Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modelled in terms of an αΩdynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Rm) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on Rm.
A simple explicit example of a Roberts-type dynamo is given in which the alpha-effect of mean-field electrodynamics exists in spite of point-wise vanishing kinetic helicity of the fluid flow. In this way it is shown that alpha-effect dynamos do not necessarily require non-zero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition numerical solutions of the original dynamo equations are given, that are independent of any approximation of that kind. Both theory and numerical results demonstrate…
Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.
Magnetic fields correlated on kiloparsec scales are seen in spiral galaxies. Their origin could be due to amplification of a small seed field by a turbulent galactic dynamo. We review the current status of the galactic dynamo, especially the constraints imposed by magnetic helicity conservation. We estimate the minimal strength of the large-scale magnetic field which could arise inspite of the helicity constraint.
Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e.intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic fi…
We demonstrate that the inclusion of the helicity flux in the magnetic helicity balance in the nonlinear stage of galactic dynamo action results in a radical change in the magnetic field dynamics. The equilibrium value of the large-scale magnetic field is then approximately the equipartition level. This is in contrast to the situation without the flux of helicity, when the magnetic helicity is conserved locally, which leads to substantially subequipartition values for the equilibrium large-scale magnetic field.
Magnetic helicity effects are discussed in laboratory and astrophysical settings. First, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Second, the build-up of a large scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils.…
We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstr…
The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted.
Magnetic helicity is nearly conserved and its evolution equation provides a dynamical feedback on the alpha effect that is distinct from the conventional algebraic alpha quenching. The seriousness of this dynamical alpha quenching is particularly evident in the case of closed or periodic boxes. The explicit connection with catastrophic alpha quenching is reviewed and the alleviating effects of magnetic and current helicity fluxes are discussed.
We study effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau-approximation and the second order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause large-scale dynamo. Mean-field dynamo can be possible when kinetic helicity fluctuations are inhomogeneous which cause a nonzero mean alpha effect in a sheared turbulence. On the other hand, shear-curren…
Dynamo action is investigated in simulations of locally isotropic and homogeneous turbulence in a slab between open boundaries. It is found that a `pseudo-vacuum' boundary condition (where the field is vertical) leads to strong helicity fluxes which significantly reduce the amplitude of the resulting large scale field. On the other hand, if there is a conducting halo outside the dynamo-active region the large scale field amplitude can reach larger values, but the time scale after which this field is reached increases linearly with the magnetic Reynolds number. In both cases most of the helicit…
We present a simple semi-analytical model of nonlinear, mean-field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the `no-$z$' approximation to a nonlinear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where nonlinear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g., due to the galactic fountain or wind) and the othe…
Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vish…
Variations of the sunspot number are important indicators of the solar activity cycles. The sunspot formation is a result of a dynamo process inside the Sun, which is far from being understood. We use simple dynamical models of the dynamo process to simulate the magnetic field evolution and investigate general properties of the sunspot number variations during the solar cycles. We have found that the classical Parker's model with a standard kinetic helicity quenching cannot represent the typical profiles of the solar-cycle variations of the sunspot number, and also does not give chaotic soluti…
We consider the magnetic helicity balance for the galactic dynamo in the framework of the local dynamo problem, as well as in the no-z model (which includes explicitly the radial distribution of the magnetic fields). When calculating the magnetic helicity balance we take into account the redistribution of the small-scale and large-scale magnetic fields between the magnetic helicities, as well as magnetic helicity transport and diffusion due to small-scale turbulence. We demonstrate that the magnetic helicity flux through the galactic disc boundaries leads to a steady-state magnetic field with …
We show that the presence of a steady $\ao$ dynamo in astrophysical rotators likely leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle acceleration in a corona. The connection between energy and magnetic helicity arises because the generation of large scale field is linked to a generation of large scale magnetic helicity. In a steady state, the relative magnetic helicity associated with the large scale field can escape, accompanied by an equal and opposite small scale contribution from the field, since the total magnetic helicity in large magnetic…
Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than res…
The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the nonlinearity. The crucial discriminant is the magnetic helicity, which is known to evolve only on a slow resistive time scale in the limit of large magnetic Reynolds number. Particular emphasis is put on the possibility of memory effects, which means that an additional explicitly time-dependent equation for the nonlinearity is solved simultaneou…
There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small sca…
We continue our attempt to connect observational data on current helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current helicity (Kleeorin et al. 2003), we argue that some information concerning the radial profile of the current helicity averaged over time and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current helicity in a given hemisph…
Dynamos in astrophysical disks are usually explained in terms of the standard alpha-omega mean field dynamo model where the local helicity generates a radial field component from an azimuthal field. The subsequent shearing of the radial field gives rise to exponentially growing dynamo modes. There are several problems with this model. The exponentiation time for the galactic dynamo is hard to calculate, but is probably uncomfortably long. Moreover, numerical simulations of magnetic fields in shearing flows indicate that the presence of a dynamo does not depend on a non-zero average helicity. H…
It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
We revisit the possible turbulent sources of the solar dynamo. Studying axisymmetric mean-field dynamo models, we find that the large-scale poloidal magnetic field could be generated not only by the famous alpha effect, but also by the Omega x J and shear-current effects. The inclusion of these additional turbulent sources alleviates several of the known problems of solar mean-field dynamo models.
