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 the resonant profile of the toroidal and poloidal frequencies modes of the dynamo force-free flow.
Using results of laboratory experiments, direct numerical simulations, geomagnetic and solar observations, it is shown that high moments of helicity distribution can dominate power spectra of the magnetic field generated by the magnetohydrodynamic (MHD) dynamo in swirling turbulence even for the cases with zero global helicity. The notion of helical distributed chaos has been used for this purpose.
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, mos…
The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two distinct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 - a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structu…
The role of the moments of helicity distribution in rotating turbulence has been studied using the notion of helical distributed chaos. Results of the direct numerical simulations, laboratory experiments and geophysical observations have been used in this investigation. It is shown, in particular, that even for the cases when the global helicity is equal to zero at least even moments are usually non-zero (due to the appearance of the local spatial regions with strong negative and positive helicity) and can play a significant role in the rotating turbulence as adiabatic invariants. Rotating buo…
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…
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…
The cross helicity (velocity--magnetic-field correlation) effects in the magnetic-field induction and momentum transport in the magnetohydrodynamic (MHD) turbulence are investigated with the aid of the multiple-scale renormalized perturbation expansion analysis. The outline of the theory is presented with reference to the role of the cross-interaction response functions between the velocity and magnetic field. In this formulation, the expressions of the turbulent fluxes: the turbulent electromotive force (EMF) in the mean induction equation and the Reynolds and turbulent Maxwell stresses in th…
We study mean-field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and nonzero correlation time ($τ$). We use plane shearing waves in terms of time-dependent exact solutions to the Navier-Stokes equation as derived by Singh \& Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues which yield the growth rate ($γ$) and the cycle period ($P_…
Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work \citep[][hereafter paper~I]{JS20}, where we have used the renovating flow based model with shearing waves. Both, the velocity and the helicity fields, are treated as stochastic variables with finite correlation times, $τ$ and $τ_h$, respectively. Growing solutions are obtained when $τ_h > τ$, even when this time-scale separation, characterised by $m=τ_h/τ$, remains below…
The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout bifurcation is conjectured to be responsible for the transition to dynamo, leading to a sudden increase in the magnetic energy of the attractor. This high-energy hydromagnetic attractor is suddenly destroyed in a boundary crisis when the helicity is decreased. Both the blowout bifurcation and the boundary crisis generate long chaotic transients that are due, respecti…
The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale $α$-type dynamo action and the inverse transfer of magnetic h…
We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than…
The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this work we show that in turbulent helical dynamos, the inverse flux of magnetic helicity towards the large scales $Π_{\mathcal{H}}$ is bounded by $|Π_{\mathcal{H}}|\le c εk_η^{-1}$, where $ε$ is the energy injection rate, $k_η$ is the Kolmogorov magnetic dissipation wavenumber and $c$ an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity $Π_{\mathcal{H}}$ decreases at least as …
We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density, nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic $α$-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field f…
Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies, and the early Universe are discussed. We focus particularly on aspects of spatio-temporal nonlocality, which is one of the main insights that emerged from applying the test-field method to magnetic fields of different length and timescales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate…
Evidence for the emergence of twisted flux tubes into the solar atmosphere has, so far, come from indirect signatures. In this work, we investigate the topological input of twisted flux tube emergence directly by studying helicity and winding fluxes. In magnetohydrodynamic simulations with domains spanning from the top of the convection zone to the lower corona, we simulate the emergence of twisted flux tubes with a range of different initial field strengths. One important feature of this work is the inclusion of a convectively-unstable layer beneath the photosphere. We find approximately self…
Pointwise zero velocity helicity density is shown not to prevent steady flows from acting as kinematic dynamos. We present numerical evidences that such flows can generate both small-scale magnetic fields as well as, by the magnetic $α$-effect or negative eddy diffusivity mechanisms, large-scale ones. The flows are constructed as curls of analytically defined space-periodic steady solenoidal flows, whose vorticity helicity (i.e., kinetic helicity) density is everywhere zero.
The buildup of small-scale magnetic helicity which accompanies the oppositely signed growth on large scales is central to conventional dynamical quenching theories of mean-field dynamos. However, the conventional formalism presumes isotropic turbulence and thereby excludes part of the magnetic Lorentz back-reaction. This renders it insufficient to predict the full quenching for general anisotropic flows. To overcome this deficiency, we derive a new generalized quenching formalism that includes the full back-reacting Lorentz force, and a new "selective-damping-$τ$" closure which conserves magne…
The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it however currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behaviour of large-scale fluid magnetism in the astrophysically-relevant but treacherous regime of large magnetic Reynolds number $Rm$ is still lacking. We explore thi…
Topology and existence of three-dimensional kinematic dynamos
计算了运动发电机流的流线磁结构的磁能的曲率和螺旋度拓扑界。通过求解三维流动的磁流体动力学方程，确定了细丝发电机的存在性，并利用该解确定了这些边界。结果表明，在零电阻率极限下，各向同性情况下，无源发电机总是存在的，然而，当考虑到Frenet标架不仅依赖于细丝长度参数s时，（各向异性情况）无源发电机结构的存在依赖于螺旋发电机情况下的曲率. Frenet曲率与forld和扭转扭转有关，这使我们能够有一个sretch，扭曲和折叠的方法来建立快速的灯丝发电机。Arnold定理的螺旋度界限的发散自由矢量场的能量是满足这些流线和常数取决于紧域$M C R^{2}$的大小，其中的矢量场的定义是确定的方面的尺寸的恒定横截面的细丝。结果表明，当磁场结构出现丝状放大而违反Arnold定理时，磁场在空间中衰减。
Turbulent dynamo theories have faced difficulties in obtaining evolution of large-scale magnetic fields on short dynamical time-scales due to the constraint imposed by magnetic helicity balance. This has critical implications for understanding the large-scale magnetic field evolution in astrophysical systems like the Sun, stars and galaxies. Direct numerical simulations (DNS) in the past with isotropically forced helical turbulence have shown that large-scale dynamo saturation time-scales are dependent on the magnetic Reynolds number (Rm). In this work, we have carried out periodic box DNS of …
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterise the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times. It follows that the Gauss-linking number is a more …
We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales.…
We show that non-axisymmetric, non-helical perturbations in an unstratified shear flow produce a shear-plane averaged electromotive force (EMF) proportional to a spatially dependent kinetic helicity. This new "shear-driven $α$-effect" can amplify shear-plane averaged magnetic fields, but is undiscoverable when invoking the homogeneity assumption for dynamo coefficients. It is a candidate mechanism underlying large scale field generation in astrophysical, laboratory, and simulated shear flows, and highlights the essentiality of correctly averaging dynamo coefficients and fields.
