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  • 1. Babkovskaia, Natalia
    et al.
    Haugen, N. E. L.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    A high-order public domain code for direct numerical simulations of turbulent combustion2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 1, 1-12 p.Article in journal (Refereed)
    Abstract [en]

    A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available PENCIL CODE is validated with the focus on hydrogen combustion. This is the first open source DNS code with detailed chemistry available. An attempt has been made to present, for the first time, the full set of evolution and auxiliary equations required for a complete description of single phase non-isothermal fluid dynamics with detailed chemical reactions. Ignition delay times (0D) and laminar flame velocities (1D) are calculated and compared with results from the commercially available Chemkin code. The scheme is verified to be fifth order in space. Upon doubling the resolution, a 32-fold increase in the accuracy of the flame front is demonstrated. Finally, also turbulent and spherical flame front velocities are calculated and the implementation of the non-reflecting so-called Navier-Stokes Characteristic Boundary Condition is validated in all three directions.

  • 2. Bejarano, Cecilia
    et al.
    Gomez, Daniel O.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    SHEAR-DRIVEN INSTABILITIES IN HALL-MAGNETOHYDRODYNAMIC PLASMAS2011In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 737, no 2, 62- p.Article in journal (Refereed)
    Abstract [en]

    The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence, or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability (MRI), which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper, we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that an instability develops when the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called MRI and quantitatively assess the role of the Hall effect on its development and evolution.

  • 3.
    Brandenburg, A.
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy.
    Kleeorin, N.
    Rogachevskii, I.
    Large-scale magnetic flux concentrations from turbulent stresses2010In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, 5-13 p.Article in journal (Refereed)
    Abstract [en]

    % In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. Using three-dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two-dimensional and three-dimensional mean-field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large-scale instability results in the formation of loop-like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean-field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena.} \begin{document

  • 4.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Chandrasekhar-Kendall functions in astrophysical dynamos2011In: Pramana (Bangalore), ISSN 0304-4289, E-ISSN 0973-7111, Vol. 77, no 1, 67-76 p.Article in journal (Refereed)
    Abstract [en]

    Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number.

  • 5.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Magnetic field evolution in simulations with Euler potentials2010In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 401, no 1, 347-354 p.Article in journal (Refereed)
    Abstract [en]

    Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.

  • 6.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers2011In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 741, no 2, 92- p.Article in journal (Refereed)
    Abstract [en]

    Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers Pr M down to 0.01. For Pr M < 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 Pr1/2 M 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 Pr M and decreases by about a factor of two as Pr M is decreased from 1 to 0.01. The possibility of dynamo action at Pr M = 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.

  • 7.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    The critical role of magnetic helicity in astrophysical large-scale dynamos2009In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 51, no 12, 4043- p.Article in journal (Refereed)
    Abstract [en]

    The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity flux of 1046 Mx2/cycle is given.

  • 8.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Candelaresi, Simon
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Chatterjee, Piyali
    Small-scale magnetic helicity losses from a mean-field dynamo2009In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 3, 1414-1422 p.Article in journal (Refereed)
    Abstract [en]

    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 from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density 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 for both large- 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 behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.

  • 9.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Turbulent diffusion and galactic magnetism2009In: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 5, 432-433 p.Article in journal (Other academic)
    Abstract [en]

    Using the test-field method for nearly irrotational turbulence driven by spherical expansion waves it is shown that the turbulent magnetic diffusivity increases with magnetic Reynolds numbers. Its value levels off at several times the rms velocity of the turbulence multiplied by the typical radius of the expansion waves. This result is discussed in the context of the galactic mean-field dynamo.

  • 10.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Haugen, Nils Erland L.
    Babkovskaia, Natalia
    Turbulent front speed in the Fisher equation: Dependence on Damkohler number2011In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 83, no 1, 016304- p.Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in cases in which the Damkohler number is large. This effect is found to saturate the front speed to values comparable with the speed of the turbulent motions. By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows. The nonlinearity of the reaction term is found to make the front speed slightly faster.

  • 11.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Nordlund, Åke
    Astrophysical turbulence modeling2011In: Reports on progress in physics (Print), ISSN 0034-4885, E-ISSN 1361-6633, Vol. 74, no 4, 046901- p.Article, review/survey (Refereed)
    Abstract [en]

    The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non-coarse-grained) fields.

