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Planetary Dynamos: Effects of Electrically Conducting flows Overlying Turbulent Regions of Magnetic field Generation

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Planetary Dynamos: Effects of Electrically Conducting flows Overlying Turbulent Regions of Magnetic field Generation Icarus 172 (2004) 305–315 www.elsevier.com/locate/icarus Planetary dynamos: effects of electrically conducting flows overlying turbulent regions of magnetic field generation Gerald Schubert a,∗, Kit H. Chan b, Xinhao Liao c, Keke Zhang d a Department of Earth and Space Sciences, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, USA b Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China c Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China d School of Mathematical Sciences, University of Exeter, EX4 4QE, United Kingdom Received 26 September 2003; revised 25 March 2004 Available online 7 August 2004 Abstract A fully three-dimensional, nonlinear, time-dependent, multi-layered spherical kinematic dynamo model is used to study the effect on the observable external magnetic field of flow in an electrically conducting layer above a spherical turbulent dynamo region in which the α effect generates the magnetic field. It is shown that the amplitude and structure of an observable planetary magnetic field are largely determined by the magnitude and structure of the flow in the overlying layer. It is also shown that a strong-field planetary dynamo can be readily produced by the effect of an electrically conducting flow layer at the top of a convective core. The overlying layer and the underlying convective region constitute a magnetically strongly coupled system. Such overlying layers might exist at the top of the Earth’s core due to chemical or thermal causes, in the cores of other terrestrial planets for similar reasons, and in Saturn due to the differentiation of helium from hydrogen. An electrically conducting and differentially rotating layer could exist above the metallic hydrogen region in Jupiter and affect the jovian magnetic field similar to the overlying layers in other planets. Lateral temperature gradients resulting in thermal winds drive the flow in the overlying layers. All planetary magnetic fields could be maintained by similar turbulent convective dynamos in the field-generation regions of planets with the differences among observable magnetic fields due to different circulations in the overlying electrically conducting layers. 2004 Elsevier Inc. All rights reserved. Keywords: Geophysics; Magnetic fields 1. Introduction where V is the typical amplitude of convective flows within the core, D is the thickness (radius) of the core and λ is It is generally accepted that planetary magnetic fields are the magnetic diffusivity (Moffatt, 1978). For Earth, we esti- ≈ −4 −1 ≈ 2 −1 = × 6 generated through magnetohydrodynamic processes in their mate that V 10 ms , λ 1m s and D 3 10 m electrically conducting fluid cores by thermal or composi- (Gubbins and Roberts, 1987) and Rm is about 300. For = × −2 −1 tional convection (Moffatt, 1978; Fearn, 1998). An essential Jupiter, if we take V 3 10 ms based on mixing ≈ × 7 condition for a planet to possess an intrinsic magnetic field length theory, D 3 10 m and the magnetic diffusiv- ≈ 2 −1 × 4 is that it has a sufficiently large magnetic Reynolds number ity λ 30 m s , Rm is about 3 10 (Stevenson, 2003). A fundamental parameter that determines the properties of Rm a convective flow, whether it is laminar or turbulent, is the VD Reynolds number Re Rm = O(10), λ VD R = e ν * Corresponding author. (or the Rayleigh number Ra ), in the convective region of a E-mail address: [email protected] (G. Schubert). planet, where ν is the kinematic viscosity. For the Earth’s 0019-1035/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2004.06.007 306 G. Schubert et al. / Icarus 172 (2004) 305–315 core, ν ≈ 10−6 m2 s−1 (Gubbins and Roberts, 1987) and oretical problem of how an inhomogeneous mantle drives 8 Re = O(10 ); for Jupiter, if we take a similar value for a dominantly toroidal flow by the thermal-wind mechanism 9 ν, Re is about O(10 ).AlargeRe (Ra) usually suggests near the core–mantle boundary was studied by Zhang and a strongly turbulent convective region (Sumita and Olson, Gubbins (1992). Experiments on convection driven by an ex- 2000), though the effect of planetary rotation and magnetic ternally imposed inhomogeneous heat flux were carried out fields would modify the features of convection. Though the by Sumita and Olson (2000). precise values of these parameters are uncertain, they clearly For Saturn, Stevenson (1980, 1982) suggested that there suggest that there exist turbulent flows in Earth and Jupiter exists a stable conducting fluid shell above the interior dy- that can readily drive and sustain dynamos. namo generation region as a result of the ongoing gravi- For a rapidly rotating planet with sufficiently large val- tational differentiation of helium from hydrogen (see also ues of Rm and Re (or Ra ), it is reasonable to assume that Fortney and Hubbard, 2003). To explain the axisymmetry