Recently Shukurov, Stepanov and Sokoloff [\textbf{Phys. Rev. E 69 (2008)}] have suggested that Moebius flows can support dynamo action. In this report, it is shown that a steady perturbation of a magnetic field in a general twisted Riemannian flux tube may support dynamo action. Instead of the twist number used in the above reference, the focus here is on the Frenet torsion of the magnetic flux tube. A relation between the constant torsion of the screw dynamo torus, its internal radius, and the ratio between toroidal and poloidal flow. Solution of self-induction equation for the screw dynamo torsioned flow, can be solved to yield a Frenet torsion as high as $τ_{0}\approx{7.5{\times}Ω^θHz^{-1}m^{-1}}$, for an applied random magnetic field of $<B^{0}>\approx{45 G}$ for an induced steady perturbation of $B_{1}\approx{0.03G}$, as in the Perm Riemannian torus experiment. The Moebius strip plays the role of the propeller divertor which imprints the angular velocity $Ω^θ$, around the torus axis, to the dynamo flow, here this role is played by torsion. Actually this situation is already familiar to plasma physicists, where in stellarators torsion substitutes very well the role played by external magnetic fields in tokamaks making magnetic fields twist along plasma toroidal devices. Weak torsion of the torus channel is assumed.
Laminar electrically conducting Couette flows with the hydrodynamically stable quasi-Keplerian rotation profile and non-uniform conductivity are probed for dynamo instability. In spherical geometry the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or -- much more complex …
The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the background of strong toroidal magnetic field. The extra invariant is used to show that the background field is maintained.
It is proposed that convection driven dynamos operating in planetary cores could be oscillatory even when the oscillations are not directly noticeable from the outside. Examples of dynamo simulations are pointed out that exhibit oscillations in the structure of the azimuthally averaged toroidal magnetic flux while the mean poloidal field shows only variations in its amplitude. In the case of the geomagnetic field, global excursions may be associated with these oscillations. Long period dynamo simulations indicate that the oscillations may cause reversals once in a while. No special attempt has…
Chicone et al [CMP (1995)] have shown that, kinematic fast dynamos in diffusive media, could exist only on a closed, 2D Riemannian manifold of constant negative curvature. This report, shows that their result cannot be extended to oscillatory $α^{2}$-dynamos, when there are resonance modes, between toroidal and poloidal frequencies of twisted magnetic flux tubes. Thus, dynamo action can be supported in regions, where Riemannian curvature is positive. For turbulent dynamos, this seems physically reasonable, since recently, [Shukurov et al PRE (2008)] have obtained a Moebius flow strip in sodium…
Here, an analytical version of numerical results is obtained in case of considering the laminar non-turbulent limit, of a twisted Riemannian thin flux tube. It is shown that the magnetic field is amplified, when electric current helicity and Riemann curvature are both negative. Thus spaces of positive and negative Riemannian curvatures seems to support dynamo action inside the torus, and not only negative Riemannian curvature surfaces as happens in 2D dynamos. New features appear in $α^{2}$-dynamo twisted flow, using the approximation of thin tubes flux tubes. These solutions are obtained in t…
We study the influence of various magnetic diffusivity profiles on the evolution of the poloidal and toroidal magnetic fields in a kinematic flux transport dynamo model for the Sun. The diffusivity is a poorly understood ingredient in solar dynamo models. We mathematically construct various theoretical profiles of the depth-dependent diffusivity, based on constraints from mixing length theory and turbulence, and on comparisons of poloidal field evolution on the Sun with that from the flux-transport dynamo model. We then study the effect of each diffusivity profile in the cyclic evolution of th…
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of t…
Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obta…
We present a new scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect-ratio. When the angular momentum sufficiently decreases outwards, an hydrodynamic instability develops in the equatorial region, characterised by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by non-axisymmetric components. We show that the critical magnetic Reynolds number seem…
A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $α$--$Ω$-type models mainly in two points. First, in addition to the usual $α$ (helicity effect) and $β$ (turbulent magnetic diffusivity), we consider the $γ$ coefficient (c…
We propose a plasma experiment to be used to investigate fundamental properties of astrophysical dynamos. The highly conducting, fast-flowing plasma will allow experimenters to explore systems with magnetic Reynolds numbers an order of magnitude larger than those accessible with liquid-metal experiments. The plasma is confined using a ring-cusp strategy and subject to a toroidal differentially rotating outer boundary condition. As proof of principle, we present magnetohydrodynamic simulations of the proposed experiment. When a von Kármán-type boundary condition is specified, and the magnetic R…
