Magnetic damping of jet flows in quasi-two-dimensional Rayleigh-Bénard convection.

The mechanism responsible for the damping of the large-scale, azimuthally directed jets observed at Jupiter's surface is not well known, but electromagnetic forces are suspected to play a role as the planet's electrical conductivity increases radially with depth. To isolate the jet damping process, we carry out a suite of direct numerical simulations of quasi-two-dimensional, horizontally periodic Rayleigh-Bénard convection with stress-free boundary conditions in the presence of an external, vertical magnetic field. Jets, punctuated by intermittent convective bursts, develop at Rayleigh numbers (Ra, ratio of buoyancy to diffusion) beyond 10^{5} when the magnetic field is relatively weak. Five primary flow regimes are found by varying 10^{3}≤Ra≤10^{10} and the Chandrasekhar number (Ch, ratio of Lorentz to viscosity) 0≤Ch≤10^{6}: (i) steady convection rolls, (ii) steady magneto-columns, (iii) unsteady to turbulent magneto-plumes, (iv) horizontally drifting magneto-plumes, and (v) jets with intermittent turbulent convective bursts. We parse the parameter space using transitions derived from the interaction parameter (N, ratio of Lorentz to inertia). The transition to the regime dominated by jets has the most immediate applications to the magnetic damping of Jovian jet flows, where the separation between jets and a magnetically constrained system occurs at a jet-based interaction parameter value of N_{J}≈1. We approximate the value of the Jovian interaction parameter as a function of depth, and find that the jets may brake at ≈6000 km below the surface, which is deeper than recent estimates from NASA's Juno mission. This suggests that mechanisms in addition to electromagnetic forces are likely required to fully truncate the jets.

The Elbert range of magnetostrophic convection. I. Linear theory.

In magnetostrophic rotating magnetoconvection, a fluid layer heated from below and cooled from above is equidominantly influenced by the Lorentz and the Coriolis forces. Strong rotation and magnetism each act separately to suppress thermal convective instability. However, when they act in concert and are near in strength, convective onset occurs at less extreme Rayleigh numbers ( R a , thermal forcing) in the form of a stationary, large-scale, inertia-less, inviscid magnetostrophic mode. Estimates suggest that planetary interiors are in magnetostrophic balance, fostering the idea that magnetostrophic flow optimizes dynamo generation. However, it is unclear if such a mono-modal theory is realistic in turbulent geophysical settings. Donna Elbert first discovered that there is a range of Ekman ( E k , rotation) and Chandrasekhar ( C h , magnetism) numbers, in which stationary large-scale magnetostrophic and small-scale geostrophic modes coexist. We extend her work by differentiating five regimes of linear stationary rotating magnetoconvection and by deriving asymptotic solutions for the critical wavenumbers and Rayleigh numbers. Coexistence is permitted if E k < 16 / ( 27 π ) 2 and C h ≥ 27 π 2 . The most geophysically relevant regime, the Elbert range, is bounded by the Elsasser numbers 4 3 ( 4 4 π 2 E k ) 1 / 3 ≤ Λ ≤ 1 2 ( 3 4 π 2 E k ) - 1 / 3 . Laboratory and Earth's core predictions both exhibit stationary, oscillatory, and wall-attached multi-modality within the Elbert range.

Jump rope vortex in liquid metal convection.

Understanding large-scale circulations (LSCs) in turbulent convective systems is important for the study of stars, planets, and in many industrial applications. The canonical model of the LSC is quasi-planar with additional horizontal sloshing and torsional modes [Brown E, Ahlers G (2009) J Fluid Mech 638:383-400; Funfschilling D, Ahlers G (2004) Phys Rev Lett 92:194502; Xi HD et al. (2009) Phys Rev Lett 102:044503; Zhou Q et al. (2009) J Fluid Mech 630:367-390]. Using liquid gallium as the working fluid, we show, via coupled laboratory-numerical experiments in tanks with aspect ratios greater than unity ([Formula: see text]), that the LSC takes instead the form of a "jump rope vortex," a strongly 3D mode that periodically orbits around the tank following a motion much like a jump rope on a playground. Further experiments show that this jump rope flow also exists in more viscous fluids such as water, albeit with a far smaller signal. Thus, this jump rope mode is an essential component of the turbulent convection that underlies our observations of natural systems.