  • 12.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Raedler, K-H
    Yoshizawa's cross-helicity effect and its quenching2013In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, no 1-2, 207-217 p.Article in journal (Refereed)
    Abstract [en]

    A central quantity in mean-field magnetohydrodynamics is the mean electromotive force , which in general depends on the mean magnetic field. It may however also have a part independent of the mean magnetic field. Here we study an example of a rotating conducting body of turbulent fluid with non-zero cross-helicity, in which a contribution to proportional to the angular velocity occurs (Yoshizawa, A., Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields. Phys. Fluids B 1990, 2, 15891600). If the forcing is helical, it also leads to an effect, and large-scale magnetic fields can be generated. For not too rapid rotation, the field configuration is such that Yoshizawa's contribution to is considerably reduced compared to the case without effect. In that case, large-scale flows are also found to be generated.

  • 13.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Sokoloff, Dmitry
    Subramanian, Kandaswamy
    Current Status of Turbulent Dynamo Theory From Large Scale to Small-Scale Dynamos2012In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 169, no 1-4, 123-157 p.Article, review/survey (Refereed)
    Abstract [en]

    Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

  • 14.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Stepanov, Rodion
    FARADAY SIGNATURE OF MAGNETIC HELICITY FROM REDUCED DEPOLARIZATION2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 786, no 2, 91- p.Article in journal (Refereed)
    Abstract [en]

    Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array.

  • 15.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Subramanian, Kandaswamy
    Balogh, Andre
    Goldstein, Melvyn L.
    SCALE DEPENDENCE OF MAGNETIC HELICITY IN THE SOLAR WIND2011In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 734, no 1, 9- p.Article in journal (Refereed)
    Abstract [en]

    We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k approximate to 2 AU(-1) (or frequency nu approximate to 2 mu Hz) at distances below 2.8 AU and at k approximate to 30 AU(-1) (or nu approximate to 25 mu Hz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 10(45) Mx(2) cycle(-1) at large scales and to a three times lower value at smaller scales.

  • 16.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Decay of helical and nonhelical magnetic knots2011In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, no 1, 016406- p.Article in journal (Refereed)
    Abstract [en]

    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.

  • 17.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kinetic helicity needed to drive large-scale dynamos2013In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 87, no 4, 043104- p.Article in journal (Refereed)
    Abstract [en]

    Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called a effect when the turbulence is helical and if the domain is large enough for the a effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos. DOI: 10.1103/PhysRevE.87.043104

  • 18.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    The kinetic helicity needed to drive large-scale dynamosIn: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376Article in journal (Refereed)
  • 19.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Hubbard, Alexander
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Magnetic helicity transport in the advective gauge family2011In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 18, no 1, 012903- p.Article in journal (Refereed)
    Abstract [en]

    Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential.

  • 20.
    Chatterjee, Piyali
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Guerrero, Gustavo
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Can catastrophic quenching be alleviated by separating shear and α effect?2010In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 104, no 5&6, 591-599 p.Article in journal (Refereed)
    Abstract [en]

    The small-scale magnetic helicity produced as a by-product of the large-scale dynamo is believed to play a major role in dynamo saturation. In a mean-field model the generation of small-scale magnetic helicity can be modelled by using the dynamical quenching formalism. Catastrophic quenching refers to a decrease of the saturation field strength with increasing Reynolds number. It has been suggested that catastrophic quenching only affects the region of non-zero helical turbulence (i.e. where the kinematic alpha operates) and that it is possible to alleviate catastrophic quenching by separating the region of strong shear from the alpha layer. We perform a systematic study of a simple axisymmetric two-layer alpha-omega dynamo in a spherical shell for Reynolds numbers in the range 1 < Rm < 10^5. In the framework of dynamical quenching we show that this may not be the case, suggesting that magnetic helicity fluxes would be necessary.

  • 21.
    Chatterjee, Piyali
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Guerrero, Gustavo
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Magnetic helicity fluxes in interface and flux transport dynamos2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 525, A5- p.Article in journal (Refereed)
    Abstract [en]

    Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims: In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods: We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula. Results: In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes.

