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  • 51. Cameron, R. H.
    et al.
    Dikpati, M.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    The Global Solar Dynamo2017In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 210, no 1-4, p. 367-395Article, review/survey (Refereed)
    Abstract [en]

    A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed.

  • 52.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Dundee, UK.
    Hillier, A.
    Maehara, H.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Shibata, K.
    SUPERFLARE OCCURRENCE AND ENERGIES ON G-, K-, AND M-TYPE DWARFS2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 792, no 1, p. 67-Article in journal (Refereed)
    Abstract [en]

    Kepler data from G-, K-, and M-type stars are used to study conditions that lead to superflares with energies above 10(34) erg. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars.

  • 53. Chan, Chi-kwan
    et al.
    Mitra, Dhrubaditya
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Dynamics of saturated energy condensation in two-dimensional turbulence2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, no 3, p. 036315-Article in journal (Refereed)
    Abstract [en]

    In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.

  • 54. Chatterjee, P.
    et al.
    Mitra, D.
    Rheinhardt, M.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Alpha effect due to buoyancy instability of a magnetic layer2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 534, p. A 46-Article in journal (Refereed)
    Abstract [en]

    Context. A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. Aims: We calculate the α effect due to helical motions caused by an unstable magnetic layer in a rotating density-stratified system with angular velocity Ω making an angle θ with the vertical. We also study the dependence of the α effect on θ and the strength of the initial magnetic field. Methods: We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent electromotive force (EMF) due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. Results: We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting α effect is non-uniform and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" α effect. The α effect is also nonlocal, i.e. scale dependent, requiring around 8-16 Fourier modes to reconstruct the actual mean EMF based on the actual mean field.

  • 55. Cole, E.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Käpylä, P. J.
    Käpylä, M. J.
    Robustness of oscillatory alpha(2) dynamos in spherical wedges2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 593, article id A134Article in journal (Refereed)
    Abstract [en]

    Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims. We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods. We solve the equations for one-dimensional time-dependent alpha(2) and alpha(2)Omega mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle theta(0) between the latitudinal boundaries and the poles in spherical coordinates. Results. In the case of constant alpha and eta(t) profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and alpha profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on theta(0). When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions. A reduced alpha effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges. For weak shear, oscillatory solutions are obtained only for perfect conductor field conditions and negative shear. Oscillatory solutions become preferred at sufficiently strong shear. Recent three-dimensional dynamo simulations producing solar-like magnetic activity are expected to lie in this range.

  • 56. Cole, Elizabeth
    et al.
    Käpylä, Petri J.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    AN AZIMUTHAL DYNAMO WAVE IN SPHERICAL SHELL CONVECTION2014In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 780, no 2, article id L22Article in journal (Refereed)
    Abstract [en]

    We report the discovery of an azimuthal dynamo wave of a low-order (m = 1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean-field dynamo theory and have been obtained previously in mean-field models. An azimuthal dynamo wave has been proposed as a possible explanation for the persistent drifts of spots observed on several rapidly rotating stars, as revealed through photometry and Doppler imaging. However, this has been judged unlikely because evidence for such waves from DNS has been lacking. Here we present DNS of large-scale magnetic fields showing a retrograde m = 1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m = 1 structures coincide reasonably well with the maxima of m = 2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave.

  • 57.
    Del Sordo, Fabio
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Guerrero, G.
    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.
    Turbulent dynamos with advective magnetic helicity flux2013In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 429, no 2, p. 1686-1694Article in journal (Refereed)
    Abstract [en]

