This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1, Rm_c is ~3 times larger than for Pm>1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm<1, the induced fluctuations are well described by the quasistatic approximation; the k^{-11/3} spectrum is confirmed for the first time in direct numerical simulations.
Is the scaling, λ\sim Rm^{1/2}, for the growth rate of small-scale dynamo instability at low magnetic Prandtl numbers and large magnetic Reynolds numbers, Rm, valid in the vicinity of the threshold? Our analysis and even numerical solution (Malyshkin and Boldyrev, 2010) of the dynamo equations for a Gaussian white-noise velocity field (the Kazantsev-Kraichnan model) imply that the answer is negative. Contrary to the claim by Malyshkin and Boldyrev (2010), there are two different asymptotics for the dynamo growth rate: in the vicinity of the threshold and far from the threshold.
We perform numerical simulation of dynamo with magnetic Prandtl number $\mathrm{Pm} =0.2$ on $1024^3$ grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our r…
We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from 0.3 to 0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velo…
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significan…
We report a series of numerical simulations showing that the critical magnetic Reynolds number Rm_c for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Pr=Rm/Re is less than some critical value Pr_c<1 even for Rm for which dynamo exists at Pr>=1. We argue that, in the limit of Re->infinity, a finite Pr_c may exist. The second possibility is that Pr_c->0 as Re->infinity, while Rm_c tends to a very large constant value inaccessible at current resolutions. If there is a finite Pr_c, the dynamo is sustainable only …
We investigate the dynamo problem in the limit of small magnetic Prandtl number ($\Pm$) using a shell model of magnetohydrodynamic turbulence. The model is designed to satisfy conservation laws of total energy, cross helicity and magnetic helicity in the limit of inviscid fluid and null magnetic diffusivity. The forcing is chosen to have a constant injection rate of energy and no injection of kinetic helicity nor cross helicity. We find that the value of the critical magnetic Reynolds number ($\Rm$) saturates in the limit of small $\Pm$. Above the dynamo threshold we study the saturated regime…
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…
In this study we discuss two key issues related to a small-scale dynamo instability at low magnetic Prandtl numbers and large magnetic Reynolds numbers, namely: (i) the scaling for the growth rate of small-scale dynamo instability in the vicinity of the dynamo threshold; (ii) the existence of the Golitsyn spectrum of magnetic fluctuations in small-scale dynamos. There are two different asymptotics for the small-scale dynamo growth rate: in the vicinity of the threshold of the excitation of the small-scale dynamo instability, $λ\propto \ln({\rm Rm}/ {\rm Rm}^{\rm cr})$, and when the magnetic Re…
We compute numerically the threshold for dynamo action in Taylor-Green swirling flows. Kinematic calculations, for which the flow field is fixed to its time averaged profile, are compared to dynamical runs for which both the Navier-Stokes and the induction equations are jointly solved. The kinematic instability is found to have two branches, for all explored Reynolds numbers. The dynamical dynamo threshold follows these branches: at low Reynolds number it lies within the low branch while at high kinetic Reynolds number it is close to the high branch.
We present an MHD shell model suitable for computation of various energy fluxes of magnetohydrodynamic turbulence for very small and very large magnetic Prandtl numbers $\mathrm{Pm}$; such computations are inaccessible to direct numerical simulations. For small $\mathrm{Pm}$, we observe that both kinetic and magnetic energy spectra scale as $k^{-5/3}$ in the inertial range, but the dissipative magnetic energy scales as $k^{-11/3}\exp(-k/k_η)$. Here, the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated b…
We present a three--pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are: (i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbul…
The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(l) \propto l^{theta}, where v(l) is the eddy v…
The existence of a weak galactic magnetic field has been repeatedly confirmed by observational data. The origin of this field has not as yet been explained in a fully satisfactory way and represents one of the main challenges of the astrophysical dynamo theory. In both the galactic dynamo theory and the primordial-origin theory, a major influence is exerted by the small-scale magnetic fluctuations. This article is devoted to constructing a systematic second-order statistical theory of such small-scale fields. The statistics of these fields are studied in the kinematic approximation and for the…
Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dy…
The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus is expected to depend crucially on the nature of turbulence. In this work, we present a model for the small-scale dynamo that takes into account the slope of the turbulent velocity spectrum v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and the typical velocity on that scale. The time evolution of the fluctuation component of the magnetic field, i.e., the small-scale field, is described by the Kazantsev equation. We solve this linear differential equation …
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow, and the ABC flow forced at two different scales. The investigation covers roughly three orders of magnitude of the magnetic Reynolds number above onset. All …
We consider the induction of magnetic field in flows of electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive lengthscales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modelled using a Large Eddy Simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: tology of the me…
