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  • 1.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gressel, Oliver
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, Petri J.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Helsinki, Finland.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mantere, M. J.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    NEW SCALING FOR THE ALPHA EFFECT IN SLOWLY ROTATING TURBULENCE2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, no 2, article id 127Article in journal (Refereed)
    Abstract [en]

    Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers and slow rotation. Thus, the contribution of density stratification is less important than that of turbulent velocity. The a effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence), we find that the contribution of density stratification might be even less important than suggested by the analytic theory.

  • 2.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kemel, Koen
    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.
    NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 749, no 2, article id 179Article in journal (Refereed)
    Abstract [en]

    To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.

  • 3.
    Brandenburg, Axel
    et al.
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    SELF-ASSEMBLY OF SHALLOW MAGNETIC SPOTS THROUGH STRONGLY STRATIFIED TURBULENCE2013In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 776, no 2, article id L23Article in journal (Refereed)
    Abstract [en]

    Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence, this was shown to lead to a large-scale instability that produces spontaneous magnetic flux concentrations. Furthermore, using a horizontal magnetic field, elongated flux concentrations with a strength of a few percent of the equipartition value were found. Here we show that a uniform vertical magnetic field leads to circular magnetic spots of equipartition field strengths. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation.

  • 4.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). 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.
    Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability2016In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, article id 125011Article in journal (Refereed)
    Abstract [en]

    In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed.

  • 5.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; University of the Negev, Israel.
    The contribution of kinetic helicity to turbulent magnetic diffusivity2017In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 338, no 7, p. 790-793Article in journal (Refereed)
    Abstract [en]

    Using numerical simulations of forced turbulence, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.

  • 6.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Ben-Gurion University of the Negev, Israel.
    Kahniashvili, Tina
    Boyarsky, Alexey
    Fröhlich, Jürg
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    The Turbulent Chiral Magnetic Cascade in the Early Universe2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, article id L21Article in journal (Refereed)
    Abstract [en]

    The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k(-2) magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed.

  • 7. Elperin, T.
    et al.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Liberman, Michael
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Moscow Institute of Physics and Technology, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Tangling clustering instability for small particles in temperature stratified turbulence2013In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 25, no 8, article id 085104Article in journal (Refereed)
    Abstract [en]

    We study tangling clustering instability of inertial particles in a temperature stratified turbulence with small finite correlation time. It is shown that the tangling mechanism in the temperature stratified turbulence strongly increases the degree of compressibility of particle velocity field. This results in the strong decrease of the threshold for the excitation of the tangling clustering instability even for small particles. The tangling clustering instability in the temperature stratified turbulence is essentially different from the inertial clustering instability that occurs in non-stratified isotropic and homogeneous turbulence. While the inertial clustering instability is caused by the centrifugal effect of the turbulent eddies, the mechanism of the tangling clustering instability is related to the temperature fluctuations generated by the tangling of the mean temperature gradient by the velocity fluctuations. Temperature fluctuations produce pressure fluctuations and cause particle accumulations in regions with increased instantaneous pressure. It is shown that the growth rate of the tangling clustering instability is root Re (l(0)/L-T)(2)/(3Ma)(4) times larger than that of the inertial clustering instability, where Re is the Reynolds number, Ma is the Mach number, l(0) is the integral turbulence scale, and L-T is the characteristic scale of the mean temperature variations. It is found that depending on the parameters of the turbulence and the mean temperature gradient there is a preferential particle size at which the particle clustering due to the tangling clustering instability is more effective. The particle number density inside the cluster after the saturation of this instability can be by several orders of magnitude larger than the mean particle number density. It is also demonstrated that the evaporation of droplets drastically changes the tangling clustering instability, e. g., it increases the instability threshold in the droplet radius. The tangling clustering instability is of a great importance, e. g., in atmospheric turbulence with temperature inversions.

  • 8.
    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.

  • 9.
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Surface flux concentrations in a spherical alpha 2 dynamo2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, article id A106Article in journal (Refereed)
    Abstract [en]

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

  • 10.
    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.

  • 11.
    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.

  • 12.
    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.

  • 13.
    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.
    Spontaneous formation of magnetic flux concentrations in stratified turbulence2012In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 280, no 2, p. 321-333Article in journal (Refereed)
    Abstract [en]

    The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L2/ηt, where ηt is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number

  • 14.
    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.

  • 15.
    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.

