depends similarly on 1/Ro in both, the NOB and the OB cases. The deviation between the Nusselt number under OB and NOB conditions is minimal when the thermal and viscous boundary layers are equal.