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumbe…
Compositional convection is thought to be an important energy source for magnetic field generation within planetary interiors. The Prandtl number, $Pr$, characterizing compositional convection is significantly larger than unity, suggesting that the inertial force may not be important on the small scales of convection as long as the buoyancy force is not too strong. We develop asymptotic dynamo models for the case of small Rossby number and large Prandtl number in which inertia is absent on the convective scale. The relevant diffusivity parameter for this limit is the compositional Roberts numb…
Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandt…
Small-scale dynamos play important roles in modern astrophysics, especially on Galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time scale of Galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra …
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…
Small-scale dynamo saturation across magnetic Prandtl numbers using the EDQNM closure
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理中心）；Department of Physics, Ashoka University（阿肖卡大学物理系）
In an experiment in the Institute of Continuous Media Mechanics in Perm (Russia) an non--stationary screw dynamo is intended to be realized with a helical flow of liquid sodium in a torus. The flow is necessarily turbulent, that is, may be considered as a mean flow and a superimposed turbulence. In this paper the induction processes of the turbulence are investigated within the framework of mean--field electrodynamics. They imply of course a part which leads to an enhanced dissipation of the mean magnetic field. As a consequence of the helical mean flow there are also helical structures in the…
Evidence from numerical simulations suggest that the nature of dynamo transition changes from supercritical to subcritical as the magnetic Prandtl number is decreased. To explore this interesting crossover we first use direct numerical simulations to investigate the hysteresis zone of a subcritical Taylor-Green dynamo. We establish that a well defined boundary exists in this hysteresis region which separates dynamo states from the purely hydrodynamic solution. We then propose simple dynamo models which show similar crossover from supercritical to subcritical dynamo transition as a function of …
We consider magnetic fields generated by homogeneous isotropic and parity invariant turbulent flows. We show that simple scaling laws for dynamo threshold, magnetic energy and Ohmic dissipation can be obtained depending on the value of the magnetic Prandtl number.
A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. Distinct equations are derived for the cas…
We construct a five-mode helical dynamo model containing three velocity and two magnetic modes and solve it analytically. This model exhibits dynamo transition via supercritical pitchfork bifurcation. We show that the critical magnetic Reynolds number for dynamo transition ($\mathrm{Rm}_c$) asymptotes to constant values for very low and very high magnetic Prandtl numbers ($\mathrm{Pm}$). Beyond dynamo transition, secondary bifurcations lead to periodic, quasi-periodic, and chaotic dynamo states as the forcing amplitude is increased and chaos appears through a quasi-periodic route.
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside the Earth core. Using an analytically prescribed flow, we apply a recently introduced iterative numerical scheme to solve the induction equation and analyze the flow response to externally applied fields with simple geometries (azimuthal, radial, etc.). Symmetry properties allow us to build selected induction modes whose interactions lead to dynamo mechanisms…
Dynamo action in a fully helical Beltrami (ABC) flow is studied using both direct numerical simulations and subgrid modeling. Sufficient scale separation is given in order to allow for large-scale magnetic energy build-up. Growth of magnetic energy obtains down to a magnetic Prandtl number PM=RM/RV close to 0.005, where RV and RM are the kinetic and magnetic Reynolds numbers. The critical magnetic Reynolds number for dynamo action RMc seems to saturate at values close to 20. Detailed studies of the dependence of the amplitude of the saturated magnetic energy with PM are presented. In order to …
The small-scale kinematic dynamo in a two-dimensional chaotic flow is studied. The analytic approach is developed in framework of the Kraichnan-Kazantsev model. It is shown that the growth of magnetic field $\bm{B}$ fluctuations stops at large times in accordance with so-called anti-dynamo theorems. The value of $\bm{B}^2$ increased therewith in square of the magnetic Prandtl number times. The spatial structure of the correlation tensor of the magnetic field is found.
We investigate the structure of magnetic field amplified by turbulent velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan model. We consider Kolmogorov distribution of velocity fluctuations, and assume that both Reynolds number and magnetic Reynolds number are very large. We present the full numerical solution of the model for the spectra and the growth rates of magnetic fluctuations. We consider astrophysically relevant limits of large and small magnetic Prandtl numbers, and address both helical and nonhelical cases.
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…
Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from ki…
We present direct numerical simulations of reversals of the magnetic field generated by swirling flows in a spherical domain. In agreement with a recent model, we observe that coupling dipolar and quadrupolar magnetic modes by an asymmetric forcing of the flow generates field reversals. In addition, we show that this mechanism strongly depends on the value of the magnetic Prandtl number.