  • 16.
    Kleeorin, Nathan
    et al.
    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.
    Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity: mean-field theory2018In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, no 3, article id 735840303Article in journal (Refereed)
    Abstract [en]

    We discuss a mean-field theory of the generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale non-uniform flow is produced due to either a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.

  • 17.
    Kleeorin, Nathan
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; University of Helsinki, Finland.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; University of Helsinki, Finland.
    Soustova, I. A.
    Troitskaya, Yu.
    Ermakova, O. S.
    Zilitinkevich, S.
    Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 6, article id 063106Article in journal (Refereed)
    Abstract [en]

    We have advanced the energy and flux budget turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGWs) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGWs, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turn, results in strong damping of IGWs. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGWs. The anisotropy of the turbulence produced by less intensive IGWs is stronger than that caused by more intensive waves. The low-amplitude IGWs produce turbulence consisting up to 90% of turbulent potential energy. This resembles the properties of the observed high-altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.

  • 18. Kleeorin, Y.
    et al.
    Safiullin, N.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Porshnev, S.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Sokoloff, D.
    The dynamics of Wolf numbers based on nonlinear dynamos with magnetic helicity: comparisons with observations2016In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 460, no 4, p. 3960-3967Article in journal (Refereed)
    Abstract [en]

    We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behaviour of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 yr ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 per cent correlation over all intervals of observation (about 270 yr). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependences are in good agreement with observations.

  • 19. Kuzanyan, K. M.
    et al.
    Safiullin, N.
    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.
    Porshnev, S.
    Large-Scale Properties of the Tilt of Sunspot Groups and Joy's Law Near the Solar Equator2019In: Astrophysics, ISSN 0571-7256, E-ISSN 1573-8191, Vol. 62, no 2, p. 261-275Article in journal (Refereed)
    Abstract [en]

    A physical mechanism is proposed for the formation of the tilt angle of groups of sunspots during the formation of active regions under the sun's photosphere. The phenomena associated with the influence of Coriolis forces on the large-scale flows in supergranular convection in turbulent media are studied in detail. Based on calculations of the magnetic field in a model of a solar nonlinear dynamo, the orders of magnitude of this effect are estimated and the tilt angle is estimated in the band of latitudes in the royal zone of sunspot activity. This dynamo model is based on the balance of small- and large-scale magnetic helicities, and describes the formation of sunspots over the last five activity cycles (since 1964) and has been adapted for a broader class of magnetic manifestations of solar activity. The variation in the average tilt over these five activity cycles has been plotted and latitude-time diagrams of the distribution of this value constructed which fully satisfy Joy's law and also show the local deviations from it within a limited range of latitudes in isolated phases of the solar cycle.

  • 20.
    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.

  • 21.
    Liberman, Michael A.
    et al.
    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.
    Haugen, Nils Erland L.
    Multipoint radiation induced ignition of dust explosions: turbulent clustering of particles and increased transparency2018In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 22, no 6, p. 1084-1102Article in journal (Refereed)
    Abstract [en]

    Understanding the causes and mechanisms of large explosions, especially dust explosions, is essential for minimising devastating hazards in many industrial processes. It is known that unconfined dust explosions begin as primary (turbulent) deflagrations followed by a devastating secondary explosion. The secondary explosion may propagate with a speed of up to 1000 m/s producing overpressures of over 8-10 atm, which is comparable with overpressures produced in detonation. Since detonation is the only established theory that allows rapid burning producing a high pressure that can be sustained in open areas, the generally accepted view was that the mechanism explaining the high rate of combustion in dust explosions is deflagration-to-detonation transition. In the present work we propose a theoretical substantiation of an alternative mechanism explaining the origin of the secondary explosion producing high speeds of combustion and high overpressures in unconfined dust explosions. We show that the clustering of dust particles in a turbulent flow ahead of the advancing flame front gives rise to a significant increase of the thermal radiation absorption length. This effect ensures that clusters of dust particles are exposed to and heated by radiation from hot combustion products of dust explosions for a sufficiently long time to become multi-point ignition kernels in a large volume ahead of the advancing flame. The ignition times of a fuel-air mixture caused by radiatively heated clusters of particles is considerably reduced compared with the ignition time caused by an isolated particle. Radiation-induced multipoint ignitions of a large volume of fuel-air ahead of the primary flame efficiently increase the total flame area, giving rise to the secondary explosion, which results in the high rates of combustion and overpressures required to account for the observed level of overpressures and damage in unconfined dust explosions, such as for example the 2005 Buncefield explosion and several vapour cloud explosions of severity similar to that of the Buncefield incident.