    Many astrophysical bodies harbour magnetic fields that are thought to be sustained by a dynamo process. However, it has been argued that the production of large-scale magnetic fields by mean-field dynamo action is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic fields by stellar and galactic winds towards the outer boundaries and away from the dynamo is expected to alleviate such quenching. Here we explore the relative roles played by advective and turbulent-diffusive fluxes of magnetic helicity in the dynamo. In particular, we study how the dynamo is affected by advection. We do this by performing direct numerical simulations of a turbulent dynamo of alpha(2) type driven by forced turbulence in a Cartesian domain in the presence of a flow away from the equator where helicity changes sign. Our results indicate that in the presence of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm an earlier result for turbulent-diffusive magnetic helicity fluxes that for small magnetic Reynolds numbers (Rm less than or similar to 100 ... 200, based on the wavenumber of the energy-carrying eddies) the magnetic helicity flux scales less strongly with magnetic Reynolds number (Rm(-1/2)) than the term describing magnetic helicity destruction by resistivity (Rm(-1)). Our new results now suggest that for larger Rm the former becomes approximately independent of Rm, while the latter falls off more slowly. We show for the first time that both for weak and stronger winds, the magnetic helicity flux term becomes comparable to the resistive term for Rm greater than or similar to 1000, which is necessary for alleviating catastrophic quenching.

  • 58. Dosopoulou, F.
    et al.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy.
    Tsagas, C. G.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Vorticity production and survival in viscous and magnetized cosmologies2012In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 85, no 6, p. 063514-Article in journal (Refereed)
    Abstract [en]

    We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length below which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.

  • 59. Gosain, Sanjay
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Spectral Magnetic Helicity of Solar Active Regions between 2006 and 20172019In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 882, no 2, article id 80Article in journal (Refereed)
    Abstract [en]

    We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006-2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6-8 Mm, while the length scale relating the magnetic and current helicities to each other is around 1.4 Mm.

  • 60. Haugen, Nils Erland L.
    et al.
    Kleeorin, Nathan
    Rogachevskii, Igor
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Detection of turbulent thermal diffusion of particles in numerical simulations2012In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 7, article id 075106Article in journal (Refereed)
    Abstract [en]

    The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux (i.e., non-counter-gradient transport) of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the formation of inhomogeneities in the spatial distribution of inertial particles whose scale is large in comparison with the integral scale of the turbulence. The strength of this effect is maximum for Stokes numbers around unity, and decreases again for larger values. The dynamics of inertial particles is studied using Lagrangian modelling in forced temperature-stratified turbulence, whereas non-inertial particles and the fluid are described using DNS in an Eulerian framework.

  • 61. Hubbard, A.
    et al.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, P. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    The α effect with imposed and dynamo-generated magnetic fields2009In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 4, p. 1891-1899Article in journal (Refereed)
    Abstract [en]

    Estimates for the non-linear α effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of α compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.

  • 62. Hubbard, Alexander
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    CATASTROPHIC QUENCHING IN alpha Omega DYNAMOS REVISITED2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 748, no 1, p. 51-Article in journal (Refereed)
    Abstract [en]

    At large magnetic Reynolds numbers, magnetic helicity evolution plays an important role in astrophysical large-scale dynamos. The recognition of this fact led to the development of the dynamical alpha quenching formalism, which predicts catastrophically low mean fields in open systems. Here, we show that in oscillatory alpha Omega dynamos this formalism predicts an unphysical magnetic helicity transfer between scales. An alternative technique is proposed where this artifact is removed by using the evolution equation for the magnetic helicity of the total field in the shearing advective gauge. In the traditional dynamical alpha quenching formalism, this can be described by an additional magnetic helicity flux of small-scale fields that does not appear in homogeneous alpha(2) dynamos. In alpha Omega dynamos, the alternative formalism is shown to lead to larger saturation fields than what has been obtained in some earlier models with the traditional formalism. We have compared the predictions of the two formalisms to results of direct numerical simulations, finding that the alternative formulation provides a better fit. This suggests that worries about catastrophic dynamo behavior in the limit of large magnetic Reynolds number are unfounded.

  • 63.
    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, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 805, no 2, article id 166Article in journal (Refereed)
    Abstract [en]

    Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75 degrees latitude and an azimuthal extent of 180 degrees. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker's Omega-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10 degrees. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.

  • 64.
    Jabbari, Sarah
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Monash University, Australia.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Sharp magnetic structures from dynamos with density stratification2017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 467, no 3, p. 2753-2765Article in journal (Refereed)
    Abstract [en]

    Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here, we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in non-linear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical.

