arXiv subjects

Axel Brandenburg

Publications and source records attributed to Axel Brandenburg.

At least 217 records · Page 12Linked to original sources

arXiv2012

Lagrangian chaos in an ABC--forced nonlinear dynamo

The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures, which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and one with intermittent bursts of magnetic energy. The Lagrangian coherent structures and the statistics of finite--time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of the magnetic energy. The relevance of this study for the solar dynamo problem is discussed.

astro-ph.SR↗

arXiv2012

Magnetic helicity fluxes and their effect on stellar dynamos

Magnetic helicity fluxes in turbulently driven alpha^2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 10^5. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $αΩ$ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.

astro-ph.SR↗

arXiv2011

Spontaneous formation of flux concentrations in a stratified layer

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNS) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in formation of large-scale inhomogeneous magnetic structures from initial uniform magnetic field. Earlier investigations of this instability in DNS of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L^2/eta_t, where eta_t is the turbulent diffusivity and L is the scale of the domain. DNS are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number.

astro-ph.SR↗

arXiv2011

Cycles and cycle modulations

Some selected concepts for the solar activity cycle are briefly reviewed. Cycle modulations through a stochastic alpha effect are being identified with limited scale separation ratios. Three-dimensional turbulence simulations with helicity and shear are compared at two different scale separation ratios. In both cases the level of fluctuations shows relatively little variation with the dynamo cycle. Prospects for a shallow origin of sunspots are discussed in terms of the negative effective magnetic pressure instability. Tilt angles of bipolar active regions are discussed as a consequence of shear rather than the Coriolis force.

astro-ph.SR↗

arXiv2011

Spontaneous chiral symmetry breaking in the Tayler instability

The chiral symmetry breaking properties of the Tayler instability are discussed. Effective amplitude equations are determined in one case. This model has three free parameters that are determined numerically. Comparison with chiral symmetry breaking in biochemistry is made.

astro-ph.SR↗

arXiv2011

Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Pèclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

astro-ph.GA↗

arXiv2011

Coronal ejections from convective spherical shell dynamos

We present a three-dimensional model of rotating convection combined with a simplified corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field that gets sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.

astro-ph.SR↗

arXiv2011

Detection of negative effective magnetic pressure instability in turbulence simulations

We present the first demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, an initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number, provided its value is large enough for the instability to be excited. Our results support earlier mean-field calculations and analytic work which identified this instability. Applications to the formation of active regions in the Sun are discussed.

astro-ph.SR↗

arXiv2011

Nonlinear small-scale dynamos at low magnetic Prandtl numbers

Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers Pm down to 0.01. For Pm < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Pm^{1/2} down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k^{-11/3} spectrum near the resistive scale also some evidence for a short k^{-1} spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of Pm and decreases by about a factor of 2 as Pm is decreased from 1 to 0.01. The possibility of dynamo action at Pm=0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber.

astro-ph.SR↗

arXiv2011

Spontaneous chiral parity breaking by hydromagnetic buoyancy

Evidence for a parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the non-helical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of an instability in magnetohydrodynamics appears to be the first of its kind and is similar to chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are being discussed.

astro-ph.SR↗

arXiv2011

Decay of trefoil and other magnetic knots

Two setups with interlocked magnetic flux tubes are used to study the evolution of magnetic energy and helicity on magnetohydrodynamical (MHD) systems like plasmas. In one setup the initial helicity is zero while in the other it is finite. To see if it is the actual linking or merely the helicity content that influences the dynamics of the system we also consider a setup with unlinked field lines as well as a field configuration in the shape of a trefoil knot. For helical systems the decay of magnetic energy is slowed down by the helicity which decays slowly. It turns out that it is the helicity content, rather than the actual linking, that is significant for the dynamics.

astro-ph.SR↗

arXiv2011

Magnetic helicity fluxes in alpha Omega dynamos

In turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be important for alleviating catastrophic quenching.

astro-ph.SR↗

arXiv2011

Influence of Magnetic Helicity in MHD

Observations have shown that the Sun's magnetic field has helical structures. The helicity content in magnetic field configurations is a crucial constraint on the dynamical evolution of the system. Since helicity is connected with the number of links we investigate configurations with interlocked magnetic flux rings and one with unlinked rings. It turns out that it is not the linking of the tubes which affects the magnetic field decay, but the content of magnetic helicity.

astro-ph.SR↗

arXiv2011

Vorticity from irrotationally forced flow

In the interstellar medium the turbulence is believed to be forced mostly through supernova explosions. In a first approximation these flows can be written as a gradient of a potential being thus devoid of vorticity. There are several mechanisms that could lead to vorticity generation, like viscosity and baroclinic terms, rotation, shear and magnetic fields, but it is not clear how effective they are, neither is it clear whether the vorticity is essential in determining the turbulent diffusion acting in the ISM. Here we present a study of the role of rotation, shear and baroclinicity in the generation of vorticity in the ISM.

astro-ph.GA↗

arXiv2011

Decay of helical and non-helical magnetic knots

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the $n$-foil knots the decay is described by power laws that range form $t^{-2/3}$ to $t^{-1/3}$, which can be as slow as the $t^{-1/3}$ behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like $t^{-1}$, which is somewhat slower than the previously obtained $t^{-3/2}$ behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.

astro-ph.SR↗

arXiv2011

Dynamo-driven plasmoid ejections above a spherical surface

We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection. A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with a helical forcing function in the interior, where the sign changes at the equator between the two hemispheres. An oscillatory large-scale dynamo with equatorward migration is found to operate in the turbulence zone. Plasmoid ejections occur in regular intervals, similar to what is seen in earlier Cartesian models. These plasmoid ejections are tentatively associated with coronal mass ejections. The magnetic helicity is found to change sign outside the turbulence zone, which is in agreement with recent findings for the solar wind.

astro-ph.SR↗

arXiv2011

Angular momentum transport in convectively unstable shear flows

Angular momentum transport owing to hydrodynamic turbulent convection is studied using local three dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (Lambda-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is of the order of the mixing length estimate and weakly affected by rotation. The Lambda-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e. when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number.

astro-ph.SR↗

arXiv2011

A model of driven and decaying magnetic turbulence in a cylinder

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries, an imposed axial magnetic and electric field. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the α-effect in astrophysical applications. Application to the reversed field pinch in plasma confinement devices is discussed.

physics.plasm-ph↗