  • 22.
    Liberman, Michael
    et al.
    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.
    Haugen, Nils Erland L.
    Mechanism of unconfined dust explosions: Turbulent clustering and radiation-induced ignition2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 5, article id 051101Article in journal (Refereed)
    Abstract [en]

    It is known that unconfined dust explosions typically start off with a relatively weak primary flame followed by a severe secondary explosion. We show that clustering of dust particles in a temperature stratified turbulent flow ahead of the primary flame may give rise to a significant increase in the radiation penetration length. These particle clusters, even far ahead of the flame, are sufficiently exposed and heated by the radiation from the flame to become ignition kernels capable to ignite a large volume of fuel-air mixtures. This efficiently increases the total flame surface area and the effective combustion speed, defined as the rate of reactant consumption of a given volume. We show that this mechanism explains the high rate of combustion and overpressures required to account for the observed level of damage in unconfined dust explosions, e.g., at the 2005 Buncefield vapor-cloud explosion. The effect of the strong increase of radiation transparency due to turbulent clustering of particles goes beyond the state of the art of the application to dust explosions and has many implications in atmospheric physics and astrophysics.

  • 23.
    Mitra, Dhrubaditya
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Haugen, Nils Erland L.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of the Negev, Israel.
    Turbophoresis in forced inhomogeneous turbulence2018In: The European Physical Journal Plus, ISSN 2190-5444, E-ISSN 2190-5444, Vol. 133, no 2, article id 35Article in journal (Refereed)
    Abstract [en]

    We show, by direct numerical simulations, that heavy inertial particles (characterized by Stokes number St) in inhomogeneously forced statistically stationary isothermal turbulent flows cluster at the minima of mean-square turbulent velocity. Two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. If the turbulent diffusivity is assumed to scale with turbulent root-mean-square velocity, as is the case for homogeneous turbulence, the turbophoretic coefficient can be calculated. Indeed, for the above assumption, the non-dimensional product of the turbophoretic coefficient and the rms velocity is shown to increase with St for small St, reach a maxima for St approximate to 10 and decrease as similar to St(-0.33) for large St.

  • 24. Rivero Losada, Illa
    et al.
    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.
    Rotational effects on the negative magnetic pressure instability2012In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 548, article id A49Article in journal (Refereed)
    Abstract [en]

    Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims. We want to understand the effects of rotation on this instability in both two and three dimensions. Methods. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results. We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions. We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.

  • 25.
    Rivero Losada, Illa
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Competition of rotation and stratification in flux concentrations2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, article id A83Article in journal (Refereed)
    Abstract [en]

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

  • 26.
    Rivero Losada, Illa
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Magnetic flux concentrations in a polytropic atmosphere2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 564, article id A2Article in journal (Refereed)
    Abstract [en]

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

  • 27.
    Rivero Losada, Illa
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Nordic Optical Telescope, Spain.
    Warnecke, Jörn
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, 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.
    Magnetic bipoles in rotating turbulence with coronal envelope2019In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, article id A61Article in journal (Refereed)
    Abstract [en]

    Context. The formation mechanism of sunspots and starspots is not yet fully understood. It is a major open problem in astrophysics.

    Aims. Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We aim to understand the important issue of whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI.

    Methods. We have used direct numerical simulations and mean-field simulations. We adopted a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigated the effects of rotation on NEMPI by changing the Coriolis number, the latitude, the strengths of the imposed magnetic field, and the box resolution.

    Results. Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress BR formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly reduce the effects of rotational suppression.

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  • 28.
    Rogachevskii, Igor
    et al.
    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.
    Generation of a large-scale vorticity in a fast-rotating density-stratified turbulence or turbulent convection2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 100, no 6, article id 063101Article in journal (Refereed)
    Abstract [en]

    We find an instability resulting in generation of large-scale vorticity in a fast-rotating small-scale turbulence or turbulent convection with inhomogeneous fluid density along the rotational axis in anelastic approximation. The large-scale instability causes excitation of two modes: (i) the mode with dominant vertical vorticity and with the mean velocity being independent of the vertical coordinate; (ii) the mode with dominant horizontal vorticity and with the mean momentum being independent of the vertical coordinate. The mode with the dominant vertical vorticity can be excited in a fast-rotating density-stratified hydrodynamic turbulence or turbulent convection. For this mode, the mean entropy is depleted inside the cyclonic vortices, while it is enhanced inside the anticyclonic vortices. The mode with the dominant horizontal vorticity can be excited only in a fast-rotating density-stratified turbulent convection. The developed theory may be relevant for explanation of an origin of large spots observed as immense storms in great planets, e.g., the Great Red Spot in Jupiter and large spots in Saturn. It may be also useful for explanation of an origin of high-latitude spots in rapidly rotating late-type stars.