  • 65.
    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). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Turbulent reconnection of magnetic bipoles in stratified turbulence2016In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 459, no 4, p. 4046-4056Article in journal (Refereed)
    Abstract [en]

    We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale-separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S > 10(3), the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings.

  • 66.
    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).
    Rivero Losada, Illa
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Rogachevskii, Igor
    Magnetic flux concentrations from dynamo-generated fields2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 568, article id A112Article in journal (Refereed)
    Abstract [en]

    Context The mean field theory of magnetized stellar convection gives rise to two distinct instabilities; the large-scale dynamo instability, operating in the bulk of the convection zone and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation. However, as follows from theoretical analysis, the growth rate of NEMPI is suppressed with increasing rotation rates. On the other hand, recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. Aims. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha(2) mean field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. Methods. We use both DNS and mean field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal held, We use the test-field method to compute relevant dynamo coefficients. Results. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively reproduced with MPS. As expected for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Conclusions. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over For the solar rotation rate, the corresponding turbulent turnover time is about 5 h, with dynamo action commencing in the layers beneath.

  • 67. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Durrer, Ruth
    Tevzadze, Alexander G.
    Yin, Winston
    Scale-invariant helical magnetic field evolution and the duration of inflation2017In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 11, article id 002Article in journal (Refereed)
    Abstract [en]

    We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Even if we just have upper bounds on the helicity, these can be used to derive constraints on the minimal duration if one assumes that the magnetic field generated during inflation is helical. Using three-dimensional simulations, we show that an initially scale-invariant field develops, which is similar both with and without magnetic helicity. In the fully helical case, however, the magnetic field appears to have a more pronounced folded structure.

  • 68. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Tevzadze, Alexander G.
    The evolution of primordial magnetic fields since their generation2016In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 91, no 10, article id 104008Article in journal (Refereed)
    Abstract [en]

    We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields.

  • 69. Kahniashvili, Tina
    et al.
    Tevzadze, Alexander G.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Neronov, Andrii
    Evolution of primordial magnetic fields from phase transitions2013In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 87, no 8, p. 083007-Article in journal (Refereed)
    Abstract [en]

    We consider the evolution of primordial magnetic fields generated during cosmological, electroweak, or QCD phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between the magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover universal'' laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low-viscosity) regime. In particular, we show that during the radiation-dominated epoch, the energy and correlation length of nonhelical magnetic fields scale as conformal time to the powers -1/2 and +1/2, respectively. For helical magnetic fields, the energy and correlation length scale as conformal time to the powers -1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of the magnetic field generated during the QCD phase transition could reach similar to 10(-9) G with the present-day correlation length similar to 50 kpc. The fields generated at the electroweak phase transition could be as strong as similar to 10(-10) G with correlation lengths reaching similar to 0.3 kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields. DOI: 10.1103/PhysRevD.87.083007

  • 70. Karak, B. B.
    et al.
    Käpylä, P. J.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Olspert, N.
    Pelt, J.
    Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles2015In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 576, article id A26Article in journal (Refereed)
    Abstract [en]

    Context. Late-type stars rotate differentially owing to anisotropic turbulence in their outer convection zones. The rotation is called solar-like (SL) when the equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations show a transition from SL to AS rotation as the influence of rotation on convection is reduced, but the opposite transition occurs at a different point in the parameter space. The system is bistable, i.e., SL and AS rotation profiles can both be stable. Aims. We study the effect of a dynamo-generated magnetic field on the large-scale flows, particularly on the possibility of bistable behaviour of differential rotation. Methods. We solve the hydromagnetic equations numerically in a rotating spherical shell that typically covers +/- 75 degrees latitude (wedge geometry) for a set of different radiative conductivities controlling the relative importance of convection. We analyse the resulting differential rotation, meridional circulation, and magnetic field and compare the corresponding modifications of the Reynolds and Maxwell stresses. Results. In agreement with earlier findings, our models display SL rotation profiles when the rotational influence on convection is strong and a transition to AS when the rotational influence decreases. We find that dynamo-generated magnetic fields help to produce SL differential rotation compared to the hydrodynamic simulations. We do not observe any bistable states of differential rotation. In the AS cases we find coherent single-cell meridional circulation, whereas in SL cases we find multi-cellular patterns. In both cases, we obtain poleward circulation near the surface with a magnitude close to that observed in the Sun. In the slowly rotating cases, we find activity cycles, but no clear polarity reversals, whereas in the more rapidly rotating cases irregular variations are obtained. Moreover, both differential rotation and meridional circulation have significant temporal variations that are similar in strength to those of the Sun. Conclusions. Purely hydrodynamic simulations of differential rotation and meridional circulation are shown to be of limited relevance as magnetic fields, self-consistently generated by dynamo action, significantly affect the flows.

