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In this paper, we study the correlation functions for magnetic energy and magnetic helicity generated by a small-scale dynamo mechanism in a mirror-asymmetric and isotropic turbulent conductive fluid. Solving the Kazantsev system for small-scale generation by an iterative approach, we restore the correlation functions in spatial and spectral representations. Studying scales of localisation and their dependence on magnetic Reynolds number, we propose approximate functions, which can be applied for energy and helicity in a spectral space. We show the absence of 3/2-spectrum for Kazantsev assumptions at and helicity sign changing at. Using our results and estimating the relation between helicity and energy at different scales, we speculate about what can be considered as a small scale in a spectral space, and how this scale can be connected with mean-field processes. [ABSTRACT FROM AUTHOR]

We propose a self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields, i.e., fields with a significant component on the scale of the system. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically.We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments. [ABSTRACT FROM AUTHOR]

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-K´arm´an-sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability μr that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rmc for dynamo action of the first non-axisymmetric mode roughly scales like Rmc μr − Rmc 1 / μ−1/2 r , i.e. the threshold decreases as μr increases. This scaling law suggests a skin effect mechanism in the soft iron discs. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high-permeability discs which becomes dominant for large μr. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disc interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of the high-permeability discs in the mode selection in the Cadarache dynamo experiment cannot be inferred from computations using idealized pseudovacuum boundary conditions (H ×n = 0). [ABSTRACT FROM AUTHOR]

Numerical dynamo models based on convection-driven flow in a rapidly rotating spherical shell frequently give rise to strong, stable, dipolar magnetic fields. Dipolar dynamos can be subcritical in the sense that strong magnetic fields are sustained at a Rayleigh number lower than that required for a dynamo to grow from a small seed field. In this paper we find subcritical behaviour in dynamos in line with previous studies. We explore the action of Lorentz force in a rotating dynamo which gives rise to a strong preference for dipolar modes over quadrupolar modes, and also makes subcritical behaviour more likely to occur. The coherent structures that arise in rapidly rotating convection are affected by the magnetic field in ways which strongly increase their helicity, particularly if the magnetic field is dipolar. As helicity enhances dynamo action, an existing magnetic field can hold itself up, which leads to subcritical behaviour in the dynamo. We investigate this mechanism by means of the asymptotic small Ekman number theory of rapidly rotating magnetoconvection, and compare our results with fully nonlinear dynamo simulations. There are also other mechanisms which can promote subcritical behaviour. When Reynolds stresses are significant, zonal flows can lower the helicity and disrupt the onset of dynamo action, but an established dipole field can suppress the zonal flow, and hence boost the helicity. Subcriticality means that a slow gradual reduction in Rayleigh number can lead to a catastrophic collapse of the dynamo once a critical Rayleigh number is reached. While there is little evidence that the Earth is currently in a subcritical regime, this may have implications for the long-term evolution of the geodynamo. [ABSTRACT FROM AUTHOR]

We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the low-conductivity limit. Our treatment is non-perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rem), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Rem. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the ‘C’ and ‘D’ terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the space–time integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the cross-shear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Rem, but to all orders in the shear strength, the D term cannot give rise to a shear-current-assisted dynamo effect; (iv) casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocity-spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shear-current-type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non-helical velocity dynamics at low fluid Reynolds number does not result in a shear-current-assisted dynamo effect. [ABSTRACT FROM AUTHOR]

Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force. [ABSTRACT FROM AUTHOR]

The backreaction of the Lorentz force on the α-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 non-linear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in the τ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find for delta-correlated forcing, in contrast to the well-known behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows. [ABSTRACT FROM AUTHOR]

The Archontis dynamo was the first stationary dynamo discovered which saturates with almost equal magnetic and kinetic energies in the limit of large Reynolds numbers. In this paper we present two further examples, one based on a series of numerical calculations and the other on the analytic rotor dynamos of Herzenberg. The forcing and flow in these new examples lack some of the symmetries of the Archontis dynamo are therefore more generic. The saturation mechanism is thus not a unique property of the Archontis dynamo. For the numerical solutions, we also have investigated the structure and stability of the flow and field near the stagnation points and those streamlines which enter and leave them. These structures play an important part in the operation of the dynamo mechanism, and the way they interact with one another is mirrored in the analytic example based on the Herzenberg rotors. [ABSTRACT FROM AUTHOR]

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case. [ABSTRACT FROM AUTHOR]

We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R⊙ has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number Rm. In the range of Rm = 104–106 the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process. [ABSTRACT FROM AUTHOR]