  • 22.
    Del Sordo, Fabio
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Vorticity production through rotation, shear, and baroclinicity2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 528, A145- p.Article in journal (Refereed)
    Abstract [en]

    Context. In the absence of rotation and shear, and under the assumption of constant temperature or specific entropy, purely potential forcing by localized expansion waves is known to produce irrotational flows that have no vorticity. Aims. Here we study the production of vorticity under idealized conditions when there is rotation, shear, or baroclinicity, to address the problem of vorticity generation in the interstellar medium in a systematic fashion. Methods. We use three-dimensional periodic box numerical simulations to investigate the various effects in isolation. Results. We find that for slow rotation, vorticity production in an isothermal gas is small in the sense that the ratio of the root-mean-square values of vorticity and velocity is small compared with the wavenumber of the energy-carrying motions. For Coriolis numbers above a certain level, vorticity production saturates at a value where the aforementioned ratio becomes comparable with the wavenumber of the energy-carrying motions. Shear also raises the vorticity production, but no saturation is found. When the assumption of isothermality is dropped, there is significant vorticity production by the baroclinic term once the turbulence becomes supersonic. In galaxies, shear and rotation are estimated to be insufficient to produce significant amounts of vorticity, leaving therefore only the baroclinic term as the most favorable candidate. We also demonstrate vorticity production visually as a result of colliding shock fronts.

  • 23.
    Del Sordo, Fabio
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Candelaresi, Simon
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Magnetic-field decay of three interlocked flux rings with zero linking number2010In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 81, no 3, 36401- p.Article in journal (Refereed)
    Abstract [en]

    The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.

  • 24.
    Devlen, Ebru
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ege University.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    A mean field dynamo from negative eddy diffusivity2013In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 432, no 2, 1651-1657 p.Article in journal (Refereed)
    Abstract [en]

    Using direct numerical simulations, we verify that Roberts-IV flow exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method, we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above approximate to 8. As expected for a dynamo of this type, but contrary to alpha-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length-scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below approximate to 0.5, the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed.

  • 25.
    Hubbard, Alexander
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Magnetic helicity fluxes in an α2 dynamo embedded in a halo2010In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 104, no 5-6, 577-590 p.Article in journal (Refereed)
    Abstract [en]

    We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical alpha quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that "softer" (halo) boundary conditions give a lower energy of the saturated mean magnetic field.

  • 26.
    Hubbard, Alexander
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rheinhardt, Matthias
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    The fratricide of αΩ dynamos by their α2 siblings2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 535, A48- p.Article in journal (Refereed)
    Abstract [en]

    Context. Helically forced magneto-hydrodynamic shearing-sheet turbulence can support different large-scale dynamo modes, although the αΩ mode is generally expected to dominate because it is the fastest growing one. In an αΩ dynamo, most of the field amplification is produced by the shear. As differential rotation is an ubiquitous source of shear in astrophysics, such dynamos are believed to be the source of most astrophysical large-scale magnetic fields. Aims: We study the stability of oscillatory migratory αΩ type dynamos in turbulence simulations. Methods: We use shearing-sheet simulations of hydromagnetic turbulence that is helically forced at a wavenumber that is about three times larger than the lowest wavenumber in the domain so that both αΩ and α2 dynamo action is possible. Results: After initial dominance and saturation, the αΩ mode is found to be destroyed by an orthogonal α2 mode sustained by the helical turbulence alone. We show that there are at least two processes through which this transition can occur. Conclusions: The fratricide of αΩ dynamos by its α2 sibling is discussed in the context of grand minima of stellar activity. However, the genesis of αΩ dynamos from an α2 dynamo has not yet been found.

  • 27.
    Jabbari, Sarah
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, I.
    Surface flux concentrations in a spherical alpha 2 dynamo2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, A106Article in journal (Refereed)
    Abstract [en]

    Context. In the presence of strong density stratification, turbulence can lead to the large-scale instability of a horizontal magnetic field if its strength is in a suitable range (around a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulent contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. Aims. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an alpha(2) dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. Methods. We adopt the mean-field approach, which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil Code for an adiabatic stratification at a total density contrast in the radial direction of approximate to 4 orders of magnitude. Results. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong alpha quenching. This instability is excited in the top 5% of the outer radius, provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. Conclusions. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched alpha effect dynamo.