  • 71.
    Karak, Bidya Binay
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    IS THE SMALL-SCALE MAGNETIC FIELD CORRELATED WITH THE DYNAMO CYCLE?2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 816, no 1, article id 28Article in journal (Refereed)
    Abstract [en]

    The small-scale magnetic field is ubiquitous at the solar surface-even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence, of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the small-scale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the smallscale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of a small-scale dynamo and tangling of the large-scale field.

  • 72.
    Karak, Bidya Binay
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kitchatinov, Leonid L.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    HYSTERESIS BETWEEN DISTINCT MODES OF TURBULENT DYNAMOS2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 803, no 2, article id 95Article in journal (Refereed)
    Abstract [en]

    Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed at probing the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov & Olemskoy with direct numerical simulations. We perform three-dimensional (3D) simulations of large-scale dynamos in a shearing box with helically forced turbulence. As an initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed.

  • 73. Karak, Bidya Binay
    et al.
    Rheinhardt, Matthias
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, Petri J.
    Käpylä, Maarit J.
    QUENCHING AND ANISOTROPY OF HYDROMAGNETIC TURBULENT TRANSPORT2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 795, no 1, article id 16Article in journal (Refereed)
    Abstract [en]

    Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the alpha effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-fieldmethod, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the alpha effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Omega x J effect nearly the same quenching exponent is obtained as for alpha. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.

  • 74.
    Kemel, Koen
    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.
    Ji, Hantao
    Model of driven and decaying magnetic turbulence in a cylinder2011In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, p. 56407-Article in journal (Refereed)
    Abstract [en]

    Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. 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. A stronger field reversal can be obtained if there is also a significant kinetic α effect. Application to the reversed field pinch in plasma confinement devices is discussed.

  • 75.
    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). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Active Region Formation through the Negative Effective Magnetic Pressure Instability2013In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 287, no 1-2, p. 293-313Article in journal (Refereed)
    Abstract [en]

    The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

  • 76.
    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). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Non-uniformity effects in the negative effective magnetic pressure instability2013In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T155, article id 014027Article in journal (Refereed)
    Abstract [en]

    In direct numerical simulations of strongly stratified turbulence we have previously studied the development of large scale magnetic structures starting from a uniform background field. This is caused by an instability resulting from a negative contribution of small-scale turbulence to the effective (mean-field) magnetic pressure, and was qualitatively reproduced in mean-field simulations (MFS) where this pressure reduction was modeled as a function of the mean magnetic field normalized by the equipartition field. We now investigate the effect of mean current density on the turbulent pressure reduction. In our MFS, such currents are associated with sharp gradients of the growing structures. We find that an enhanced mean current density increases the suppression of the turbulent pressure.

