The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths-a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors. © 2007 Elsevier Inc. All rights reserved.

Temporal variations of Saturn's equatorial jet and magnetic field hint at rich dynamics coupling the atmosphere and the deep interior. However, it has been assumed that rotation of the interior dynamo must be steady over tens of years of modern observations. Here we use a numerical convection model and scaling estimates to show how equatorial convective bursts can transfer angular momentum to the deeper interior. The numerical model allows angular momentum transfer between a fluid outer spherical shell and a rigid inner sphere. Convection drives a prograde equatorial jet exhibiting quasiperiodic bursts that fill the equatorial volume outside the tangent cylinder. For each burst strong changes in the equatorial surface velocity are associated with retrograde torque on the inner sphere. Our results suggest that Saturn's Great White Spot, a giant storm that was observed to fill the equatorial region in 1990, could mobilize a volume of fluid carrying roughly 15% of Saturn's moment of inertia. Conservation of angular momentum then implies that a 20% change in the equatorial jet angular velocity could change the average interior rotation rate by about 0.1% - roughly an order of magnitude less than the apparent rotation rate changes associated with Saturn's kilometric radio (SKR) signal. However, if the SKR signal originates outside the liquid metal core in a "planetary tachocline" that separates the layer of fast zonal flow from the magnetically controlled and slowly convecting deep interior, then convective bursts can provide a possible mechanism for the observed 1% SKR changes. © 2012. The American Astronomical Society. All rights reserved.

The bands of Jupiter represent a global system of powerful winds. Broad eastward equatorial jets are flanked by smaller-scale, higher-latitude jets flowing in alternating directions. Jupiter's large thermal emission suggests that the winds are powered from within, but the zonal flow depth is limited by increasing density and electrical conductivity in the molecular hydrogen-helium atmosphere towards the centre of the planet. Two types of planetary flow models have been explored: shallow-layer models reproduce multiple high-latitude jets, but not the equatorial flow system, and deep convection models only reproduce an eastward equatorial jet with two flanking neighbours. Here we present a numerical model of three-dimensional rotating convection in a relatively thin spherical shell that generates both types of jets. The simulated flow is turbulent and quasi-two-dimensional and, as observed for the jovian jets, simulated jet widths follow Rhines' scaling theory. Our findings imply that Jupiter's latitudinal transition in jet width corresponds to a separation between the bottom-bounded flow structures in higher latitudes and the deep equatorial flows.

Large-scale zonal flows, as observed on the giant planets, can be driven by thermal convection in a rapidly rotating spherical shell. Most previous models of convectively-driven zonal flow generation have utilized stress-free mechanical boundary conditions (FBC) for both the inner and the outer surfaces of the convecting layer. Here, using 3D numerical models, we compare the FBC case to the case with a stress free outer boundary and a non-slip inner boundary, which we call the mixed case (MBC). We find significant differences in surface zonal flow profiles produced by the two cases. In low to moderate Rayleigh number FBC cases, the main equatorial jet is flanked by a strong, high-latitude retrograde jets in the northern and southern hemispheres. For the highest Rayleigh number FBC case, the equatorial jet is flanked by strong reversed jets as well as two additional large-scale alternating jets at higher latitudes. The MBC cases feature stronger equatorial jets but, much weaker, small-scale alternating zonal flows are found at higher latitudes. Our high Rayleigh number FBC results best compare with the zonal flow pattern observed on Jupiter, where the equatorial jet is flanked by strong retrograde jets as well as small-scale alternating jets at high latitude. In contrast, the MBC results compare better with the observed flow pattern on Saturn, which is characterized by a dominant prograde equatorial jet and a lack of strong high latitude retrograde flow. This may suggest that the mechanical coupling at the base of the jovian convection zone differs from that on Saturn. © 2004 Elsevier Inc. All rights reserved.

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively. © 2007 Elsevier Inc. All rights reserved.

Jupiter and Saturn emit nearly twice the thermal energy they receive from the Sun. Although insolation decreases toward the poles, the large-scale outward heat flux is nearly uniform, with smaller-scale latitudinal undulations that correlate with the zonal jet streams. Here we present numerical models of rapidly rotating, turbulent 3-D convection in geometrically thin, uniformly forced layers of Boussinesq fluid that approximate the deep convection zones of Jupiter and Saturn. In previous studies we have demonstrated that such models generate zonal flows comparable to those observed on the gas giants. By analysing the simulated patterns of convective heat transfer, we show here that deep convection in the gas giants can explain the anomalously uniform large-scale thermal emissions as well as the jet-scale variations. In particular, we find that convective heat transfer by quasi-geostrophic thermal plumes in relatively thin spherical shell geometry generates an outward heat flow pattern with a broad equatorial minimum and peaks at the poles. The results suggest an alternative to the hypothesis that insolation controls the large-scale patterns of heat flux and zonal flow on the gas giants. Instead, we propose that the large-scale thermal and zonal flow fields originate deep within the planets' molecular envelopes. © 2008 The Authors Journal compilation © 2008 RAS.

Current geophysical knowledge of the planet Mercury is based upon observations from ground-based astronomy and flybys of the Mariner 10 spacecraft, along with theoretical and computational studies. Mercury has the highest uncompressed density of the terrestrial planets and by implication has a metallic core with a radius approximately 75% of the planetary radius. Mercury's spin rate is stably locked at 1.5 times the orbital mean motion. Capture into this state is the natural result of tidal evolution if this is the only dissipative process affecting the spin, but the capture probability is enhanced if Mercury's core were molten at the time of capture. The discovery of Mercury's magnetic field by Mariner 10 suggests the possibility that the core is partially molten to the present, a result that is surprising given the planet's size and a surface crater density indicative of early cessation of significant volcanic activity. A present-day liquid outer core within Mercury would require either a core sulfur content of at least several weight percent or an unusual history of heat loss from the planet's core and silicate fraction. A crustal remanent contribution to Mercury's observed magnetic field cannot be ruled out on the basis of current knowledge. Measurements from the MESSENGER orbiter, in combination with continued ground-based observations, hold the promise of setting on a firmer basis our understanding of the structure and evolution of Mercury's interior and the relationship of that evolution to the planet's geological history. © 2007 Springer Science+Business Media B.V.