Influence of boundary conditions on rapidly rotating convection and its dynamo action in a plane fluid layer

The Childress-Soward model, consisting of a an electrically conducting RayleighBenard layer rotating about a vertical axis, is the conceptually simplest model configuration that captures all essentials of convectively driven dynamos. Here we study the effects of different boundary conditions on this type of dynamo. This closes a gap in the existing literature, which has primarily focused on simple, but geophysically not very realistic, cases. Furthermore, the extensive literature on boundary layers in nonrotating and rotating Rayleigh-Benard convection makes the Childress-Soward model an ideal test bed for illuminating the fundamental effects that the boundary conditions have on convection-driven dynamos. In this study we systematically vary the thermal, mechanical, and electrical boundary conditions in direct numerical simulations, with a focus on flow regimes characterized by geostrophic turbulence. One key result applies to both dynamos and nonmagnetic, rotating convection. We show that for no-slip boundaries, the Nusselt number increases significantly when a fixed heat flux is imposed instead of a given temperature difference. This effect can be explained by an interplay of Ekman pumping and the internal structure of the thermal boundary layer, which is very sensitive to thermal boundary conditions. Dynamical changes are shown to exist only within the boundary layers, such that the bulk dynamics remains largely unaffected. In the dynamo case, we argue that care needs to be taken in order to ensure comparable energetics when changing from fixed-temperature to fixed-flux conditions. If done properly, no significant differences in the leading order features of the resulting dynamos are observed. In particular, the thermal boundary conditions have no noticeable influence on the horizontal flow scales, as might have been expected from studies in spherical geometry. In contrast, the mechanical boundary conditions largely control whether or not large-scale flows and fields can be generated. For no-slip boundaries, Ekman friction strongly suppresses upscale transport and eliminates the large-scale vortex dynamos that exist in the stress-free case. Finally, the magnetic boundary conditions are shown to strongly affect the topology of the generated magnetic fields. For an insulating exterior, the magnetic field is most intense in the central part of the fluid layer, whereas we observe a strong magnetic field buildup close to perfectly conducting boundaries. For large magnetic Reynolds numbers, we further observe thin layers of intense horizontal field attached to perfect conductors. The horizontal flow scales, however, remain largely unaffected in the investigated parameter regime.