Multiple zonal jets and drifting: Thermal convection in a rapidly rotating spherical shell compared to a quasigeostrophic model

Abstract

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.

Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores

“…Using a QG model of thermal convection, Rotvig (2007) shows that zonal jets drift inwards provided that the slope β has a significant dependence on radius, while QG models with constant β produce multiple jets that do not drift (e.g. Jones et al, 2003).…”

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

“…This result relates well to Gilman (1978b) and Christensen (2001), who find only two-jet solutions outside the tangent cylinder at relatively high Ekman numbers. Rotvig (2006) demonstrated that in a three-dimensional Boussinesq shell with non-slip boundaries, imposed temperature contrast, and a ratio of 0.35 between the inner and outer radius, multi-jet solutions begin to emerge when E < 5 × −6 .…”

“…The form of C is given by equation (2.8), but in more complex models, involving curved boundaries, compressibility and magnetic fields, the functional form of C may alter. Rotvig (2006) analyses a duct with curved top and bottom boundaries. In a simplified version of this system, β(y) and C(y) may be identified as the coefficients in front of −∂ x V and −|β| 1/2 ∇ 2 V , respectively in equation (2.6).…”

“…The annulus model developed in Busse (1970) exploits this fact. Also the models in Aubert, Gillet & Cardin (2003), Gillet & Jones (2006) and Rotvig (2006) belong to this family of quasi-geostrophic models. They show that their models in many respects compare well with corresponding three-dimensional results in the region outside the tangent cylinder.…”

On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus

“…However, performing three-dimensional nonlinear simulations in spherical geometry can be computationally expensive. Quasi-geostrophic models 7,10,11 assume that the rapid rotation leads to columnar structures with little z-dependence, leading to two-dimensional models. The Busse annulus 7,[12][13][14][15] is one such quasi-geostrophic model.…”