[1] We investigate the occurrence of multiple jet zonal flows in the 2D rotating annulus model, extended to include the possibility of boundary friction. We consider Rayleigh numbers up to 10 times critical. Without boundary friction the majority of our solutions are single-jet zonal flows, but when boundary friction is present, persistent multiple jet solutions are found much more easily. Compared to the stress-free case, the number of jets increases, though the strength of the zonal flow decreases. The dependence of these features on Ekman and Rayleigh number is discussed, suggesting that at values well beyond the reach of present 3D simulations, solutions resembling the observed jovian zonal flow may exist. The boundary condition at the metallic/insulating hydrogen interface will be an important part of any explanation of the occurrence of multiple jets on the planet Jupiter.

We present a fully 3D self-consistent convection-driven dynamo model with reference to the geodynamo. A relatively low Ekman number regime is reached, with the aim of investigating the dynamical behavior at low viscosity. This regime is computationally very demanding, which has prompted us to adopt a plane layer model with an inclined rotation vector, and to make use of efficiently parallelized code. No hyperdiffusion is used, all diffusive operators are in the classical form. Our model has infinite Prandtl number, a Rayleigh number that scales as E(-1/3) (E being the Ekman number), and a constant Roberts number. The optimized model allows us to study dynamos with Ekman numbers in the range [10(-5),10(-4)]. In this regime we find strong-field dynamos where the induced magnetic fields satisfy Taylor's constraint to good accuracy. The solutions are characterized by (i) a MAC balance within the bulk, i.e., Coriolis, pressure, Lorentz, and buoyancy forces are of comparable magnitude, while viscous forces are only significant in thin boundary layers, (ii) the Elsasser number is O(10), (iii) the strong magnetic fields cannot prevent small-scale structures from becoming dominant over the large-scale components, (iv) the Taylor-Proudman effect is detectable, (v) the Taylorization decreases as the Ekman number is lowered, and (vi) the ageostrophic velocity component makes up 80% of the flow.

We analyse numerical solutions in the annulus model of rotating convection outside the tangent cylinder in a spherical shell. This model is capable of producing zonal flows with multiple jets. We investigate the conditions under which multi-jet solutions can be found. Although boundary friction reduces the strength of the zonal flow, it enhances the formation of multi-jets. More general models have a well-defined Ekman-layer term. In the annulus model, the Ekman-layer term has a similar form, but with variable strength. We have explored how the strength of the Ekman-layer term affects the form and strength of the zonal flows. We find that strong multi-jet zonal flows can be found for realistic values of the boundary friction, and hence have implications for convection in experiments and enclosed planetary cores. In addition, at higher Rayleigh numbers the importance of boundary friction is enhanced relative to bulk viscosity. Convection in the annulus model often occurs in the form of shortlived bursts as opposed to quasi-steady equilibriums. We have investigated when these events occur and their characteristics. In particular, we find precursors and afterglows of the convective bursts. We have obtained the β-scaling for a range of quantities when the thermal forcing is moderate. An examination of the components of the energy rate of change shows that the total Ekman-layer dissipation is of second order in the large β limit. However, the β-scaling of the forces driving the zonal flow seems to suggest that the zonal Ekman-layer dissipation remains important. We have introduced the concept of flow Taylorization, an analogue to the Taylorization used in magnetohydrodynamics studies and find a β-scaling of this quantity compatible with the moderate strength of the zonal flow. We also determine the typical length scale on which convection operates and compare this to the numerically determined length scale.

We demonstrate that thermal convection in a rapidly rotating spherical shell may produce zonal flows outside the tangent cylinder that consist of multiple alternating jets drifting towards the interior. A quasigeostrophic model that in model space is located between the classical annulus and the spherical shell, has been constructed. In this generalized annulus model we allow for terms in the Ekman correction to the flow that are usually neglected. It is shown that these terms may create observable effects at low Ekman numbers. Some of the remaining differences between the two-dimensional (2D) and 3D model may be explained by the missing heat transport along the rotation axis of the 2D model. The 2D model makes it possible to show that the occurrence of jet drift requires a significant radial dependence of the beta parameter. In addition, the relatively low numerical costs of the 2D model allow extensive parameter studies. For an increasing rotation rate and fixed moderate thermal driving, the 2D model predicts (i) an increased zonal flow strength, (ii) an increased number of jets related to Rhines length scale, and (iii) an inward drift of the center jets. For an increasing thermal driving and fixed rotation rate, the solutions of the 2D model develop stronger zonal flows with a reduced number of still faster drifting jets. The jet drift is ultimately converted into fluctuations of a couple of steady jets as the center region outside the tangent cylinder is being cleared of jets. These solutions, that display reduced Ekman layer effects, resemble solutions obtained with stress-free boundary conditions.

No abstract