The theory of planetary dynamos and its applications to observed phenomena of planetary magnetism are outlined. It is generally accepted that convection flows driven by thermal or compositional buoyancy are the most likely source for the sustenance of global planetary magnetic fields. While the existence of dynamos in electrically conducting fluid planetary cores provides constraints on properties of the latter, the lack of knowledge about time dependences of the magnetic fields and about their toroidal components together with the restricted parameter regions accessible to theory have prevent…
The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three dimensional numerical computation. A simple impeller model drives a flow which can generate a growing magnetic field, depending upon the magnetic Reynolds number, Rm, and the fluid Reynolds number. When the flow is laminar, the dynamo transition is governed by a simple threshold in Rm, above which a growing magnetic eigenmode is observed. The eigenmode is primarily a dipole field tranverse to axis of symmetry o…
We have performed numerical simulations of boundary-driven dynamos using a three-dimensional non-linear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion by the counter-rotation of the two hemispheric walls. The resulting flow is of von Kármán type, consisting of a layer of zonal velocity close to the outer wall and a secondary meridional circulation. Above a certain forcing threshold, the mean flow is unstable to non-axisymmetric motions within an equatorial belt. For fixed forcing above this threshold, we ha…
The $Ω$-phase of the liquid sodium $α$-$Ω$ dynamo experiment at NMIMT in cooperation with LANL has successfully demonstrated the production of a high toroidal field, $B_ϕ \simeq 8\times B_r$ from the radial component of an applied poloidal magnetic field, $B_r$. This enhanced toroidal field is produced by rotational shear in stable Couette flow within liquid sodium at $Rm \simeq 120$. The small turbulence in stable Taylor-Couette flow is caused by Ekman flow where $ (δv/v)^2 \sim 10^{-3} $. This high $Ω$-gain in low turbulence flow contrasts with a smaller $Ω$-gain in higher turbulence, Helmho…
The inverse solution of the 1D Parker dynamo equations is considered. The method is based on minimization of the cost-function, which characterize deviation of the model solution properties from the desired ones. The output is the latitude distribution of the magnetic field generation sources: the $α$- and $ω$-effects. Minimization is made using the Monte-Carlo method. The details of the method, as well as some applications, which can be interesting for the broad dynamo community, are considered: conditions when the invisible for the observer at the surface of the planet toroidal part of the m…
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.
A numerical study of the magnetic induction equation has been performed on von Karman type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Karman 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…
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…
The value of the Prandtl number $P$ exerts a strong influence on convection-driven dynamos in rotating spherical shells filled with electrically conducting fluids. Low Prandtl numbers promote dynamo action through the shear provided by differential rotation, while the generation of magnetic fields is more difficult to sustain in high-Prandtl-number fluids where higher values of the magnetic Prandtl number $P_m$ are required. The magnetostrophic approximation often used in dynamo theory appears to be valid only for relatively high values of $P$ and $P_m$. Dynamos with a minimum value of $P_m$ s…
The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic…
A general type of mathematical argument is described, which applies to all the cases in which dynamo maintenance of a steady magnetic field by motion in a uniform density is known to be impossible. Previous work has demonstrated that magnetic field decay is unavoidable under conditions of axisymmetry and in spherical or planar incompressible flows. These known results are encompassed by a calculation for flows described in terms of a generalized poloidal-toroidal representation of the magnetic field with respect to an arbitrary two dimensional surface. We show that when the velocity field is t…
Transport coefficients in turbulence are comprised of correlation functions between turbulent fluctuations and efficient methods to calculate them are desirable. For example, in mean field dynamo theories used to model the growth of large scale magnetic fields of stars and galaxies, the turbulent electromotive force is commonly approximated by a series of tensor products of turbulent transport coefficients with successively higher order spatial derivatives of the mean magnetic field. One ingredient of standard models is the kinematic coefficient of the zeroth order term, namely the averaged ki…
The dynamics of stably stratified stellar radiative zones is of considerable interest due to the availability of increasingly detailed observations of Solar and stellar interiors. This article reports the first non-axisymmetric and time-dependent simulations of flows of anelastic fluids driven by baroclinic torques in stably stratified rotating spherical shells -- a system serving as an elemental model of a stellar radiative zone. With increasing baroclinicity a sequence of bifurcations from simpler to more complex flows is found in which some of the available symmetries of the problem are bro…
Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much larger values than is possible through laminar proc…
