Using a one-dimensional $αω$-dynamo model appropriate to galaxies, we study the possibility of dynamo action driven by a stochastic alpha effect and shear. To determine the field evolution, one needs to examine a large number of different realizations of the stochastic component of $α$. The net growth or decay of the field depends not only on the dynamo parameters but also on the particular realization, the correlation time of the stochastic $α$ compared to turbulent diffusion timescale and the time over which the system is evolved. For dynamos where both a coherent and fluctuating $α$ are present, the stochasticity of $α$ can help alleviate catastrophic dynamo quenching, even in the absence of helicity fluxes. One can obtain final field strengths up to a fraction $\sim 0.01$ of the equipartition field $ B_{eq}$ for dynamo numbers $| D| \sim 40$, while fields comparable to $ B_{eq}$ require much larger degree of $α$ fluctuations or shear. This type of dynamo may be particularly useful for amplifying fields in the central regions of disk galaxies.
By incorporating a large-scale shear flow into turbulent rotating convection, we show that a sufficiently strong shear can promote dynamo action in flows that in the absence of shear do not act as dynamos. Our results are consistent with a dynamo driven by either the shear-current effect or by the interaction between a fluctuating $α$-effect and the velocity shear; they are though inconsistent with either a classical $α^2$ or $αω$ mean field dynamo.
Until recently, the existence of oscillatory mean-field dynamos of the alpha^2-type with spherically symmetric and isotropic alpha was an open question. We find such dynamos by means of an evolutionary strategy, and we illustrate the spectral properties of the corresponding dynamo operators.
Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the shear strength. We derive the integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For non helical turbulence the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, …
We analyse the role of a fluctuating alpha-effect in alpha-omega dynamo models, and show that there is a mechanism for magnetic field generation, valid at large scale separation, deriving from the interaction of mean shear and a fluctuating alpha-effect. It is shown that this effect can act as a dynamo even in the absence of a mean alpha-effect, and that the timescale for dynamo waves is strongly affected by the presence of fluctuations.
Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, are discussed. Based on the angular velocities of magnetic tracers it is argued that the observations are compatible with a distributed dynamo that may be strongly shaped by the near-surface shear layer. Direct simulations of dynamo action in a slab with turbulence and shear are presented to discuss filling factor and tilt angles of bipolar regio…
The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that the solar dynamo may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo disposing of its excess small scale magnetic helicity.
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…
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…
The consequences of the shear-induced alpha effect to the long-term modulation of magnetic activity are examined with the help of the axisymmetric numerical dynamo model that includes the self-consistent description of the angular momentum balance, heat transport and magnetic field generation in the spherical shell. We find that the shear contributions to alpha effect can complicate the long-term behaviour of the large-scale magnetic activity and differential rotation in nonlinear dynamo. Additionally we consider the impact secular magnetic activity variations to the secular modulations of the…
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…
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…
Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a mean-field dynamo. Exponential growth of magnetic field at scales larger than the outer (forcing) scale of the turbulence is found. Over a range of values of the shearing rate S spanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, gamma ~ S, while the characteristic spatial scale of the field is l_b ~ S^(-1/2). The effect is quite general: ea…
The question is answered whether kinematic alpha^2-shell-dynamos are able to produce a cyclic activity or not. The alpha-effect is allowed to be latitudinally inhomogeneous and/or anisotropic, but it is assumed as radially uniform in the turbulent shell. For a symmetric alpha-tensor we only find oscillatory solutions if i) the alpha_zz vanishes or is of the opposite sign as alpha_{phi phi}, ii) the alpha-effect is strongly concentrated to the equatorial region and iii) the alpha-effect is concentrated to a rather thin outer shell. In the other cases almost always the nonaxisymmetric field mode…
Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non-rotating wall-bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear fl…
We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time dependent model for alpha quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e. the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for…
The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic di…
(abridged) Aims: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. Methods: We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results: Without shear no large-scale dynamos are found even if the ingre…
We present a new fast dynamo model for galactic magnetic fields, which is based on the Parker-shearing instability and magnetic reconnection, in the spirit of the model proposed by Parker (1992). We introduce a new scenario of flux tube interactions and estimate the dynamo transport coefficient basing on simple geometrical arguments. The obtained expressions are equivalent to the formally derived helicity $α_d$ and diffusivity $η_d$ in the first paper of this series. The model we propose predicts that the $α$-effect in galactic discs has opposite sign with respect to that resulting directly fr…
The role of shear in alleviating catastrophic quenching by shedding small-scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force-free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5-fold decrease of the magnetic diffusivity as the magnetic Reynolds numbe…