  • 77.
    Kemel, Koen
    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).
    Kleeorin, Nathan
    Rogachevskii, Igor
    Nonuniformity effects in the negative effective magnetic pressure instabilityIn: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896Article in journal (Other academic)
  • 78.
    Kemel, Koen
    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.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben‐Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben‐Gurion University of the Negev, Israel.
    Properties of the negative effective magnetic pressure instability2012In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, no 2, p. 95-100Article in journal (Refereed)
    Abstract [en]

    As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter beta(star) characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter beta(star). The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

  • 79. Käpylä, M. J.
    et al.
    Käpylä, P. J.
    Olspert, N.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Warnecke, J.
    Karak, B. B.
    Pelt, J.
    Multiple dynamo modes as a mechanism for long-term solar activity variations2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 589, article id A56Article in journal (Refereed)
    Abstract [en]

    Context. Solar magnetic activity shows both smooth secular changes, such as the modern Grand Maximum, and quite abrupt drops that are denoted as grand minima, such as the Maunder Minimum. Direct numerical simulations (DNS) of convection-driven dynamos off er one way of examining the mechanisms behind these events. Aims. In this work, we analyze a solution of a solar-like DNS that was evolved for roughly 80 magnetic cycles of 4.9 years and where epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. Methods. The DNS employed is a semi-global (wedge-shaped) magnetoconvection model. For the data analysis tasks we use Ensemble Empirical Mode Decomposition and phase dispersion methods, as they are well suited for analyzing cyclic (non-periodic) signals. Results. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like (equatorward migration at low latitudes and poleward at high latitudes). This mode is accompanied by a higher frequency mode near the surface and at low latitudes, showing poleward migration, and a low-frequency mode at the bottom of the convection zone. The low-frequency mode is almost purely antisymmetric with respect to the equator, while the dominant mode has strongly fluctuating mixed parity. The overall behavior of the dynamo solution is extremely complex, exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum; during this epoch the bottom toroidal magnetic field obtains a maximum, demonstrating that the interpretation of grand minima-type events is non-trivial. The hemispherical asymmetries are seen only in the magnetic field, while the velocity field exhibits considerably weaker asymmetry. Conclusions. We interpret the overall irregular behavior as being due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low-activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.

  • 80. Käpylä, P. J.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Kleeorin, N.
    Käpylä, M. J.
    Rogachevskii, I.
    Magnetic flux concentrations from turbulent stratified convection2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 588, article id A150Article in journal (Refereed)
    Abstract [en]

    Context. The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation is unexplained. Aims. We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods. We perform simulations of magnetoconvection in Cartesian domains representing the uppermost 8 : 5 24 Mm of the solar convection zone with the horizontal size of the domain varying between 34 and 96 Mm. The density contrast in the 24 Mm deep models is more than 3 x 10(3) or eight density scale heights, corresponding to a little over 12 pressure scale heights. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow in set-ups where no small-scale dynamos are present. In the most highly stratified cases we employ the reduced sound speed method to relax the time step constraint arising from the high sound speed in the deep layers. We model radiation via the diffusion approximation and neglect detailed radiative transfer in order to concentrate on purely magnetohydrodynamic effects. Results. We find that super-equipartition magnetic flux concentrations are formed near the surface in cases with moderate and high density stratification, corresponding to domain depths of 12 : 5 and 24 Mm. The size of the concentrations increases as the box size increases and the largest structures (20 Mm horizontally near the surface) are obtained in the models that are 24 Mm deep. The field strength in the concentrations is in the range of 3-5 kG, almost independent of the magnitude of the imposed field. The amplitude of the concentrations grows approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in most of the domain, which is unfavourable for the operation of the negative effective magnetic pressure instability (NEMPI). Simulations in which a passive vector field is evolved do not show a noticeable difference from magnetohydrodynamic runs in terms of the growth of the structures. Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions. The linear growth of large-scale flux concentrations implies that their dominant formation process is a tangling of the large-scale field rather than an instability. One plausible mechanism that can explain both the linear growth and the concentration of the flux in the regions of converging flow pattern is flux expulsion. A possible reason for the absence of NEMPI is that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign. Furthermore, there may not be sufficient scale separation, which is required for NEMPI to work.

  • 81. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Open and closed boundaries in large-scale convective dynamos2010In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 518, article id A22Article in journal (Refereed)
    Abstract [en]

    Context. Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. Aims: Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Methods: Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos. Open (vertical-field) and closed (perfect- conductor) boundary conditions are used for the magnetic field. The shear flow is such that the contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. Results: We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate of the field in this regime increases as Rm1/2. Regarding the nonlinear regime, the saturation level of the energy of the total magnetic field is independent of Rm when open boundaries are used. In the case of perfect-conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm-1 for Rm ⪆ 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

  • 82. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    The alpha effect in rotating convection with sinusoidal shear2010In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 402, no 3, p. 1458-1466Article in journal (Refereed)
    Abstract [en]

    Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic alpha effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of alpha using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the alpha effect.