  • 29.
    Rogachevskii, Igor
    et al.
    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.
    Mean-field theory of differential rotation in density stratified turbulent convection2018In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, no 2, article id 735840201Article in journal (Refereed)
    Abstract [en]

    A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach, which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

  • 30.
    Rogachevskii, Igor
    et al.
    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.
    Turbulent fluxes of entropy and internal energy in temperature stratified flows2015In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 81, article id 395810504Article in journal (Refereed)
    Abstract [en]

    We derive equations for the mean entropy and the mean internal energy in low-Mach-number temperature stratified turbulence (i.e. for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by F-s = (rho) over bar(us) over bar, where (rho) over bar is the mean fluid density, s is fluctuation of entropy and overbars denote averaging over an ensemble of turbulent velocity fields, u. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, F-c = (T) over bar(rho) over bar(us) over bar, of the fluid internal energy, where (T) over bar is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equations for the velocity-entropy correlation, (us) over bar, in the limits of small and large Peclet numbers, using the quasi-linear approach and the spectral tau approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.

  • 31.
    Rogachevskii, Igor
    et al.
    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.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory2018In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, no 5, article id 735840502Article in journal (Refereed)
    Abstract [en]

    We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral tau-approach. We find that compressibility decreases the a effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Peclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Peclet numbers. It can be interpreted as compressible turbophoresis of non-inertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.

  • 32.
    Rogachevskii, Igor
    et al.
    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.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichler, David
    COSMIC-RAY CURRENT-DRIVEN TURBULENCE AND MEAN-FIELD DYNAMO EFFECT2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 753, no 1, article id 6Article in journal (Refereed)
    Abstract [en]

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

  • 33.
    Rogachevskii, Igor
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; University of Colorado, USA.
    Ruchayskiy, Oleg
    Boyarsky, Alexey
    Fröhlich, Jürg
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory2017In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 846, no 2, article id 153Article in journal (Refereed)
    Abstract [en]

    The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right-and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfven wave for incompressible flows, increases the frequencies of the Alfven wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark-gluon plasma.

  • 34. Saullin, N.
    et al.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Porshnev, S.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Ruzmaikin, A.
    Nonlinear mean-field dynamo and prediction of solar activity2018In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, no 3, article id 735840306Article in journal (Refereed)
    Abstract [en]

    We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations.

  • 35. 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.

  • 36.
    Schober, Jennifer
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Laboratoire d ’ Astrophysique, EPFL, Switzerland.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; 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.
    Boyarsky, Alexey
    Fröhlich, Jürg
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations2018In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 858, no 2, article id 124Article in journal (Refereed)
    Abstract [en]

    Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left-and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (alpha(mu) effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The alpha(mu) effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of protoneutron stars are discussed.

  • 37.
    Warnecke, Jörn
    et al.
    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).
    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; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Bipolar Magnetic Structures Driven by Stratified Turbulence with a Coronal Envelope2013In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 777, no 2, article id L37Article in journal (Refereed)
    Abstract [en]

    We report the spontaneous formation of bipolar magnetic structures in direct numerical simulations of stratified forced turbulence with an outer coronal envelope. The turbulence is forced with transverse random waves only in the lower (turbulent) part of the domain. Our initial magnetic field is either uniform in the entire domain or confined to the turbulent layer. After about 1-2 turbulent diffusion times, a bipolar magnetic region of vertical field develops with two coherent circular structures that live during one turbulent diffusion time, and then decay during 0.5 turbulent diffusion times. The resulting magnetic field strengths inside the bipolar region are comparable to the equipartition value with respect to the turbulent kinetic energy. The bipolar magnetic region forms a loop-like structure in the upper coronal layer. We associate the magnetic structure formation with the negative effective magnetic pressure instability in the two-layer model.

  • 38.
    Warnecke, Jörn
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Rivero Losada, Illa
    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.
    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.
    Bipolar region formation in stratified two-layer turbulence2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 589, article id A125Article in journal (Refereed)
    Abstract [en]

    Aims. This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. Methods. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In most cases, it is horizontal, but a vertical and an inclined field are also considered. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Results. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around 100 across the turbulent layer. For the fluid Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. A small imposed horizontal field component is necessary to generate bipolar structures. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.

1 - 38 of 38
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