In order better to understand how dynamo systems saturate, we study the kinematic dynamo properties of velocity fields that arise from nonlinearly saturated dynamos. The technique is implemented by solving concurrently, in addition to the momentum equation, two induction equations, one for the actual magnetic field, and one for an independent passive field. We apply this technique to two illustrative examples: convectively driven turbulence, and turbulence represented by a shell model. In all cases we find that the velocity remains an efficient kinematic dynamo even after nonlinear saturation occurs. We discuss the implications to the process of dynamo saturation.
Large-scale magnetic fields in stars and galaxies are thought to arise by mean-field dynamo action due to the combined influence of both helical turbulence and shear. Those systems are also highly conducting and the turbulence therein leads to a fluctuation (or small-scale) dynamo which more rapidly amplifies magnetic field fluctuations on the eddy scales and smaller. Will this then interfere with and suppress the mean (or large-scale) field growth? Using direct numerical simulations of helical turbulence (with and without shear), we identify a novel quasi-kinematic large-scale dynamo which op…
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…
The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The ampli…
It is shown, that the saturated $α$-effect taken from the nonlinear dynamo equations for the thin disk can still produce exponentially growing magnetic field in the case, when this field does not feed back on the $α$. For negative dynamo number (stationary regime) stability is defined by the structure of the spectra of the linear problem for the positive dynamo numbers. Stability condition for the oscillatory solution (positive dynamo number) is also obtained and related to the phase shift of the original magnetic field, which produced saturated $α$ and magnetic field in the kinematic regime. …
Recent MHD dynamo simulations for magnetic Prandtl number $>1$ demonstrate that when MHD turbulence is forced with sufficient kinetic helicity, the saturated magnetic energy spectrum evolves from having a single peak below the forcing scale to become doubly peaked with one peak at the system (=largest) scale and one at the forcing scale. The system scale field growth is well modeled by a recent nonlinear two-scale nonlinear helical dynamo theory in which the system and forcing scales carry magnetic helicity of opposite sign. But a two-scale theory cannot model the shift of the small-scale peak…
The evolution of a Taylor-Green forced magnetohydrodynamic (MHD) system showing dynamo activity is analyzed via direct numerical simulations. The statistical properties of the velocity and magnetic field in Eulerian coordinates and along trajectories of fluid elements (Lagrangian coordinates) are found to change between the kinematic, non-linear and saturated regime. Fluid element (tracer) trajectories change from chaotic quasi-isotropic (kinematic phase) to mean magnetic field aligned (saturated phase). The probability density functions (PDFs) of the magnetic field change from strongly non-Ga…
We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier-Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping velocity. The model can be studied down to arbitrarily low viscosity and naturally leads to the strong-field scaling regime for the magnetic energy produced above threshold: the magnetic energy is proportional to the global rotation rate and independent of the viscosity. Depending on the relative orientations of global rotation and large-scale sweeping, the dyn…
After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.
We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential mu_5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of mu_5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuation…
The homogeneous dynamo effect is at the root of magnetic field generation in cosmic bodies, including planets, stars and galaxies. While the underlying theory had increasingly flourished since the middle of the 20th century, hydromagnetic dynamos were not realized in laboratory until 1999. On 11 November 1999, this situation changed with the first observation of a kinematic dynamo in the Riga experiment. Since that time, a series of experimental campaigns has provided a wealth of data on the kinematic and the saturated regime. This paper is intended to give a comprehensive survey about these e…
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）
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…
The VKS experiment has evidenced dynamo action in a highly turbulent liquid sodium von Kármán flow [R. Monchaux et al., Phys. Rev. Lett. {\bf 98}, 044502 (2007)]. However, the existence and the onset of a dynamo happen to depend on the exact experimental configuration. By performing kinematic dynamo simulations on real flows, we study their influence on dynamo action, in particular the sense of rotation and the presence of an annulus in the shear layer plane. The 3 components of the mean velocity fields are measured in a water prototype for different VKS configurations through Stereoscopic Par…
A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo -- in some sense the inverse of dynamo quenching. The dynamo is nonhelical, with the mean-field $α$ coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, th…
In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal d…
The Universe at present is highly magnetized, with fields of the order of a few 10^-5 G and coherence lengths larger than 10 kpc in typical galaxies like the Milky Way. We propose that the magnetic field was amplified to this values already during the formation and the early evolution of the galaxies. Turbulence in young galaxies is driven by accretion as well as by supernova (SN) explosions of the first generation of stars. The small-scale dynamo can convert the turbulent kinetic energy into magnetic energy and amplify very weak primordial magnetic seed fields on short timescales. The amplifi…
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…
Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as pert…
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…
In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it was shown that a simple mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha can exhibit a number of features which are typical for Earth's magnetic field reversals. In particular, the model produces asymmetric reversals, a positive correlation of field strength and interval length, and a bimodal field distribution. All these features are attributable to the magnetic field dynamics in the vicinity of an exceptional point of the spectrum of the non-selfadjoint dynamo operator. The negat…
The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it however currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behaviour of large-scale fluid magnetism in the astrophysically-relevant but treacherous regime of large magnetic Reynolds number $Rm$ is still lacking. We explore thi…
Fluctuations of the alpha-effect which break equatorial symmetry of the flow in the kinematic Parker's dynamo are considered. We show, that even small (a few percents) fluctuation can leed to the substantial assymmetry of the magnetic field in the hemispheres as well as the propagation of the dynamo wave through the equator plane. We also consider how change of the dynamo number can be used to explain different regimes of magnetic field generation in geodynamo.
Using the domino dynamo model, we show how variations of the heat flux at the core-mantle boundary change the frequency of geomagnetic field reversals. In fact, we are able to demonstrate the effect known from the modern 3D planetary dynamo models using an ensemble of interacting spins, which obey equations of the Langevin type with a random force. We also consider applications to the giant planets and offer explanations of some specific episodes of the geomagnetic field in the past.
Understanding large-scale magnetic field growth in astrophysical objects is a persistent challenge. We tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of the magnetic Reynolds number (Rm) in a closed volume. From modest-Rm numerical simulations, we identify a pre-saturation regime when the large-scale field grows independently of Rm, but to an Rm-dependent magnitude. For plausible magnetic spectra however, the analysis predicts the magnitude to be Rm-independent and substantial as Rm$\to\infty$. This gives renewed optimism for the relevance of…
We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical, and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.
A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit-type. The flows are unstable against nonaxisymmetric perturbations which form electromotive forces defining $α$ effect and eddy diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same power then the global $α$ effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite $α$ effects if only an isolated mode is considered but this intrinsic helicity of the single-mode…
We consider rotating, kinematic dynamos at low magnetic Prandtl number $Pm$. We show that the inclusion of rotation leads to an increase in spatio-temporal coherence and a modification of the turbulent spectrum. These effects make the flow more efficient in driving the dynamo, in the sense that the energy injection rate required to reach the critical value of the magnetic Reynolds number $Rm_c$ is reduced in comparison with a non-rotating dynamo (Seshasayanan et al. 2017). For random dynamos it is known that the growth-rate would largely be determined by the spectral index of the flow at the r…