The problem of the dynamo effect for a Kraichnan incompressible helicity-free velocity field is considered. Exploiting a quantum formalism first introduced by Kazantsev (A.P. Kazantsev, Sov. Phys. JETP 26, 1031-1034 (1968)), we show that a critical magnetic Reynolds number exists for the presence of dynamo. The value of the Prandtl number influences the spatial distribution of the magnetic field and its growth in time. The magnetic field correlation length is always the largest between the diffusive scale and the viscous scale of the flow. In the same way the field growth is characterized by a…
Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasi-linear statistical simulation methods. It is found that homogenous turbulence is unstable to a large scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasi-linear model is qualitatively similar to that of nonlinear MRI turbulence. This indicates that recent convergence problems may be related to large scale …
Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers, Pm=0.5, the decrease of magnetic energy, ohmic dissipation and power of the Lorentz force during a reversal is followed by an increase of the power injected by the force driving the flow and an increase of viscous dissipation. Cross correlations show that the Lorentz energy flux is in advance with respect to the other energy fluxes. We also observe that during a …
In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for magnetic Prandtl number $\mathrm{Pm}=20$ on $1024^3$ grid using pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason why the integral scale of…
While the saturated magnetic energy is independent of viscosity in dynamo experiments, it remains viscosity-dependent in state-of-the-art 3D direct numerical simulations (DNS). Extrapolating such viscous scaling-laws to realistic parameter values leads to an underestimation of the magnetic energy by several orders of magnitude. The origin of this discrepancy is that fully 3D DNS cannot reach low enough values of the magnetic Prandtl number $Pm$. To bypass this limitation and investigate dynamo saturation at very low $Pm$, we focus on the vicinity of the dynamo threshold in a rapidly rotating f…
In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and study the dynamo's mode of operation during both the linear and non-linear saturation regime: It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number is on the order of unity. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non…
We explore the effect of the magnetic Prandtl number Pm on energy and dissipation in fully resolved direct numerical simulations of steady-state, mechanically forced homogeneous magnetohydrodynamic turbulence in the range Pm = 1/32 to 32. We compare the spectra and show that if the simulations are not fully resolved, the steepness of the scaling of the kinetic-to-magnetic dissipation ratio with Pm is overestimated. We also present results of decaying turbulence with helical and nonhelical magnetic fields, where we find nonhelical reverse spectral transfer for Pm < 1. The results of this system…
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the…
We study dynamo action using numerical simulations of planar Boussinesq convection at rapid rotation (low Ekman numbers, Ek), focusing on subcritical dynamo action in which the dynamo is sustained for Rayleigh numbers, Ra, below the critical Rayleigh number for the onset of nonmagnetic convection, Ra$_c$. These solutions are found by first investigating the supercritical regime, in which the dynamo is able to generate a large-scale magnetic field that significantly influences the convective motions, with an associated Elsasser number of order Ek$^{1/3}$. Subcritical solutions are then found by…
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…
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independe…
The statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo are investigated during the kinematic, nonlinear and statistically saturated stages. We carry out an a priori analysis of data obtained from an ensemble of direct numerical simulations on $512^3$ grid points and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS) modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, we consider the SGS stress tensors originating from inertial dynamics, Lorentz force and the magnetic induction separ…
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…
We investigate the Lagrangian mechanism of the kinematic ``fluctuation'' magnetic dynamo in turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely many field lines to each space point, with the resultant magnetic field at that point given by the average over all the individual line vectors. As a consequence of the roughness of the advecting velocity, this remains true even in the limit of zero resistivity. We show that the presence of dynamo effect requires sufficient angular correlation of the passive l…
We present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method (SPMHD) with the geometric density average force expression (GDSPH). We perform shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained turbulence can be simulated successfully with SPH, with results consistent with prior work with grid-based codes. In particular, for the stratified boxes, our simulations reproduce the characteristic butterfly diagram of the MRI dynamo with saturat…
The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions for a self-sustaining dynamo. Within the interior of a field producing domain geometric constraints or varying material properties (e.g. electrical conductivity of the container walls or localized high-permeability material) might also play a role. Combining a grid based finite volume approach with the boundary element method in a hybrid FV-BEM scheme offers the flexibility of a local discretization with a stringent treatm…
Magnetic field generation in three-dimensional Rayleigh-Bénard convection of an electrically conducting fluid is studied numerically by fixing the Prandtl number at $P=0.3$ and varying the Rayleigh number (Ra) as a control parameter. A recently reported route to hyperchaos involving quasiperiodic regimes, crises and chaotic intermittent attractors is followed, and the critical magnetic Prandtl number ($P_m^c$) for dynamo action is determined as a function of Ra. A mechanism for the onset of intermittency in the magnetic energy is described, the most beneficial convective regimes for dynamo act…
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…
Studies of magnetic induction in von Kármán swirling flows have so far linked the time-averaged induced magnetic field to the structure of the mean flow. They have evidenced the Omega and Parker mechanism generated respectively by the flow differential rotation and helicity, which underly the Duddley and James \cite{DuddleyJames} dynamos. Using an array of Hall probes we study here the dynamical regime. In the experimental flow, turbulence is fully developed and large fluctuations are observed in the magnetic induction processes. We find that the large scale turbulent fluctuations have differe…
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.