Geomagnetic polar minima do not arise from steady meridional circulation.

Observations of the Earth's magnetic field have revealed locally pronounced field minima near each pole at the core-mantle boundary (CMB). The existence of the polar magnetic minima has long been attributed to the supposed large-scale overturning circulation of molten metal in the outer core: Fluid upwells within the inner core tangent cylinder toward the poles and then diverges toward lower latitudes when it reaches the CMB, where Coriolis effects sweep the fluid into anticyclonic vortical flows. The diverging near-surface meridional circulation is believed to advectively draw magnetic flux away from the poles, resulting in the low intensity or even reversed polar magnetic fields. However, the interconnections between polar magnetic minima and meridional circulations have not to date been ascertained quantitatively. Here, we quantify the magnetic effects of steady, axisymmetric meridional circulation via numerically solving the axisymmetric magnetohydrodynamic equations for Earth's outer core under the magnetostrophic approximation. Extrapolated to core conditions, our results show that the change in polar magnetic field resulting from steady, large-scale meridional circulations in Earth's outer core is less than [Formula: see text] of the background field, significantly smaller than the [Formula: see text] polar magnetic minima observed at the CMB. This suggests that the geomagnetic polar minima cannot be produced solely by axisymmetric, steady meridional circulations and must depend upon additional tangent cylinder dynamics, likely including nonaxisymmetric, time-varying processes.

Regimes of Coriolis-Centrifugal Convection.

Centrifugal buoyancy affects all rotating turbulent convection phenomena, but is conventionally ignored in rotating convection studies. Here, we include centrifugal buoyancy to investigate what we call Coriolis-centrifugal convection (C^{3}), characterizing two so far unexplored regimes, one where the flow is in quasicyclostrophic balance (QC regime) and another where the flow is in a triple balance between pressure gradient, Coriolis and centrifugal buoyancy forces (CC regime). The transition to centrifugally dominated dynamics occurs when the Froude number Fr equals the radius-to-height aspect ratio γ. Hence, turbulent convection experiments with small γ may encounter centrifugal effects at lower Fr than traditionally expected. Further, we show analytically that the direct effect of centrifugal buoyancy yields a reduction of the Nusselt number Nu. However, indirectly, it can cause a simultaneous increase of the viscous dissipation and thereby Nu through a change of the flow morphology. These direct and indirect effects yield a net Nu suppression in the CC regime and a net Nu enhancement in the QC regime. In addition, we demonstrate that C^{3} may provide a simplified, yet self-consistent, model system for tornadoes, hurricanes, and typhoons.

Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: Single mode solutions.

The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. This multiscale model represents an asymptotically exact form of an α^{2} mean field dynamo model in which the small-scale convection is represented explicitly by finite amplitude, single mode solutions. Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinetic helicity is observed to be a monotonically increasing function of the Rayleigh number. As a result, very small magnetic Prandtl number dynamos can be found for sufficiently large Rayleigh numbers. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Kinematic dynamo action is strongly controlled by the profile of the helicity; single mode solutions which exhibit boundary layer behavior in the helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection. With regard to planetary dynamos, these results suggest that the low magnetic Prandtl number dynamos typical of liquid metals are more easily driven by thermal convection than by compositional convection.

Magnetostrophic balance as the optimal state for turbulent magnetoconvection.

