Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically forced two-vortex flow inside a sphere are reported. The simulations are performed in the intermediate regime between the laminar flow and developed turbulence where a hydrodynamic instability is found to generate internal waves with a characteristic m=2 zonal wave number. It is shown that this time-periodic flow acts as a dynamo although snapshots of the flow as well as the mean flow are not dynamos. The magnetic fields' growth rate exhibits resonance effects depending on the wave frequency. Furthermore, a cyclic self-killing and self-recovering dynamo based on the relative alignment of the velocity and magnetic fields is presented. The phenomena are explained in terms of a mixing of non-orthogonal eigenstates of the time dependent linear operator of the magnetic induction equation. The potential relevance of this mechanism to dynamo experiments is discussed.
Using results of laboratory experiments, direct numerical simulations, geomagnetic and solar observations, it is shown that high moments of helicity distribution can dominate power spectra of the magnetic field generated by the magnetohydrodynamic (MHD) dynamo in swirling turbulence even for the cases with zero global helicity. The notion of helical distributed chaos has been used for this purpose.
We report the results of three-dimensional numerical simulations of convection-driven dynamos in relatively thin rotating spherical shells that show a transition from an strong non-oscillatory dipolar magnetic field to a weaker regularly oscillating dipolar field. The transition is induced primarily by the effects a stress-free boundary condition. The variation of the inner to outer radius ratio is found to have a less important effect.
A parametric study of the magnetic dipole behavior in resistive incompressible MHD inside a rotating sphere is performed, using direct numerical simulations and considering Reynolds and Ekman numbers as controlling parameters. The tendency is to obtain geodynamo-like magnetic dipole reversal regimes for sufficiently small Ekman and large Reynolds numbers. The typical dipole latitude obtained in the reversal regime is around 40 degrees (with respect to the rotation axis of the sphere). A statistical analysis of waiting times between dipole reversals is also performed, obtaining a non-Poissonian…
We have derived the closed system of averaged MHD-equations for general oscillating flows, which are purely oscillating in the main approximation. We have used the mathematical approach which combines the two-timing method and the notion of the distinguished limit. Properties of the commutators are used to simplify calculations. The direct connection with a vortex dynamo (or the Langmuir circulations) has been demonstrated and a conjecture on the MHD-dynamo has been formulated.
In this paper we describe the mode-to-mode energy transfers and energy fluxes of MHD turbulence. These energy transfers are very useful for understanding the turbulence dynamics, as well as for applications such as dynamo. We illustrate how the energy fluxes provide valuable insights into the mechanism of growth of the large-scale magnetic energy in dynamo.
The standard magnetohydrodynamic (MHD) description of the plasma in the hot, magnetized gas of the intra-cluster (ICM) medium is not adequate because it is weakly collisional. In such collisionless magnetized gas, the microscopic velocity distribution of the particles is not isotropic, giving rise to kinetic effects on the dynamical scales. These kinetic effects could be important in understanding the turbulence, as so as the amplification and maintenance of the magnetic fields in the ICM. It is possible to formulate fluid models for collisonless or weakly collisional gas by introducing modifi…
We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
We investigate three-dimensional magnetohydrodynamics turbulence in the presence of both a large-scale velocity and non-uniform magnetic field. By assuming a turbulence driven by an external forcing with both helical and non-helical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, $α$ and $β$ effect) in analogy with Reynolds. We show that turbulence viscosity and diffusivity are quenched for strong flow shear and magnetic field in the limits of weak and strong magnetic fi…
Rational large Reynolds number matched asymptotic expansions of three-dimensional nonlinear magneto-hydrodynamic (MHD) states are concerned. The nonlinear MHD states, assumed to be predominantly driven by a unidirectional shear, can be sustained without any linear instability of the base flow and hence are responsible for subcritical transition to turbulence. Two classes of nonlinear MHD states are found. The first class of nonlinear states emerged out of a nice combination of the purely hydrodynamic vortex/wave interaction theory by Hall \& Smith (1991) and the resonant absorption theories on…