of the core turbulence is associated with an α effect and that Saturn’s magnetic field, Stevenson (1980, 1982) considered the form of α has a symmetry reflecting the rapid rotation. a multilayered Saturn model with a stably stratified conduct- In this case, we would expect to observe a planetary mag- ing fluid shell between the dynamo generation interior and netic field dominated by a dipole positioned at the planet’s the external region (see also Love, 2000). In Stevenson’s center and aligned with the axis of rotation (Roberts, 1972). (1982) model, a toroidal flow is driven in the shell by an Nevertheless, the observed magnetic fields of the planets are equator-to-pole temperature difference arising from the tem- significantly different (Connerney, 1993). We explain this by perature condition of Saturn’s atmosphere. He argued that proposing that the observed structure of a planetary magnetic the conducting layer is stably stratified and the axisymmet- field is largely determined by the amplitude and pattern of ric toroidal flow in the layer tends to make the external flow in an electrically conducting flow layer that lies above field of Saturn axisymmetric. For Jupiter, shock wave ex- the turbulent convective magnetic field generation region. periments (Nellis et al., 1996) indicate that magnetic dif- The existence of a stably stratified electrically conducting fusivity in the jovian interior increases gradually from the layer at the top of the Earth’s outer core has been suggested field-generation metallic core to the outer semi-conducting by a number of authors (e.g., Braginsky, 1984, 1998, 1999, flow region. The electrically conducting and differentially 2000; Whaler, 1980; Lister and Buffett, 1998). During the rotating layer above the metallic hydrogen region in Jupiter general cooling of the Earth, the inner core grows and the would affect the jovian magnetic field similar to the overly- light constituents excluded from the inner core rise upward ing layers in other planets. through the outer core, perhaps as blobs. Some fraction of The primary aim of this paper is to understand the gen- the light constituents might survive remixing to create and eral effects of an electrically conducting flow layer on the sustain a stable layer at the top of the core (Braginsky, 1984; amplitude and structure of a planetary magnetic field gener- Moffatt and Loper, 1994). Because of the small density dif- ated by dynamo action in an underlying turbulent convecting ference between the stable layer and the outer core, the exis- core. It is not our purpose to model the magnetic field of tence of the layer would be difficult to detect seismically. a particular planet. We investigate the following scenario As a result, this stable layer has been referred to as “the through numerical simulations. An electrically conducting, hidden ocean” (Braginsky, 1998, 1999, 2000; Shearer and thin flow layer at the top of a core or regions of magnetic Roberts, 1997). An alternative argument for the existence of field generation by turbulent convection is thermally cou- a stably stratified conducting shell was put forward by Lister pled with the lateral thermal heterogeneity of the overlying and Buffett (1998). They suggested that a negative buoyancy region (the lower mantle in the case of the Earth). This ther- flux across the core–mantle boundary (the heat flux imposed mal coupling drives thermal winds in the thin conducting by the slowly convecting mantle is less than the value that layer. The conducting layer is, in turn, magnetically coupled could be conducted up the core adiabat) can form a stable to the turbulent convective core through the magnetic inter- layer of sufficiently strong stratification to prevent substan- face conditions at the base of the layer, which influences the tial penetration of rising blobs from below (see also Labrosse whole process of magnetic field generation. This scenario is et al., 1997). However, there is no conclusive evidence to fundamentally different from that discussed by Zhang and support the existence of a stably stratified conducting layer Gubbins (1992) and Olson and Christensen (2002) for the at the top of the Earth’s outer core (Lay and Young, 1990). Earth. These authors considered how the convective flow The important influence of the inhomogeneous mantle on and the generated magnetic field in the outer core are di- core convection and the geodynamo has been recognized for rectly affected by the nonuniform temperature or heat flux a long time and there is a large literature on possible ob- boundary conditions in the absence of an overlying layer. servational effects and on the possible existence of toroidal The influence of this direct thermal coupling between the flows in the stable layer that could arise from lateral hetero- lower mantle and outer core is quite weak when convection geneity on the core–mantle boundary (e.g., Gubbins, 1987; is fully turbulent and has small scales incompatible with the Gubbins and Bloxham, 1987; Gubbins and Richards, 1986; large lateral scale of the core–mantle boundary.
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