The magnetic fields of Earth and other planets are generated by turbulent convection in the vast oceans of liquid metal within them. Although direct observation is not possible, this liquid metal circulation is thought to be dominated by the controlling influences of planetary rotation and magnetic fields through the Coriolis and Lorentz forces. Theory famously predicts that planetary dynamo systems naturally settle into the so-called magnetostrophic state, where the Coriolis and Lorentz forces partially cancel, and convection is optimally efficient. Although this magnetostrophic theory correctly predicts the strength of Earth's magnetic field, no laboratory experiments have reached the magnetostrophic regime in turbulent liquid metal convection. Furthermore, computational dynamo simulations have as yet failed to produce a magnetostrophic dynamo, which has led some to question the existence of the magnetostrophic state. Here, we present results from the first, to our knowledge, turbulent, magnetostrophic convection experiments using the liquid metal gallium. We find that turbulent convection in the magnetostrophic regime is, in fact, maximally efficient. The experimental results clarify these previously disparate results, suggesting that the dynamically optimal magnetostrophic state is the natural expression of turbulent planetary dynamo systems.

Turbulent convection in liquid metal with and without rotation.

The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr << 1. Most analog models of planetary dynamos, however, use moderate Pr fluids, and the systematic influence of reducing Pr is not well understood. We perform rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0.025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr < 1 and Pr > 1 fluids, respectively.

Thermal evidence for Taylor columns in turbulent rotating Rayleigh-Bénard convection.

We investigate flow structures in rotating Rayleigh-Bénard convection experiments in water using thermal measurements. We focus on correlations between time series measurements of temperature in the top and bottom boundaries. Distinct anticorrelations are observed for rapidly rotating convection, which are argued to attest to heat transport by convective Taylor columns. In support of this argument, these quasigeostrophic flow structures are directly observed in flow visualizations, and their thermal signature is qualitatively reproduced by a simple model of heat transport by columnar flow. Weakly rotating and nonrotating convection produces positively correlated temperature changes across the layer, indicative of heat transport by large-scale circulation. We separate these regimes using a transition parameter that depends on the Rayleigh and Ekman numbers, RaE3/2.

Boundary layer control of rotating convection systems.

Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments, and is broadly applicable to natural convection systems.

A reappraisal of the habitability of planets around M dwarf stars.

Stable, hydrogen-burning, M dwarf stars make up about 75% of all stars in the Galaxy. They are extremely long-lived, and because they are much smaller in mass than the Sun (between 0.5 and 0.08 M(Sun)), their temperature and stellar luminosity are low and peaked in the red. We have re-examined what is known at present about the potential for a terrestrial planet forming within, or migrating into, the classic liquid-surface-water habitable zone close to an M dwarf star. Observations of protoplanetary disks suggest that planet-building materials are common around M dwarfs, but N-body simulations differ in their estimations of the likelihood of potentially habitable, wet planets that reside within their habitable zones, which are only about one-fifth to 1/50th of the width of that for a G star. Particularly in light of the claimed detection of the planets with masses as small as 5.5 and 7.5 M(Earth) orbiting M stars, there seems no reason to exclude the possibility of terrestrial planets. Tidally locked synchronous rotation within the narrow habitable zone does not necessarily lead to atmospheric collapse, and active stellar flaring may not be as much of an evolutionarily disadvantageous factor as has previously been supposed. We conclude that M dwarf stars may indeed be viable hosts for planets on which the origin and evolution of life can occur. A number of planetary processes such as cessation of geothermal activity or thermal and nonthermal atmospheric loss processes may limit the duration of planetary habitability to periods far shorter than the extreme lifetime of the M dwarf star. Nevertheless, it makes sense to include M dwarf stars in programs that seek to find habitable worlds and evidence of life. This paper presents the summary conclusions of an interdisciplinary workshop (http://mstars.seti.org) sponsored by the NASA Astrobiology Institute and convened at the SETI Institute.

New perspectives on ancient Mars.

Mars was most active during its first billion years. The core, mantle, and crust formed within approximately 50 million years of solar system formation. A magnetic dynamo in a convecting fluid core magnetized the crust, and the global field shielded a more massive early atmosphere against solar wind stripping. The Tharsis province became a focus for volcanism, deformation, and outgassing of water and carbon dioxide in quantities possibly sufficient to induce episodes of climate warming. Surficial and near-surface water contributed to regionally extensive erosion, sediment transport, and chemical alteration. Deep hydrothermal circulation accelerated crustal cooling, preserved variations in crustal thickness, and modified patterns of crustal magnetization.