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  • 1.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Das, Upasana
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    The time step constraint in radiation hydrodynamics2020In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, no 1-2, p. 162-195Article in journal (Refereed)
    Abstract [en]

    Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations.

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

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

  • 3.
    Chatterjee, Piyali
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Guerrero, Gustavo
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Can catastrophic quenching be alleviated by separating shear and α effect?2010In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 104, no 5&6, p. 591-599Article in journal (Refereed)
    Abstract [en]

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

  • 4.
    Hubbard, Alexander
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Magnetic helicity fluxes in an α2 dynamo embedded in a halo2010In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 104, no 5-6, p. 577-590Article in journal (Refereed)
    Abstract [en]

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

  • 5.
    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.

  • 6.
    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.

  • 7. Qian, Chengeng
    et al.
    Wang, Cheng
    Liu, JianNan
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Haugen, Nils E. L.
    Liberman, Mikhael A.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Convergence properties of detonation simulations2020In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, no 1-2, p. 58-76Article in journal (Refereed)
    Abstract [en]

    We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width like down to. With the WENO scheme, solutions are smooth at, but no detonation is obtained for. This is argued to be an artifact of a decoupling between pressure and reaction fronts.

  • 8. Roper Pol, Alberto
    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 Universiy, USA.
    Kahniashvili, Tina
    Kosowsky, Arthur
    Mandal, Sayan
    The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence2020In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, no 1-2, p. 130-161Article in journal (Refereed)
    Abstract [en]

    Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the Pencil Code - a code which uses a third order timestep and sixth order finite differences. Using direct numerical integration of the GW equations, we study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep - even when the Courant-Friedrichs-Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. To mitigate numerical degradation effects, we alternatively use the exact solution of the GW equations under the assumption that the source is constant between subsequent timesteps. This allows us to use a much longer timestep, which cuts the computational cost by a factor of about ten.

  • 9. Schober, J.
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Energetics of turbulence generated by chiral MHD dynamos2019In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 113, no 1-2, p. 107-130Article in journal (Refereed)
    Abstract [en]

    An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, . In particular, we determine the ratio of kinetic to magnetic energy, , in chiral magnetically driven turbulence. Within the parameter space explored in this study, reaches a value of approximately 0.064-0.074-independently of the initial chiral asymmetry and for . Our simulations suggest, that decreases as a power law when increasing by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.

  • 10. Singh, Nishant K.
    et al.
    Raichur, Harsha
    Käpylä, Maarit J.
    Rheinhardt, Matthias
    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.
    Käpylä, Petri J.
    f-mode strengthening from a localised bipolar subsurface magnetic field2020In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, no 1-2, p. 196-212Article in journal (Refereed)
    Abstract [en]

    Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the f-mode is significantly larger at high horizontal wavenumbers k, but the fanning is weaker for the localised subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the f-mode in the diagram increases proportionally in such a way that the normalised f-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localised magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the f-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

  • 11. Yoshizawa, A.
    et al.
    Kobayashi, H.
    Sugimoto, N.
    Yokoi, N.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Shimomura, Y.
    A Reynolds-averaged turbulence modelling approach to the maintenance of the Venus superrotation2013In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, no 6, p. 614-639Article in journal (Refereed)
    Abstract [en]

    A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modelling approach. The basic framework is similar to that of Gierasch (Meridional circulation and maintenance of the Venus atmospheric rotation. J. Atmos. Sci. 1975, 32, 1038-1044) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a non-local time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the non-local time scale. The relationship of the present model with the current general circulation model simulation is discussed in light of a crucial role of the vertical viscosity.

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