The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast inertial waves slightly modified by the magnetic field and buoyancy are dominant under weak fields. However, the dominance of the slow waves is evident for strong fields satisfying $|ω_M/ω_C| \sim $ 0.1, where $ω_M$ and $ω_C$ are the frequencies of the Alfvén and inertial waves respectively. A MAC wave window of azimuthal wavenumbers is identified wherein helicity generation by the slow waves strongly correlates with dipole generation. Analysis of the magnetic induction equation suggests a poloidal--poloidal field conversion in the formation of the dipole. Finally, the attenuation of slow waves may result in polarity reversals in a strongly driven Earth's core.
A weak turbulence theory is derived for magnetohydrodynamics under rapid rotation and in the presence of a large-scale magnetic field. The angular velocity $Ω_0$ is assumed to be uniform and parallel to the constant Alfvén speed ${\bf b_0}$. Such a system exhibits left and right circularly polarized waves which can be obtained by introducing the magneto-inertial length $d \equiv b_0/Ω_0$. In the large-scale limit ($kd \to 0$; $k$ being the wave number), the left- and right-handed waves tend respectively to the inertial and magnetostrophic waves whereas in the small-scale limit ($kd \to + \inft…
Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly-nonlinear, long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ODE, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical-wire field, and …
The value of the Prandtl number $P$ exerts a strong influence on convection-driven dynamos in rotating spherical shells filled with electrically conducting fluids. Low Prandtl numbers promote dynamo action through the shear provided by differential rotation, while the generation of magnetic fields is more difficult to sustain in high-Prandtl-number fluids where higher values of the magnetic Prandtl number $P_m$ are required. The magnetostrophic approximation often used in dynamo theory appears to be valid only for relatively high values of $P$ and $P_m$. Dynamos with a minimum value of $P_m$ s…
The mechanism by which the Earth's magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Computational considerations previously restricted most numerical simulations to a regime where the diffusivities of momentum and electric current are roughly equal, leading to similar spectra for both velocities and magnetic fields. Here we present results of a suite of self-consistent spherical shell computations with ultra-low viscosities. The most Earth-like of our models (S4) has a twenty-fold difference in the aforementioned diffusivities, leading to signif…
In this study, we investigate preferences of dipolar magnetic structure from a seed magnetic field in the rapidly rotating spherical shell dynamo models. In this study, we set up a realistic model to show the effect of the Lorentz force in the polarity selection. The important results that has come out from our study is that the magnetic field acts on the flow much before the saturation. Our study suggests that the growth of the magnetic field is not a kinematic effect as one might think off, rather a dynamic effect. This dynamic effect grows as the field generated with time and finally brings…
Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions. Oscillations of the flow are introduced by varying the flow …
We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic $α^{2}$ dynamos in a finite cylinder. The dynamo action is due to an anisotropic $α$ effect which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the K…
Starting from the present version of the Riga dynamo experiment with its rotating magnetic eigenfield dominated by a single frequency we ask for those modifications of this set-up that would allow for a non-trivial magnetic field behaviour in the saturation regime. Assuming an increased ratio of azimuthal to axial flow velocity, we obtain energy oscillations with a frequency below the eigenfrequency of the magnetic field. These new oscillations are identified as magneto-inertial waves that result from a slight imbalance of Lorentz and inertial forces. Increasing the azimuthal velocity further,…
We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 1000. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. …
We report experimental results from three successful runs of a Bullard-type homopolar disc dynamo. The set-up consisted of a copper disc with a radius of 30 cm and thickness of 3 cm which was placed co-axially beneath a flat, multi-arm spiral coil of the same size and connected to it electrically at the centre and along the circumference by sliding liquid-metal contacts. The magnetic field was measured using Hall probes which were fixed on the top face of the coil. We measured also the radial voltage drop across the coil. When the disc rotation rate reached $Ω\approx 7$ Hz, the magnetic field …
Numerical simulations of the geodynamo in presence of an heterogeneous heating are presented. We study the dynamics and the structure of the magnetic field when the equatorial symmetry of the flow is broken. If the symmetry breaking is sufficiently strong, the m = 0 axial dipolar field is replaced by an hemispherical magnetic field, dominated by an oscillating m = 1 magnetic field. Moreover, for moderate symmetry breaking, a bistability between the axial and the equatorial dipole is observed. In this bistable regime, the axial magnetic field exhibits chaotic switches of its polarity, involving…
The dynamo effect is the most popular candidate to explain the non-primordial magnetic fields of astrophysical objects. Although many systematic studies of parameters have already been made to determine the different dynamical regimes explored by direct numerical geodynamo simulations, it is only recently that the regime corresponding to the outer core of the Earth characterized by a balance of forces between the Coriolis and Lorentz forces is accessible numerically. In most previous studies, the Lorentz force played a relatively minor role. For example, they have shown that a purely hydrodyna…
Field reversals are the most spectacular changes in the geomagnetic field but remain little understood. Paleomagnetic data primarily constrain the reversal rate and provide few additional clues. Reversals and excursions are characterized by a low in dipole moment that can last for some 10kyr. Some paleomagnetic records also suggest that the field decreases much slower before an reversals than it recovers afterwards and that the recovery phase may show an overshoot in field intensity. Here we study the dipole moment variations in several extremely long dynamo simulation to statistically explore…
We test the ability of large scale velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth.Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo.Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk.As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field again…
We study predictions of reversals of Earth's axial magnetic dipole field that are based solely on the dipole's intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical mod…