Flux-dominated solar dynamo models have demonstrated to reproduce the main features of the large scale solar magnetic cycle, however the use of a solar like differential rotation profile implies in the the formation of strong toroidal magnetic fields at high latitudes where they are not observed. In this work, we invoke the hypothesis of a thin-width tachocline in order to confine the high-latitude toroidal magnetic fields to a small area below the overshoot layer, thus avoiding its influence on a Babcock-Leighton type dynamo process. Our results favor a dynamo operating inside the convection …
A magnetic dynamo experiment is under construction at the New Mexico Institute of Mining and Technology. The experiment is designed to demonstrate in the laboratory the alpha-omega magnetic dynamo, which is believed to operate in many rotating and conducting astrophysical objects. The experiment uses the Couette flow of liquid sodium between two cylinders rotating with different angular velocities to model the omega-effect. The alpha-effect is created by the rising and expanding jets of liquid sodium driven through a pair of orifices in the end plates of the cylindrical vessel, presumably simu…
In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $αΩ$ dynamos with a dynamic $α$ were studied with respect to a number of changes in the driving term of the dynamic $α$ equation, which was considered previously by Schmalz and Stix (1991) to be of the form $\sim A_ϕB_ϕ$. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form $α|B|^2$. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbe…
A plane-shear flow in a fluid with forced turbulence is considered. If the fluid is electrically-conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self-excitation of a large-scale magnetic field is possible (so-called WxJ-dynamo) and the answer is NO. The calculations reveal the cross-stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with m…
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.
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…
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…
Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $α$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $α$ appears to be complicated and is affected by the region of parameter space examined.
The possibility of the magnetic flux expulsion from the Galaxy in the superbubble (SB) explosions, important for the Alpha-Omega dynamo, is considered. Special emphasis is put on the investigation of the downsliding of the matter from the top of the shell formed by the SB explosion which is able to influence the kinematics of the shell. It is shown that either Galactic gravity or the development of the Rayleigh-Taylor instabilities in the shell limit the SB expansion, thus, making impossible magnetic flux expulsion. The effect of the cosmic rays in the shell on the sliding is considered and it…
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.
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 develop a model based on 3D mean-field MHD for the generation of large scale magnetic fields in fully convective objects like low-mass stars, brown dwarfs and possibly gaseous planets. The dynamo process is of alpha^2 type and thus differs from the shell-dynamo at work in more massive stars.The alpha^2 dynamo becomes supercritical for Rossby numbers Ro\la 10. It generates a large-scale, non-axisymmetric, steady field that is symmetric with respect to the equatorial plane. Saturation of the alpha^2-generated field at the equipartition yields strengths of several kGauss, in agreement with obs…
An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha-effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a new ''shear-current" effect. A contribution to the electromotive force related with the symmetric parts of the gradient tensor of the mean magnetic field (the kappa-effect) is found in a nonrotating turbulent flows with a mean shear.…
A rigorous theory for the generation of a large-scale magnetic field by random non-helically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low Rm and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wavenumber and growth rate of the fastest growing mode,…
The nonlinear theory of a "shear-current" effect in a nonrotating and nonhelical homogeneous turbulence with an imposed mean velocity shear is developed. The ''shear-current" effect is associated with the $\bar{\bf W} {\bf \times} \bar{\bf J}$-term in the mean electromotive force and causes the generation of the mean magnetic field even in a nonrotating and nonhelical homogeneous turbulence (where $\bar{\bf W}$ is the mean vorticity and $\bar{\bf J}$ is the mean electric current). It is found that there is no quenching of the nonlinear "shear-current" effect contrary to the quenching of the no…
We provide a theory of dynamo ($α$ effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the $α$ effect is severely reduced by the shear even in the absence of magnetic field. The $α$ effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magne…
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…
The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of larg…
We investigate the behaviour of $αΩ$ dynamos with a dynamic $α$, whose evolution is governed by the imbalance between a driving and a damping term. We focus on truncated versions of such dynamo models which are often studied in connection with solar and stellar variability. Given the approximate nature of such models, it is important to study how robust they are with respect to reasonable changes in the formulation of the driving and damping terms. For each case, we also study the effects of changes of the dynamo number and its sign, the truncation order and initial conditions. Our results sho…
We develop a model of the solar dynamo in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes like the production of poloidal field from the decay of active regions, and, on the other hand, we attempt to develop a mean field theory that can be studied in quantitative detail. One of the main challenges in developing such models is to treat the buoyant rise of toroidal field and the production of poloidal field from it near the surface. We build up a dynamo model with two contrasting methods of treating buoyancy. In one method, we incorporate the generati…
