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In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are simultaneously representative of the energy contained in the solution (energetically relevant) and also indicative of the established force balance (dynamically relevant). In the case of numerical simulations of rotating convection and magnetohydrodynamic dynamos in spherical shells, it has remained difficult to measure length scales that are both energetically and dynamically relevant, a situation that has led to conflicting interpretations, and sometimes misrepresentations of the underlying force balance. By analysing an extensive set of magnetic and non-magnetic models, we focus on two length scales that achieve both energetic and dynamical relevance. The first one is the peak of the poloidal kinetic energy spectrum, which we successfully compare to crossover points on spectral representations of the force balance. In most dynamo models, this result confirms that the dominant length scale of the system is controlled by a previously proposed quasi-geostrophic (QG-) MAC (Magneto-Archimedean-Coriolis) balance. In non-magnetic convection models, the analysis generally favours a QG-CIA (Coriolis-Inertia-Archimedean) balance. Viscosity, which is typically a minor contributor to the force balance, does not control the dominant length scale at high convective supercriticalities in the non-magnetic case, and in the dynamo case, once the generated magnetic energy largely exceeds the kinetic energy. In dynamo models, we introduce a second energetically relevant length scale associated with the loss of axial invariance in the flow. We again relate this length scale to another crossover point in scale-dependent force balance diagrams, which marks the transition between large-scale geostrophy (the equilibrium of Coriolis and pressure forces) and small-scale magnetostrophy, where the Lorentz force overtakes the Coriolis force. Scaling analysis of these two energetically and dynamically relevant length scales suggests that the Earth's dynamo is controlled by a QG-MAC balance at a dominant scale of about |$200 \, \mathrm{km}$|⁠ , while magnetostrophic effects are deferred to scales smaller than |$50 \, \mathrm{km}$|⁠. [ABSTRACT FROM AUTHOR]

We present a numerical study on convection in a rotating spherical shell that explores the influence of the two possible driving sources in planetary iron cores: temperature differences exceeding the adiabatic gradient and compositional differences that arise from the rejection of light elements at the inner core freezing front. Similarly, both effects play an important role in driving convection in Earth's outer core but their individual contribution remains uncertain. Dynamically, both components significantly differ in terms of their diffusion timescales since heat diffuses much faster than chemical elements. To investigate the influence of the driving mechanisms on the convective flow pattern, we consider different scenarios including the two extreme cases of purely thermally and purely compositionally driven convection and the more likely situation of a joint action of both sources. We solely focus on implications resulting from the given difference in the thermal and chemical diffusivity. For the present, we disregard the effects that might arise from the more realistic case of distinct thermal and chemical boundary conditions. We show that the driving mechanism strongly affects the resulting flow pattern, for example, differential rotation and global quantities such as mean energy and transport efficiencies. Additionally, we use a selected case for a specific comparison of two different codes based on a pseudospectral and a finite volume formulation, respectively. [ABSTRACT FROM AUTHOR]

We propose a spectral transfer model for the secular variation of the geomagnetic core field to explain the simultaneous decrease in dipole field intensity and the increase in non-dipole field intensity from 1840 to the present in terms of a dynamo cascade process. The main assumption of this model is that magnetic energy is transferred between adjacent spherical harmonic degrees in the Mauersberger–Lowes spectrum of the geomagnetic field. The key parameters are a set of coefficients that indicate the rate and direction of magnetic energy transfer through the spectrum. Applying the spectral transfer model to the historical period, we find that the quadrupole family of the core field can be characterized by a persistent inverse magnetic energy cascade from higher towards lower spherical harmonics. In the dipole family of the core field, we find cascade behaviour generally from lower to higher spherical harmonics, consistent with axial dipole decrease, but with a high level of time variability that correlates with variations in the dipole family intensity. During time intervals when the dipole family intensity rapidly decreases, energy appears to cascade towards higher spherical harmonics, beyond the limit of the observable part of the core field spectrum. During time intervals when the dipole family intensity is nearly constant, a more limited forward cascade appears to trap energy at intermediate spherical harmonics. Similar fluctuations in the rate and direction of spectral transfer are also seen in the Mauersberger–Lowes spectrum of a numerical dynamo model during a dipole decrease event that led to a polarity excursion. We discuss the possibility of this scenario for the current geomagnetic dipole decrease. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, here we show that excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus, we discuss how our results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: ). [ABSTRACT FROM AUTHOR]

Numerical simulations of rotating convection-driven dynamos have been found very useful to understand the inner workings of the geodynamo. Parametrization of small-scale processes can allow the simulations to approach a more realistic parameter range provided that these processes are modelled properly. In line with this effort, two turbulent models, the scale-similar model of Bardina et al. and a dynamic similarity model, have been applied to a rotating convection-driven plane-layer dynamo simulation with an infinite Pr number in this paper. The results from the similarity model are satisfactory: the large-scale magnetic/kinetic energies and rms magnetic/velocity field fluctuations are in much better agreement with the highly resolved solution than with the low-resolution direct simulation. The model is found to be much less sensitive to the filter scale than the a priori test. Implementation of a dynamic procedure to the similarity model gives better agreement provided that the two filtering scales are properly chosen. Effect of aspect ratio on the performance of the models is also studied by carrying out simulations with aspect ratio 1 and 2. The results show that performances of the models are not influenced by the aspect ratio chosen. [ABSTRACT FROM AUTHOR]