  • 28. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Campanelli, Leonardo
    Ratra, Bharat
    Tevzadze, Alexander G.
    Evolution of inflation-generated magnetic field through phase transitions2012In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 86, no 10, 103005- p.Article in journal (Refereed)
    Abstract [en]

    We study the evolution of an inflation-generated magnetic field, due to its coupling to fluid motions, during cosmological phase transitions. We find that the magnetic field stays almost unchanged on large scales, while on small scales, the spectrum is modified in such a way that power at small scales becomes progressively suppressed. We also show that the magnetic field generates turbulent motions in the initially turbulence-free plasma. On large scales, the slope of the resulting kinetic energy spectrum is consistent with that of white noise.

  • 29. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Tevzadze, Alexander G.
    Ratra, Bharat
    Numerical simulations of the decay of primordial magnetic turbulence2010In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 81, no 12, 123002- p.Article in journal (Refereed)
    Abstract [en]

    We perform direct numerical simulations of forced and freely decaying 3D magnetohydrodynamic turbulence in order to model magnetic field evolution during cosmological phase transitions in the early Universe. Our approach assumes the existence of a magnetic field generated either by a process during inflation or shortly thereafter, or by bubble collisions during a phase transition. We show that the final configuration of the magnetic field depends on the initial conditions, while the velocity field is nearly independent of initial conditions.

  • 30.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Spontaneous formation of magnetic flux concentrations in stratified turbulence2012In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 280, no 2, 321-333 p.Article in journal (Refereed)
    Abstract [en]

    The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) 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 the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β 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, L2/ηt, where ηt is the turbulent diffusivity and L is the scale of the domain. DNSs 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

  • 31. Käpylä, P. J.
    et al.
    Mantere, M. J.
    Guerrero, G.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Chatterjee, P.
    Reynolds stress and heat flux in spherical shell convection2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 531, A162Article in journal (Refereed)
    Abstract [en]

    Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims. Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong banana cells. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

  • 32. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    CYCLIC MAGNETIC ACTIVITY DUE TO TURBULENT CONVECTION IN SPHERICAL WEDGE GEOMETRY2012In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 755, no 1, L22Article in journal (Refereed)
    Abstract [en]

    We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the first time a pronounced equatorward branch at around 20 degrees latitude, reminiscent of the solar cycle.

  • 33.
    Losada, Illa Rivero
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    Rogachevskii, I.
    Competition of rotation and stratification in flux concentrations2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, A83Article in journal (Refereed)
    Abstract [en]

    Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the tau approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

  • 34.
    Losada, Illa Rivero
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    Rogachevskii, I.
    Magnetic flux concentrations in a polytropic atmosphere2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 564, A2Article in journal (Refereed)
    Abstract [en]

    Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods. To allow for a continuous transition from isothermal to poly tropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MPS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results. Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the potato-sack effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field. Conclusions. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

  • 35.
    Madarassy, Eniko J. M.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Calibrating passive scalar transport in shear-flow turbulence2010In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 82, no 1, 16304Article in journal (Refereed)
    Abstract [en]

    The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.

  • 36. Mitra, D.
    et al.
    Candelaresi, S.
    Chatterjee, P.
    Tavakol, R.
    Brandenburg, A.
    Stockholm University, Faculty of Science, Department of Astronomy.
    Equatorial magnetic helicity flux in simulations with different gauges2010In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, 130-135 p.Article in journal (Refereed)
    Abstract [en]

    % We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges.

  • 37. Mitra, D.
    et al.
    Moss, D.
    Tavakol, R.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Alleviating alpha quenching by solar wind and meridional flows2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 526, A138- p.Article in journal (Refereed)
    Abstract [en]

    Aims. We study the ability of magnetic helicity expulsion to alleviate catastrophic alpha-quenching in mean field dynamos in two-dimensional spherical wedge domains. Methods. Motivated by the physical state of the outer regions of the Sun, we consider alpha(2)Omega mean field models with a dynamical a quenching. We include two mechanisms which have the potential to facilitate helicity expulsion, namely advection by a mean flow (solar wind) and meridional circulation. Results. We find that a wind alone can prevent catastrophic quenching, with the field saturating at finite amplitude. In certain parameter ranges, the presence of a large-scale meridional circulation can reinforce this alleviation. However, the saturated field strengths are typically below the equipartition field strength. We discuss possible mechanisms that might increase the saturated field.

