arXiv subjects

Axel Brandenburg

Publications and source records attributed to Axel Brandenburg.

At least 271 records · Page 15Linked to original sources

arXiv2009

Turbulent dynamos in spherical shell segments of varying geometrical extent

We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative time scales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios.

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arXiv2009

Paradigm shifts in solar dynamo modeling

Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear layer is discussed. The role of turbulent downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic field would be rapidly lost from the convection zone by magnetic buoyancy. It is argued that shear-mediated small-scale magnetic helicity fluxes are responsible for the success of some of the recent large-scale dynamo simulations. These fluxes help in disposing of excess small-scale magnetic helicity. This small-scale magnetic helicity, in turn, is generated in response to the production of an overall tilt in each Parker loop. Some preliminary calculations of this helicity flux are presented for a system with uniform shear. In the Sun the effects of magnetic helicity fluxes may be seen in coronal mass ejections shedding large amounts of magnetic helicity.

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arXiv2009

Turbulent diffusion with rotation or magnetic fields

The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length scales, i.e., when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.

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arXiv2009

Large-scale dynamos at low magnetic Prandtl numbers

Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat.

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arXiv2009

Small-scale magnetic helicity losses from a mean-field dynamo

Using mean-field models with a dynamical quenching formalism we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result either from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity concentration, or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong both for large-scale and small-scale fields. In the presence of shear there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behavior emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.

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arXiv2009

From fibril to diffuse fields during dynamo saturation

The degree of intermittency of the magnetic field of a large-scale dynamo is considered. Based on simulations it is argued that there is a tendency for the field to become more diffuse and non-intermittent as the dynamo saturates. The simulations are idealized in that the turbulence is strongly helical and shear is strong, so the tendency for the field to become more diffuse is somewhat exaggerated. Earlier results concerning the effects of magnetic buoyancy are discussed. It is emphasized that the resulting magnetic buoyancy is weak compared with the stronger effects of simultaneous downward pumping. These findings are used to support the notion that the solar dynamo might operate in a distributed fashion where the near-surface shear layer could play an important role.

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arXiv2009

Advances in theory and simulations of large-scale dynamos

Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.

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arXiv2009

Numerical study of large-scale vorticity generation in shear-flow turbulence

Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii in 2003 (Phys. Rev. E 68, 016311). This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wavenumber of the energy-carrying eddies.

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arXiv2008

Alpha effect and diffusivity in helical turbulence with shear

We study the dependence of turbulent transport coefficients, such as the components of the $α$ tensor ($α_{ij}$) and the turbulent magnetic diffusivity tensor ($η_{ij}$), on shear and magnetic Reynolds number in the presence of helical forcing. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. We find that with increasing shear the diagonal components of $α_{ij}$ quench, whereas those of $η_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $γ$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $α_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.

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arXiv2008

A growing dynamo from a saturated Roberts flow dynamo

Using direct simulations, weakly nonlinear theory and nonlinear mean-field theory, it is shown that the quenched velocity field of a saturated nonlinear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by F. Cattaneo & S. M. Tobias (arXiv:0809.1801) for the more complicated case of turbulent convection, suggesting that this may be a common property of nonlinear dynamos; see also the talk given also online at the Kavli Institute for Theoretical Physics (http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued that this property can be used to test nonlinear mean-field dynamo theories.

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arXiv2008

Mean-field effects in the Galloway-Proctor flow

The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane.

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arXiv2008

Nonlinear aspects of astrobiological research

Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain handedness include mechanisms involving either autocatalysis or, alternatively, epimerization as governing effects. Concepts for establishing hereditary information are discussed in terms of the theory of hypercycles. Instabilities toward parasites and possible remedies by invoking spatial extent are reviewed. Finally, some effects of early life are discussed that contributed to modifying and regulating atmosphere and climate of the Earth, and that could have contributed to the highly oxidized state of its crust.

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arXiv2008

The dual role of shear in large-scale dynamos

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 number based on the wavenumber of the energy-carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large-scale fields by the magneto-rotational instability is emphasized. New simulations are presented and the 3pi/4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean-field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane.

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arXiv2008

Turbulent protostellar discs

Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic field generation in turbulent discs is emphasized in connection with driving outflows and with star-disc coupling.

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arXiv2008

Core Mass Function: The Role of Gravity

We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a log-normal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance with the IMF when cores are selected with an increasing density threshold in the observations.

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arXiv2008

Decomposition of Complex Reaction Networks into Reactons

The analysis of complex reaction networks is of great importance in several chemical and biochemical fields (interstellar chemistry, prebiotic chemistry, reaction mechanism, etc). In this article, we propose to simultaneously refine and extend for general chemical reaction systems the formalism initially introduced for the description of metabolic networks. The classical approaches through the computation of the right null space leads to the decomposition of the network into complex ``cycles'' of reactions concerned with all metabolites. We show how, departing from the left null space computation, the flux analysis can be decoupled into linear fluxes and single loops, allowing a more refine qualitative analysis as a function of the antagonisms and connections among these local fluxes. This analysis is made possible by the decomposition of the molecules into elementary subunits, called "reactons" and the consequent decomposition of the whole network into simple first order unary partial reactions related with simple transfers of reactons from one molecule to another. This article explains and justifies the algorithmic steps leading to the total decomposition of the reaction network into its constitutive elementary subpart.

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arXiv2008

Alpha-effect dynamos with zero kinetic helicity

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 the possibility of dynamo action in the absence of kinetic helicity.

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arXiv2007

Kinematic alpha effect in isotropic turbulence simulations

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 alpha 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 $\Rm$, alpha and turbulent diffusivity are proportional to $\Rm$. Over finite time intervals meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that small-scale dynamo-generated fields do not make a correlated contribution to the mean electromotive force.

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