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.

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.

Several recent studies have used palaeomagnetic estimates of the virtual axial dipole moment to construct a quantitative stochastic model for fluctuations and reversals in the Earth's dipole field. We investigate the physical significance of the terms in a standard stochastic (Langevin) model using output from a numerical geodynamo model. The first term, known as the drift term, characterizes the slow adjustment of the dipole field toward a time-averaged state. We find that the timescale for this slow adjustment is set by the magnetic decay time of dipole fluctuations. These fluctuations are typically be represented by the first few decay modes. The second term is often called the noise term because it characterizes the influence of short-period convective fluctuations in the core. We establish a connection between the noise term and the rms variation in magnetic induction. Applying these results to the palaeomagnetic field suggests that the rms variation in dipole generation exceeds the mean rate of generation. Such large fluctuations may be necessary to permit magnetic reversals. Palaeomagnetic estimates of the drift term favour a high electrical conductivity in the core. A lower bound on electrical conductivity is 0.6 × 106 S m-1. Similarly, we establish an upper bound on turbulent magnetic diffusivity (0.8 m2 s-1), although realistic estimates may be much less. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

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.

The magnetic fields of planets and stars are thought to play an important role in the fluid motions responsible for their field generation, as magnetic energy is ultimately derived from kinetic energy. We investigate the influence of magnetic fields on convective dynamo models by contrasting them with non-magnetic, but otherwise identical, simulations. This survey considers models with Prandtl number Pr=1; magnetic Prandtl numbers up to Pm=5; Ekman numbers in the range 10 -3≥E≥10 -5; and Rayleigh numbers from near onset to more than 1000 times critical. Two major points are addressed in this letter. First, we find that the characteristics of convection, including convective flow structures and speeds as well as heat transfer efficiency, are not strongly affected by the presence of magnetic fields in most of our models. While Lorentz forces must alter the flow to limit the amplitude of magnetic field growth, we find that dynamo action does not necessitate a significant change to the overall flow field. By directly calculating the forces in each of our simulations, we show that the traditionally defined Elsasser number, λ i, overestimates the role of the Lorentz force in dynamos. The Coriolis force remains greater than the Lorentz force even in cases with λ i≃100, explaining the persistence of columnar flows in λ i>1 dynamo simulations. We argue that a dynamic Elsasser number, λ d, better represents the Lorentz to Coriolis force ratio. By applying the λ d parametrization to planetary settings, we predict that the convective dynamics (excluding zonal flows) in planetary interiors are only weakly influenced by their large-scale magnetic fields. The second major point addressed here is the observed transition between dynamos with dipolar and multipolar magnetic fields. We find that the breakdown of dipolar field generation is due to the degradation of helicity in the flow. This helicity change does not coincide with the destruction of columnar convection and is not strongly influenced by the presence of magnetic fields. Force calculations suggest that this transition may be related to a competition between inertial and viscous forces. If viscosity is indeed important for large-scale field generation, such moderate Ekman number models may not adequately simulate the dynamics of planetary dynamos, where viscous effects are expected to be negligible. © 2012 Elsevier B.V.

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.

The magnetic fields of planets and stars are generated by the motions of electrically conducting fluids within them. These fluid motions are thought to be driven by convective processes, as internal heat is transported outward. The efficiency with which heat is transferred by convection is integral in understanding dynamo processes. Several heat transfer scaling laws have been proposed, but the range of parameter space to which they apply has not been firmly established. Following the plane layer convection study by King et al. (2009), we explore a broad range of buoyancy forcing (Ra) and rotation strength (E-1) to show that heat transfer (Nu) in spherical dynamo simulations occurs in two distinct regimes. We argue that heat transfer scales as Nu ∼ Ra6/5 in the rapidly rotating regime and Nu ∼ Ra2/7 in the weakly rotating regime. The transition between these two regimes is controlled by the competition between the thermal and viscous boundary layers. Boundary layer scaling theory allows us to predict that the transition between the regimes occurs at a transitional Rayleigh number, Rat = E -7/4. Furthermore, boundary layer control of heat transfer is shown to relate to the interior temperature profiles of the models. In the weakly rotating regime, the interior fluid is nearly adiabatic. In the rapidly rotating regime, adverse mean temperature gradients abide, irrespective of the Reynolds number (Re). Extrapolating our results to Earth's core, we estimate that core convection resides in the rapidly rotating regime, with Ra ≈ 2 × 1024 (Ra/Rat ≈ 0.02), corresponding to a superadiabatic density variation of Δρ/ρ ≈ 10-7, which is significantly below the sensitivity of present seismic observations. Copyright 2010 by the American Geophysical Union.