  • 38.
    Mitra, Dhrubaditya
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Scaling and intermittency in incoherent alpha-shear dynamo2012In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 420, no 3, 2170-2177 p.Article in journal (Refereed)
    Abstract [en]

    We consider mean-field dynamo models with fluctuating a effect, both with and without large-scale shear. The a effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent a2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.

  • 39. Plasson, Raphael
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Jullien, Ludovic
    Bersini, Hugues
    Autocatalyses2011In: Journal of Physical Chemistry A, ISSN 1089-5639, E-ISSN 1520-5215, Vol. 115, no 28, 8073-8085 p.Article in journal (Refereed)
    Abstract [en]

    Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. With the notion of autocatalysis covering a large variety of mechanistic realizations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form.

  • 40. Plasson, Raphael
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Jullien, Ludovic
    Bersini, Hugues
    Autocatalysis: At the Root of Self-Replication2011In: Artificial Life, ISSN 1064-5462, E-ISSN 1530-9185, Vol. 17, no 3, 219-236 p.Article in journal (Refereed)
    Abstract [en]

    Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets and autopoietic systems.

  • 41. Plasson, Raphaël
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Homochirality and the Need for Energy2010In: Origins of life and evolution of the biosphere, ISSN 0169-6149, E-ISSN 1573-0875, Vol. 40, 93-110 p.Article in journal (Refereed)
    Abstract [en]

    The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object—that can be intrinsically asymmetric—and a collection of objects—whose racemic state is the more stable one—must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.

  • 42.
    Poole, A
    et al.
    Stockholm University, Faculty of Science, Department of Molecular Biology and Functional Genomics.
    Hode, T
    Brandenburg, A
    Holm, N G
    Life Up North: Meeting Report: Nordic Astrobiology 2006: Origins & Distribution of Life in the Universe2006In: Astrobiology, Vol. 6, no 6, 815-818 p.Article in journal (Other academic)
  • 43. Rempel, E. L.
    et al.
    Chian, A. C. -L
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    LAGRANGIAN COHERENT STRUCTURES IN NONLINEAR DYNAMOS2011In: The Astrophysical Journal Letters, ISSN 2041-8205, Vol. 735, no 1, L9- p.Article in journal (Refereed)
    Abstract [en]

    Turbulence and chaos play a fundamental role in stellar convective zones through the transport of particles, energy, and momentum, and in fast dynamos, through the stretching, twisting, and folding of magnetic flux tubes. A particularly revealing way to describe turbulent motions is through the analysis of Lagrangian coherent structures (LCSs), which are material lines or surfaces that act as transport barriers in the fluid. We report the detection of LCSs in helical MHD dynamo simulations with scale separation. In an Arnold-Beltrami-Childress flow, two dynamo regimes, a propagating coherent mean-field regime and an intermittent regime, are identified as the magnetic diffusivity is varied. The sharp contrast between the chaotic tangle of attracting and repelling LCSs in both regimes permits a unique analysis of the impact of the magnetic field on the velocity field. In a second example, LCSs reveal the link between the level of chaotic mixing of the velocity field and the saturation of a large-scale dynamo when the magnetic field exceeds the equipartition value.

  • 44. Rheinhardt, M.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Modeling spatio temporal nonlocality in mean field dynamos2012In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, no 1, 71-77 p.Article in journal (Refereed)
    Abstract [en]

    When scale separation in space or time is poor, the mean-field alpha effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean-field equations are solved for oscillatory alpha-shear dynamos as well as alpha(2) dynamos with alpha linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio-temporal nonlocality.

  • 45.
    Rheinhardt, M.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Test-field method for mean-field coefficients with MHD background2010In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 520, A28- p.Article in journal (Refereed)
    Abstract [en]

    Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background.

    Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we obtain linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts-flow like geometry.

    Results: Examples with purely magnetic as well as MHD backgrounds are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. In particular, there is a contribution to the mean Lorentz force that is linear in the mean field and hence reverses sign upon a reversal of the mean field. For strong mean fields, α is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.