  • 83. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    The α effect in rotating convection with sinusoidal shear2010In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 402, no 3, p. 1458-1466Article in journal (Refereed)
    Abstract [en]

    Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic α effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of α using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the α effect.

  • 84. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mitra, D.
    Tavakol, R.
    Convective dynamos in spherical wedge geometry2010In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, p. 73-81Article in journal (Refereed)
    Abstract [en]

    Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made.

  • 85. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Confirmation of bistable stellar differential rotation profiles2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 570, article id A43Article in journal (Refereed)
    Abstract [en]

    Context. Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow. Aims. We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive (A effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods. We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. To avoid this problem while still representing the same rotational influence on the flow as in the Sun, we increase the luminosity by a factor of roughly 106 and the rotation rate by a factor of 10(2). We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results. Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. The anti-solar profiles are found to be more stable against perturbations in the level of convective turbulent velocity than the solar-type solutions. Conclusions. Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers, and thus longer in time, before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.

  • 86. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, Colorado; Laboratory for Atmospheric and Space Physics, Colorado.
    Small-scale dynamos in simulations of stratified turbulent convection2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 2-3, p. 127-133Article in journal (Refereed)
    Abstract [en]

    Small-scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high-resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm(1/2) scaling. No evidence for a logarithmic increase of the growth rate with Rm is found.

  • 87. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Olspert, N.
    Warnecke, J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Convection-driven spherical shell dynamos at varying Prandtl numbers2017In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 599, article id A4Article in journal (Refereed)
    Abstract [en]

    Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims. We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods. We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results. We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions. Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here.

  • 88. Käpylä, P. J.
    et al.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Effects of stratification in spherical shell convection2011In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 332, article id 883Article in journal (Refereed)
    Abstract [en]

    We report on simulations of mildly turbulent convection in spherical wedge geometry with varying density stratification. We vary the density contrast within the convection zone by a factor of 20 and study the influence of rotation on the solutions. We demonstrate that the size of convective cells decreases and the anisotropy of turbulence increases as the stratification is increased. Differential rotation is found to change from anti-solar (slow equator) to solar-like (fast equator) at roughly the same Coriolis number for all stratifications. The largest stratification runs, however, are sensitive to changes of the Reynolds number. Evidence for a near-surface shear layer is found in runs with strong stratification and large Reynolds numbers.

  • 89. Käpylä, Petri J.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Turbulent Dynamos with Shear and Fractional Helicity2009In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 699, p. 1059-1066Article in journal (Refereed)
    Abstract [en]

    Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an αΩ dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re M ) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M .

  • 90. Käpylä, Petri J.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Korpi, Maarit J.
    Snellman, Jan E.
    Narayan, Ramesh
    Angular Momentum Transport in Convectively Unstable Shear Flows2010In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 719, p. 67-76Article in journal (Refereed)
    Abstract [en]

    Angular momentum transport due 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 (Λ-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is on the order of the mixing length estimate and weakly affected by rotation. The Λ-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.

  • 91.
    Käpylä, Petri. J.
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Helsinki, Finland.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Oscillatory large-scale dynamos from Cartesian convection simulations2013In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, no 1-2, p. 244-257Article in journal (Refereed)
    Abstract [en]

    We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of 2 type, which is generally expected to be relevant for the Sun, whereas the latter case refers to 2 dynamos that are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated regimes when the negative ratio of shear to rotation rates, qS/, is between 1.5 and 2, i.e. when shear and rotation are of comparable strengths. Other regions of oscillatory solutions are found with small values of q, i.e. when shear is weak in comparison to rotation, and in the regime of large negative qs, when shear is very strong in comparison to rotation. However, exceptions to these rules also appear so that for a given ratio of shear to rotation, solutions are non-oscillatory for small and large shear, but oscillatory in the intermediate range. Changing the boundary conditions from vertical field to perfect conductor ones changes the dynamo mode from oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution exists only in the kinematic regime whereas in the nonlinear stage the mean fields are stationary. However, the cases with rotation and no shear are always oscillatory in the parameter range studied here and the dynamo mode does not depend on the magnetic boundary conditions. The strengths of total and large-scale components of the magnetic field in the saturated state, however, are sensitive to the chosen boundary conditions.