We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results…
The DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) is intended as a platform both for large scale experiments related to geo- and astrophysics as well as for experiments related to thermohydraulic and safety aspects of liquid metal batteries and liquid metal fast reactors. The most ambitious projects in the framework of DRESDYN are a homogeneous hydromagnetic dynamo driven solely by precession and a large Taylor-Couette type experiment for the combined investigation of the magnetorotational instability and the Tayler instability. In this paper we give a short summary …
This Special Topic focuses on magnetohydrodynamic (MHD) processes in deep interiors of planets, in which their fluid dynamos are in operation. The dynamo-generated, global, magnetic fields provide a background for our solar-terrestrial environment. Probing the processes within the dynamos is a significant theoretical and computational challenge and any window into interior dynamics greatly increases our understanding. Such a window is provided by exploring rapid dynamics, particularly MHD waves about the dynamo-defined basic state. This field is the subject of current attention as geophysical …
Intense spin-down flows allow one to reach high Rm in relatively small laboratory setups using moderate mass of liquid metals. The spin-down flow in toroidal channels was the first flow configuration used for studying dynamo effects in non-stationary flows. In this paper, we estimate the effect of small-scale dynamo in liquid metal spin-down flows realized in laboratory experiments. Our simulations have confirmed the conclusion that the dynamo effects observed in the experiments done on gallium are weak -- a slight burst of small-scale magnetic energy arises only at the highest available rotat…
The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, both in the incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and its dependence with both rotating and precession frequency was analyzed. For the MHD case no self-sustaining dynamos were found for the prograde precession case, whereas on the other hand a critical retrograde precession frequency was found above which dynamo action is self-sustained. It was also found that these correspond to small-scale dynamos with a develo…
It is shown, using results of direct numerical simulations, that the spontaneous breaking of local reflectional symmetry (and corresponding localized kinetic and magnetic helicities) can dominate chaotic dynamics of the small-scale MHD dynamo in the Rayleigh-B{é}nard convection, in kinetically forced flows under strong stratification, in the near-surface solar convection, and in kinetically forced flows at large magnetic Reynolds numbers. The notions of deterministic and helical distributed chaos have been used for this purpose. The coexistence of large- and small-scale dynamo mechanisms and a…
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD.
This paper aims to numerically verify the large Reynolds number asymptotic theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper Deguchi (2019). To avoid any complexity associated with the chaotic nature of turbulence and flow geometry, nonlinear steady solutions of the viscous-resistive magneto-hydrodynamic equations in plane Couette flow have been utilised. Two classes of nonlinear MHD states, which convert kinematic energy to magnetic energy effectively, have been determined. The first class of nonlinear states can be obtained when a small spanwise uniform magnetic fiel…
We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessary local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume in phase space (Liouville's theorem) apart from the effects of external forcing, viscous dissipation and magnetic diffusion. In the absence of magnetic field the model exhibits a statistically stationary kinetic energy solution with a Kolmogorov spectrum. The dynamo action from a seed magnetic field by the turbulent flow and the non linear interactions are st…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these attractors is established as a function of the rotation parameter \ttau. The width of the basins of attraction is also estimated.
It is numerically demonstrated by means of a magnetohydrodynamics (MHD) code that precession can trigger the dynamo effect in a cylindrical container. This result adds credit to the hypothesis that precession can be strong enough to be one of the sources of the dynamo action in some astrophysical bodies.