  • 46. Rogachevskii, Igor
    et al.
    Kleeorin, Nathan
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Eichler, David
    COSMIC-RAY CURRENT-DRIVEN TURBULENCE AND MEAN-FIELD DYNAMO EFFECT2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 753, no 1, 6- p.Article in journal (Refereed)
    Abstract [en]

    We show that an a effect is driven by the cosmic-ray (CR) Bell instability exciting left-right asymmetric turbulence. Alfven waves of a preferred polarization have maximally helical motion, because the transverse motion of each mode is parallel to its curl. We show how large-scale Alfven modes, when rendered unstable by CR streaming, can create new net flux over any finite region, in the direction of the original large-scale field. We perform direct numerical simulations (DNSs) of a magnetohydrodynamic fluid with a forced CR current and use the test-field method to determine the alpha effect and the turbulent magnetic diffusivity. As follows from DNS, the dynamics of the instability has the following stages: (1) in the early stage, the small-scale Bell instability that results in the production of small-scale turbulence is excited; (2) in the intermediate stage, there is formation of larger-scale magnetic structures; (3) finally, quasi-stationary large-scale turbulence is formed at a growth rate that is comparable to that expected from the dynamo instability, but its amplitude over much longer timescales remains unclear. The results of DNS are in good agreement with the theoretical estimates. It is suggested that this dynamo is what gives weakly magnetized relativistic shocks such as those from gamma-ray bursts (GRBs) a macroscopic correlation length. It may also be important for large-scale magnetic field amplification associated with CR production and diffusive shock acceleration in supernova remnants (SNRs) and blast waves from GRBs. Magnetic field amplification by Bell turbulence in SNRs is found to be significant, but it is limited owing to the finite time available to the super-Alfvenicly expanding remnant. The effectiveness of the mechanisms is shown to be dependent on the shock velocity. Limits on magnetic field growth in longer-lived systems, such as the Galaxy and unconfined intergalactic CRs, are also discussed.

  • 47. Ruediger, G.
    et al.
    Kitchatinov, L. L.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone2011In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 269, no 1, 3-12 p.Article in journal (Refereed)
    Abstract [en]

    In a density-stratified turbulent medium, the cross helicity (u' . B') is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s(-1). Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.

  • 48. Rädler, K.-H.
    et al.
    Brandenburg, A.
    Stockholm University, Faculty of Science, Department of Astronomy.
    Mean electromotive force proportional to mean flow in MHD turbulence2010In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, 14-21 p.Article in journal (Refereed)
    Abstract [en]

    In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the \alpha effect, is important for large-scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed.

  • 49. Snellman, J. E.
    et al.
    Rheinhardt, M.
    Käpylä, P. J.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mean-field closure parameters for passive scalar turbulence2012In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 86, no 1, 018406Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations (DNSs) of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar flux and variance. Triple correlations of fluctuations appearing in these equations are described in terms of relaxation terms proportional to the quadratic correlations. Three methods are used to extract the relaxation timescales tau(i) from DNSs. Firstly, we insert the closure ansatz into our equations, assume stationarity and solve for tau(i). Secondly, we use only the closure ansatz itself and obtain tau(i) from the ratio of quadratic and triple correlations. Thirdly, we remove the imposed passive scalar gradient and fit an exponential law to the decaying solution. We vary the Reynolds (Re) and Peclet numbers (while fixing their ratio at unity) and the degree of scale separation and find for large Re a fair correspondence between the different methods. The ratio of the turbulent relaxation time of the passive scalar flux to the turnover time of the turbulent eddies is of the order of 3, which is in remarkable agreement with earlier work. Finally, we make an effort to extract the relaxation timescales relevant for the viscous and diffusive effects. We find two regimes that are valid for small and large Re, respectively, but the dependence of the parameters on scale separation suggests that they are not universal.

  • 50.
    Sordo, Fabio Del
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    How can vorticity be produced in irrotationally forced flows?2010In: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 6, 373-375 p.Article in journal (Refereed)
    Abstract [en]

    A spherical hydrodynamical expansion flow can be described as the gradient of a potential. In that case no vorticity should be produced, but several additional mechanisms can drive its production. Here we analyze the effects of baroclinicity, rotation and shear in the case of a viscous fluid. Those flows resemble what happens in the interstellar medium. In fact in this astrophysical environment supernovae explosion are the dominant flows and, in a first approximation, they can be seen as spherical. One of the main difference is that in our numerical study we examine only weakly supersonic flows, while supernovae explosions are strongly supersonic.

12 1 - 50 of 57
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