The shear-current effect in a nonrotating homogeneous turbulent convection with a large-scale constant shear is studied. The large-scale velocity shear causes anisotropy of turbulent convection, which produces the mean electromotive force $\bec{\cal E}^{(W)} \propto {\bf W} {\bf \times} {\bf J}$ and the mean electric current along the original mean magnetic field, where ${\bf W}$ is the background mean vorticity due to the shear and ${\bf J}$ is the mean electric current. This results in a large-scale dynamo even in a nonrotating and nonhelical homogeneous sheared turbulent convection, whereby…
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 he…
The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed bu…
The backreaction of the Lorentz force on the alpha-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear alpha-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can…
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 present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence …
A magnetic field dynamo in the inner regions of the accretion disk surrounding the supermassive black holes in AGNs may be the mechanism for the generation of magnetic fields in galaxies and in extragalactic space. We argue that the two coherent motions produced by 1) the Keplerian motion and 2) star-disk collisions, numerous in the inner region of AGN accretion disks, are both basic to the formation of a robust, coherent dynamo and consequently the generation of large scale magnetic fields. They are frequent enough to account for an integrated dynamo gain, e^{10^{9}} at 100 gravitational radi…
The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of Biot-Savart's law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most…
A review of recent studies on a new mechanism of generation of large-scale magnetic field in a sheared turbulent plasma is presented. This mechanism is associated with the shear-current effect which is related to the W x J-term in the mean electromotive force. This effect causes the generation of the large-scale magnetic field even in a nonrotating and nonhelical homogeneous sheared turbulent convection whereby the alpha effect vanishes. It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current eff…
In this paper we investigate the idea of Hanasz & Lesch 1993 that the galactic dynamo effect is due to the Parker instability of magnetic flux tubes. In addition to the former approach, we take into account more general physical conditions in this paper, by incorporating cosmic rays and differential forces due to the axisymmetric differential rotation and the density waves as well. We present the theory of slender magnetic flux tube dynamics in the thin flux tube approximation and the Lagrange description. This is the application of the formalism obtained for solar magnetic flux tubes by Sprui…
Increasing observations are becoming available about a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. It indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric alpha2-Omega dynamo model is set up to discuss the characteristics of the axisymmetric m=0 and the first non-axisymmetric m=1 modes and to provide further the theoretical bases to explain the active longitude, flip-flop and other non-axisymmetric phenomena. The model consists of a …
We analyze the electromotive force (EMF) terms and basic assumptions of the linear and nonlinear dynamo theories in our three-dimensional (3D) numerical model of the Parker instability with cosmic rays and shear in a galactic disk. We also apply the well known prescriptions of the EMF obtained by the nonlinear dynamo theory (Blackman & Field 2002 and Kleeorin et al. 2003) to check if the EMF reconstructed from their prescriptions corresponds to the EMF obtained directly from our numerical models. We show that our modeled EMF is fully nonlinear and it is not possible to apply any of the conside…
A three-dimensional nonlinear dynamo process is identified in rotating plane Couette flow in the Keplerian regime. It is analogous to the hydrodynamic self-sustaining process in non-rotating shear flows and relies on the magneto-rotational instability of a toroidal magnetic field. Steady nonlinear solutions are computed numerically for a wide range of magnetic Reynolds numbers but are restricted to low Reynolds numbers. This process may be important to explain the sustenance of coherent fields and turbulent motions in Keplerian accretion disks, where all its basic ingredients are present.
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…
A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac equation and to extract non-numerical information about the dynamo spectrum.
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust and accurate tools for the numerical solution of many problems in other fields of physics. The paper is intended to facilitate the use of integral equation solvers in dynamo theory. In concrete, the integral equation method is employed to solve the eigenvalue problem for a hydromagnetic dynamo model with a spherically symmetric, isotropic helical turbulence …
(abridged) Results from kinematic solar dynamo models employing alpha-effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2-3 m/s. The rotation profile of the Sun as obtained from helioseismology is applied. We obtain an estimate of the ratio of the two induction effects, C_alpha/C_Omega \approx 10^-3, which we keep fixed in all models. We also include a one-cell meridional circulation pattern having a magnitude of 10-20 m/s near the surface and 1-2 m/s at the bottom of the convection zone. The model essentially…
We consider the backreaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the backreaction on the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo coefficient $\a$, have a stringent upper limit that depends on the magnetic Reynolds number $R_M$ to a power of order -1. This is not a dynamic suppression but results just because of the imposed boundary conditions. In con…
A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large scale field on the scale of the box (at wavenumber k=1; forcing is at k=5). This large scale field is nearly force-free and exceeds the equipartition value. As the magnetic Reynolds number R_m increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to built up the large scale field from equ…
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 …
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.