We present a new scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, an hydrodynamic instability develops in the equatorial region, characterised by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by non-axisymmetric components. We show that the critical magnetic Reynolds number seem…
We study the amplification of magnetic fields during the formation of primordial halos. The turbulence generated by gravitational infall motions during the formation of the first stars and galaxies can amplify magnetic fields very efficiently and on short timescales up to dynamically significant values. Using the Kazantsev theory, which describes the so-called small-scale dynamo - a magnetohydrodynamical process converting kinetic energy from turbulence into magnetic energy - we can then calculate the growth rate of the small-scale magnetic field. Our calculations are based on a detailed chemi…
We study semi-analytically and in a consistent manner, the generation of a mean velocity field $\bar{\mathbf{U}}$ by helical MHD turbulence, and the effect that this field can have on a Mean Field Dynamo. Assuming a prescribed, maximally helical small scale velocity field, we show that large scale flows can be generated in MHD turbulent flows, via small scale Lorentz force. These flows back-react on the mean electromotive force of a Mean Field Dynamo through new terms, leaving the original $α$ and $β$ terms explicitly unmodified. Cross-helicity plays the key role in interconnecting all the eff…
Some concepts used in the theory of convection-driven dynamos in rotating spherical fluid shells are discussed. The analogy between imposed magnetic fields and those generated by dynamo action is evaluated and the role of the Elsasser number is considered. Eddy diffusivities are essential ingredients in numerical dynamo simulations, but their effects could be misleading. New aspects of the simultaneous existence of different dynamo states are described.
We study numerically the dynamo transition of an incompressible electrically conducting fluid filling the gap between two concentric spheres. In a first series of simulations, the fluid is driven by the rotation of a smooth inner sphere through no-slip boundary conditions, whereas the outer sphere is stationary. In a second series a volume force intended to simulate a rough surface drives the fluid next to the inner sphere within a layer of thickness one tenth of the gap width. We investigate the effect of the boundary layer thickness on the dynamo threshold in the turbulent regime. The simula…
The dynamics of convecting fluids in rotating spherical shells is governed at Prandtl numbers of the order unity by the interaction between differential rotation and roll-like convection eddies. While the differential rotation is driven by the Reynolds stresses of the eddies, its shearing action inhibits convection and causes phenomena such as localized convection and turbulent relaxation oscillations. The response of the system is enriched in the case of dynamo action. Lorentz forces may brake either entirely or partially the geostrophic differential rotation and give rise to two rather diffe…
This paper concerns kinematic helical dynamos in a spherical fluid body surrounded by an insulator. In particular, we examine their behaviour in the regime of large magnetic Reynolds number $\Rm$, for which dynamo action is usually concentrated upon a simple resonant stream-surface. The dynamo eigensolutions are computed numerically for two representative single-roll flows using a compact spherical harmonic decomposition and fourth-order finite-differences in radius. These solutions are then compared with the growth rates and eigenfunctions of the Gilbert and Ponty (2000) large $\Rm$ asymptoti…
To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenche…
This paper considers magnetic field generation by a fluid flow in a system referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic (MHD) state is driven by a prescribed body force. The field and flow become almost equal and dissipation is concentrated in cigar-like structures centred on straight-line separatrices. Numerical scaling laws for energy and dissipation are given that extend previous calculations to smaller diffusivities. The symmetries of the dynamo are set out, together with their implications for the structure of field and flow along the separatrices. The scali…
The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the background of strong toroidal magnetic field. The extra invariant is used to show that the background field is maintained.
