Multiple jets and bursting in the rapidly rotating convecting two-dimensional annulus model with nearly plane-parallel boundaries

Abstract

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 short-lived 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 $\beta$-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 $\beta$ limit. However, the $\beta$-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 $\beta$-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.