  • 92. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elisabeth
    Warnecke, Jörn
    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.
    Effects of strong stratification on equatorward dynamo wave propagationManuscript (preprint) (Other academic)
    Abstract [en]

    We present results from simulations of rotating magnetized  turbulent convection in spherical wedge geometry representing parts  of the latitudinal and longitudinal extents of a star.  Here we consider a set of runs for which the density stratification is  varied, keeping the  Reynolds and Coriolis numbers at similar values. In the case of weak  stratification we find quasi-steady solutions for moderate rotation and oscillatory dynamos with poleward migration of activity belts  for more rapid rotation. For stronger stratification a similar transition as a function of the Coriolis number is found, but with an equatorward migrating branch near the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal  extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an  m=1 mode is excited for a full 2π φ-extent, reminiscent of the  field configurations deduced from observations of rapidly rotating late-type stars.

  • 93. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elizabeth
    Warnecke, Jörn
    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.
    EFFECTS OF ENHANCED STRATIFICATION ON EQUATORWARD DYNAMO WAVE PROPAGATION2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 778, no 1, article id 41Article in journal (Refereed)
    Abstract [en]

    We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about pi/2, which can be explained by an oscillatory alpha(2) dynamo caused by the sign change of the alpha-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2 pi azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.

  • 94. Käpylä, Petri J.
    et al.
    Rheinhardt, Matthias
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Arlt, Rainer
    Käpylä, Maarit J.
    Lagg, Andreas
    Olspert, Nigul
    Warnecke, Joern
    Extended Subadiabatic Layer in Simulations of Overshooting Convection2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, article id L23Article in journal (Refereed)
    Abstract [en]

    We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.

  • 95.
    Käpylä, Petri J.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Georg-August-Universität Göttingen, Germany; Leibniz-Institut für Astrophysik, Germany; ReSoLVE Centre of Excellence, Finland, Max-Planck-Institut für Sonnensystemforschung, Germany.
    Viviani, M.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Spada, F.
    Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations2019In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 113, no 1-2, p. 149-183Article in journal (Refereed)
    Abstract [en]

    We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated towards the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively towards the equator in runs with a thicker stably stratified layer.

  • 96.
    Li, Xiang-Yu
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology . Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Haugen, N. E. L.
    Svensson, Gunilla
    Stockholm University, Faculty of Science, Department of Meteorology . Swedish e-Science Research Centre, Sweden; National Center for Atmospheric Research, USA.
    Eulerian and Lagrangian approaches to multidimensional condensation and collection2017In: Journal of Advances in Modeling Earth Systems, ISSN 1942-2466, Vol. 9, no 2, p. 1116-1137Article in journal (Refereed)
    Abstract [en]

    Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence. Plain Language Summary The bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 mu m similar to 40 mu m [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the Lagrangian and Eulerian schemes in detail to tackle with the turbulence-generated collection.

  • 97.
    Li, Xiang-Yu
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology . Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Svensson, Gunilla
    Stockholm University, Faculty of Science, Department of Meteorology . Swedish e-Science Research Centre, Sweden.
    Haugen, Nils E. L.
    Mehlig, Bernhard
    Rogachevskii, Igor
    Condensational and collisional growth of cloud droplets in a turbulent environmentIn: Article in journal (Refereed)
    Abstract [en]