The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the ${\bf W} {\bf \times} {\bf J}$ term in the mean electromotive force, where ${\bf W}$ is the mean vorticity due to the large-scale shear motions and ${\bf J}$ is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. T…
Dynamical studies of MHD turbulence on the one hand, and arguments based upon magnetic helicity on the other, have yielded seemingly contradictory estimates for the $α$ parameter in turbulent dynamo theory. Here we show, with direct numerical simulation of three-dimensional magnetohydrodynamic turbulence with a mean magnetic field, $\OB$, that the constraint on the dynamo $α$-effect set by the magnetic helicity is time-dependent. A time-scale $t_c$ is introduced such that for $t<t_c$, the $α$-coefficient calculated from the simulation is close to the result of Pouquet et al and Field et al, $-…
We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the comb…
The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios…
Mean field dynamo theory is a leading candidate to explain the observed large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of premature quenching by the backreaction of the growing field. We distinguish between rapid mean field dynamo action, which is required by astrophysical systems, and resistively limited action. We show how the flow of magnetic helicity is important for rapid action. Existing numerical and analytic work suggesting that mean field dynamos are prematurely quenched and resistively limited include approximations or boundary conditio…
We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the grow…
Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong…
The paper deals with a simple spherical mean-field dynamo model of $α^2$-type in the case of high electrical conductivity. A spherically symmetric distribution of turbulent motions is assumed inside a spherical fluid body surrounded by free space, and some complete form of the corresponding mean electromotive force is taken into account. For a turbulence lacking reflectional symmetry finite growth rates of magnetic fields prove to be possible even in the limit of perfect conductivity, that is, the model corresponds to a fast dynamo. In accordance with the theorem by Bondi and Gold the dynamo-g…
Magnetic field amplification in astrophysics ultimately requires an understanding of magnetohydrodynamic turbulence. Kinetic helicity has long been known to be important for large scale field growth in forced MHD turbulence, and has been recently demonstrated numerically to be asymptotically consistent with slow mean field dynamo action in a periodic box. Here we show numerically that the magnetic spectrum at and below the forcing scale is also strongly influenced by kinetic helicity. We identify a critical value, $f_{h,crit}$ above which the magnetic spectrum develops maxima at wavenumber $= …
The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal MHD equations and can hence only change on a resistive time scale. This constrains strongly the growth time of the large scale magnetic field, but less strongly the length of the cycle period. Comparing with the case without shear, the time scale for large scale fiel…
The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields.
The possibility of non-helical large scale dynamo action is investigated using three-dimensional simulations of global accretion discs as well as idealized local simulations without rotation and only shear. Particular emphasis is placed on a certain correlation between vorticity and azimuthal velocity gradient which has been predicted to drive large scale dynamo action, independent of the presence or absence of kinetic helicity. In the global disc simulations two types of behaviours are found: those which do show this type of velocity correlation and those which do not. The former ones are typ…
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no the back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of the kinematic dynamo theory to protogalaxies is rather limited. The reason is th…
The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic f…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large scale magnetic helicity, small scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large scale helical field growth on dynamical (Alfvén crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing ki…
With a non local shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers ($Pm$). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy transfers. In both cases the magnetic energy grows at small scale and saturates as an inverse `` cascade ''.
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies …
Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally strong and `catastrophic'.