The inverse cascade of magnetic energy occurs when helicity or rotational instability exists in the magnetohydrodynamic (MHD) system. This well known phenomenon has been considered as a basis for the large scale magnetic field in universe. However nonhelical magnetic energy in a decaying MHD system also migrates toward the large scale, which holds vital clues to the origin of large scale magnetic field in a quiescent astrophysical system. Zeldovich's rope dynamo model is considered as a basic and symbolistic model of magnetic field amplification. However, the rope model assuming specific exter…
Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obta…
Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary a…
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…
We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude, for other parameters, the modulation is of Type 2, where the ampl…
We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare between axisymmetric (2D) and fully three dimensional flows, between low and high global rotation rates, between prograde and retrograde differential rotations, between weak and strong nonlinear inertial forces, between insulating and conducting boundaries, and between two aspect ratios. The main results are as follows. Azimuthally drifting Rossby waves arising…
For the understanding of planetary and stellar dynamos an overview of the major parameter dependences of convection driven dynamos in rotating spherical fluid shells is desirable. Although the computationally accessible parameter space is limited, earlier work is extended with emphasis on higher Prandtl numbers and uniform heat flux condition at the outer boundary. The transition from dynamos dominated by non-axisymmetric components of the magnetic field to those dominated by the axisymmetric components depends on the magnetic Prandtl number as well as on the ordinary Prandtl number for higher…
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
Numerical models of the geodynamo are usually classified in two categories: those denominated dipolar modes, observed when the inertial term is small enough, and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution co-exists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which vis…
The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two distinct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 - a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structu…
Using a mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha which is dynamically quenched and disturbed by additional noise, the basic features of geomagnetic polarity reversals are shown to be generic consequences of the dynamo action in the vicinity of exceptional points of the spectrum. This simple paradigmatic model yields long periods of constant polarity which are interrupted by self-accelerating field decays leading to asymmetric polarity reversals. It shows the recently discovered bimodal field distribution, and it gives a natural explanation of the …
We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales.…
Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $\approx 250$ were examined and multiple resolutions used for con…
An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of th…
Dynamo action in planetary cores has been extensively studied in the context of convectively-driven flows. We show in this letter that mechanical forcings, namely tides, libration and precession, are also able to kinematically sustain a magnetic field against ohmic diffusion. Previous attempts published in the literature focused on the laminar response or considered idealized spherical configurations. In contrast, we focus here on the developed turbulent regime and we self-consistently solve the magnetohydrodynamic (MHD) equations in an ellipsoidal container. Our results open new avenues of re…
We propose a plasma experiment to be used to investigate fundamental properties of astrophysical dynamos. The highly conducting, fast-flowing plasma will allow experimenters to explore systems with magnetic Reynolds numbers an order of magnitude larger than those accessible with liquid-metal experiments. The plasma is confined using a ring-cusp strategy and subject to a toroidal differentially rotating outer boundary condition. As proof of principle, we present magnetohydrodynamic simulations of the proposed experiment. When a von Kármán-type boundary condition is specified, and the magnetic R…
In this study we present a compressible test-field method (CTFM) for computing $α$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare it to the quasi-kinematic test-field method, and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that, for moderate imposed fie…
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of t…
The dynamics of stably stratified stellar radiative zones is of considerable interest due to the availability of increasingly detailed observations of Solar and stellar interiors. This article reports the first non-axisymmetric and time-dependent simulations of flows of anelastic fluids driven by baroclinic torques in stably stratified rotating spherical shells -- a system serving as an elemental model of a stellar radiative zone. With increasing baroclinicity a sequence of bifurcations from simpler to more complex flows is found in which some of the available symmetries of the problem are bro…
Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos.The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate.However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies.We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence, and magnetic field generation.We observ…
Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva et al., 2019, Geophys. Astrophys. Fluid Dyn., doi:10.1080/03091929.2019.1640875) are found to persist significantly beyond the onset of ins…
The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (\emph{chiral magnetic effect}). We present a self-consistent treatment of the \emph{chiral MHD equations}, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with th…
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modeling and the geophysical motivation, {it is necessary to use} scaling laws. Such scaling laws establish the dependence of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical {constraints}. (...) We show that previous empirical scaling laws for the magnetic…
Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo proble…
We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, bu…
We have performed numerical simulations of boundary-driven dynamos using a three-dimensional non-linear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion by the counter-rotation of the two hemispheric walls. The resulting flow is of von Kármán type, consisting of a layer of zonal velocity close to the outer wall and a secondary meridional circulation. Above a certain forcing threshold, the mean flow is unstable to non-axisymmetric motions within an equatorial belt. For fixed forcing above this threshold, we ha…