    The effect of turbulence on combined condensational and collisional growth of cloud droplets is investigated using high-resolution direct numerical simulations. The motion of droplets is subjected to both turbulence and gravity. We solve the thermodynamic equations that govern the supersaturation field together with the hydrodynamic equations describing the turbulence. The collision-coalescence process is approximated by a superparticle approach assuming unit collision and coalescence efficiency, i.e., droplet coalesce upon collision. Condensational growth of cloud droplets due to supersaturation fluctuations depends on the Reynolds number, while the collisional growth was previously found to depend on the mean energy dissipation rate. Here we show that the combined processes depend on both Reynolds number and the mean energy dissipation rate. Droplet size distributions broaden either with increasing Reynolds number or mean energy dissipation rate in the range explored here. Even though collisional growth alone is insensitive to Reynolds number, it is indirectly affected by the large scales of turbulence through condensation. This is argued to be due to the fact that condensational growth results in wider droplet-size distributions, which triggers collisional growth. Since turbulence in warm clouds has a relatively small mean energy dissipation rate, but a large Reynolds number, turbulence mainly affects the condensational growth and thus influences the collisional growth indirectly through condensation. Thus, the combined condensational and collisional growth of cloud droplets is mostly dominated by Reynolds number. This work, for the first time, numerically demonstrates that supersaturation fluctuations enhance the collisional growth. It supports the findings from laboratory experiments and the observations that supersaturation fluctuations are important for precipitation.

  • 98.
    Li, Xiang-Yu
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology . Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado Boulder, USA.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado Boulder, USA.
    Svensson, Gunilla
    Stockholm University, Faculty of Science, Department of Meteorology . Swedish e-Science Research Centre, Sweden.
    Haugen, Nils E. L.
    Mehlig, Bernhard
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment2020In: Journal of the Atmospheric Sciences, ISSN 0022-4928, E-ISSN 1520-0469, Vol. 77, no 1, p. 337-353Article in journal (Refereed)
    Abstract [en]

    We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

  • 99.
    Li, Xiang-Yu
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology . Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Svensson, Gunilla
    Stockholm University, Faculty of Science, Department of Meteorology . Swedish e-Science Research Centre, Sweden; Global & Climate Dynamics, National Center for Atmospheric Research, USA.
    Haugen, Nils E. L.
    Mehlig, Bernhard
    Rogachevskii, Igor
    Effect of turbulence on collisional growth of cloud droplets2018In: Journal of the Atmospheric Sciences, ISSN 0022-4928, E-ISSN 1520-0469, Vol. 75, p. 3469-3487Article in journal (Refereed)
    Abstract [en]

    We investigate the effect of turbulence on the collisional growth of um-sized droplets through high- resolution numerical simulations with well resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate, but only weakly on the Reynolds number. This can be explained through the energy dissipation rate dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as the square root of the energy dissipation rate even when coalescence is invoked. The size distribution exhibits power law behavior with a slope of -3.7 between a maximum at approximately 10 um up to about 40 um. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is due to the fact that turbulence enhances the collisional growth between similar sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.

  • 100.
    Li, Xiang-Yu
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology . Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mehlig, Bernhard
    Svensson, Gunilla
    Stockholm University, Faculty of Science, Department of Meteorology .
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Haugen, Nils
    Fluctuations and growth histories of cloud droplets: super-particle simulations of the collision-coalescence processManuscript (preprint) (Other academic)
    Abstract [en]

    Direct numerical simulations of collisional aggregation in turbulent aerosols are computationally demanding. Many authors therefore use an approximate model of the collision-coalescence process that is computationally more efficient: it relies on representing physical particles in terms of ‘superparticles’. One monitors collisions between superparticles and accounts for collisions between physical particles using a Monte-Carlo algorithm. It has been shown that this algorithm can faithfully represent mean particle growth in turbulent aerosols. Here we investigate how fluctuations are represented in this algorithm. We study particles of different sizes settling under gravity, assuming that the effect of turbulence is simply to mix the particles horizontally. We compute the statistics of growth histories and analyze their fluctuations in terms of the ‘lucky-droplet’ model. We discuss under which circumstances artefacts change the fluctuations of the growth histories, how these can be avoided, and which questions remain to be answered when turbulent fluctuations are explicitly incorporated.

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