We generalize the derivation of dynamo coefficient $α$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $α$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $α$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorte…
The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The rea…
Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It is shown that even at the largest currently available resolution there is no clear evidence of power law scaling of the magnetic and kinetic energy spectra in turbulence. However, using subgrid scale modeling, some indications of asymptotic equipartition can be found. The frequently used first order smoothing approach to calculate the alpha effect and other …
A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the alpha-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of `catastrophic' quenching of the alpha-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large s…
The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. In this work, we have explored the effects of the turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. The results reveal the importance of the pumping mechanism for solving current limitations in mean field dynamo modeling such as…
The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field s…
Analytical solution of first order torsion $α$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while grow exponentially in time. The rate of speed of the helical dynamo depends upon the value of Frenet curvature of the tube. The $α$ factor possesses a fundamental contribution from constant torsion tube approximation. It is also assumed that the curvature of the magnetic axis of the tube is constant. Though $α$-effect dynamo equations are rather more complex in Riema…
Mechanisms of nonhelical large-scale dynamos (shear-current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large-scale shear are discussed. We have found that the shear-current dynamo can act even in random flows with small Reynolds numbers. However, in this case mean-field dynamo requires small magnetic Prandtl numbers (i.e., ${\rm Pm} < {\rm Pm}^{\rm cr}<1$). The threshold in the magnetic Prandtl number, ${\rm Pm}^{\rm cr} = 0.24$, is determined using second order correlation approximation (or first-order smoothing approximatio…
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arg…
Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a …
Two questions about the solar magnetic field might be answered together once their connection is identified. The first is important for large scale dynamo theory: what prevents the magnetic backreaction forces from shutting down the dynamo cycle? The second question is: what determines the handedness of twist and writhe in magnetized coronal ejecta? Magnetic helicity conservation is important for answering both questions. Conservation implies that dynamo generation of large scale writhed structures is accompanied by the oppositely signed twist along these structures. The latter is associated w…
The generation of large-scale magnetic fields is generically accompanied by the more rapid growth of small-scale fields. The growing Lorentz force due to these fields back reacts on the turbulence to saturate the mean-field and small-scale dynamos. For the mean-field dynamo, in a quasi-linear treatment of this saturation, it is generally thought that, while the alpha-effect gets renormalised and suppressed by non-linear effects, the turbulent diffusion is left unchanged. We show here that this is not true and the effect of the Lorentz forces, is also to generate additional non-linear hyperdiff…
Large-scale magnetic fields in galaxies are thought to be generated by a turbulent dynamo. However the same turbulence also leads to a small-scale dynamo which generates magnetic noise at a more rapid rate. The efficiency of the large-scale dynamo depends on how this noise saturates. We examine this issue taking into account ambipolar drift, which obtains in a galaxy with significant neutral gas. We argue that, (1) the small-scale dynamo generated field does not fill the volume, but is concentrated into intermittent rope like structures. The flux ropes are curved on the turbulent eddy scales. …
We present and analyze a simplified stochastic $αΩ-$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $α-$% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the $α-$parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic …
The magnetic helicity has paramount significance in nonlinear saturation of galactic dynamo. We argue that the magnetic helicity conservation is violated at the lepton stage in the evolution of early Universe. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains from the beginning a substantial magnetic helicity which has to be taken into account in the magnetic helicity balance at the later stage of galactic dynamo.
Small scale turbulent dynamo action in compressible transonic turbulence is discussed. It is shown that the critical value of the magnetic Reynolds number displays a bimodal behavior and changes from a typical value of 35 for small Mach numbers to about 80 for larger Mach numbers. The transition between the two regimes is relatively sharp. The direct simulations are then compared with simulations where shocks are captured using a shock viscosity that becomes large at locations where there are shocks. In the presence of shear it is shown that large scale dynamo action is possible.
We present results from numerical simulations of nonlinear MHD dynamo action produced by three-dimensional flows that become turbulent for high values of the fluid Reynolds number. The magnitude of the forcing function driving the flow is allowed to evolve with time in such way as to maintain an approximately constant velocity amplitude (and average kinetic energy) when the flow becomes hydrodynamically unstable. It is found that the saturation level of the dynamo increases with the fluid Reynolds number (at constant magnetic Prandtl number), and that the average growth rate approaches an asym…
