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  • 1.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gressel, Oliver
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Jabbari, Sarah
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 562, p. A53-Article in journal (Refereed)
    Abstract [en]

    Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims. We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods. We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results. Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being ≤1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability. Conclusions. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility.

  • 2.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gressel, Oliver
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, Petri J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, M. J.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    New scaling for the alpha effect in slowly rotating turbulence2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, no 2, p. 127-Article 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.

  • 3.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Self-assembly of shallow magnetic spots through strongly stratified turbulence2013In: Astrophysical Journal Letters, ISSN 2041-8205, Vol. 776, no 2, p. L23-Article 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Magnetic concentrations in stratified turbulence: The negative effective magnetic pressure instability2016In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, no 12, 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado; Department of Astronomy, AlbaNova University Center, Stockholm University, Stockholm, Sweden.
    Schober, J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Schober, Jennifer
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Kahniashvili, Tina
    Boyarsky, Alexey
    Frohlich, Jog
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Liberman, Mikhail
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Tangling clustering instability for small particles in temperature stratified turbulence2013In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 25, no 8, p. 085104-Article 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Surface flux concentrations in a spherical alpha 2 dynamo2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, p. A106-Article 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Monash Univ, Australia; Stockholm Univ, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Univ Colorado, USA; Lab Atmospher & Space Phys, USA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ 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.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, 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.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Rivero Losada, Illa
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel .
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel .
    Magnetic flux concentrations from dynamo-generated fields2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 568, p. A112-Article in journal (Refereed)
    Abstract [en]

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

  • 13.
    Kemel, Koen
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.

  • 14.
    Kemel, Koen
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.

  • 15. Kleeorin, Y.
    et al.
    Safiullin, N.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Porshnev, S.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.

  • 16.
    Käpylä, Petri
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Aalto University, Finland.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Kapyla, M. J.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Magnetic flux concentrations from turbulent stratified convection2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 588, article id A150Article in journal (Refereed)
    Abstract [en]

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

  • 17.
    Käpylä, Petri J.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, M. J.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Flux concentrations in turbulent convection2012In: Proceedings of the International Astronomical Union, Cambridge University Press, 2012, no S294, p. 283-288Conference paper (Refereed)
    Abstract [en]

    We present preliminary results from high resolution magneto-convection simulations where we find the formation of flux concentrations from an initially uniform magnetic field. The structures appear in roughly ten convective turnover times and live close to a turbulent diffusion time. The time scales are compatible with the negative effective magnetic pressure instability (NEMPI), although structure formation is not restricted to regions where the effective magnetic pressure is negative.

  • 18.
    Liberman, Michael
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; 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.

  • 19. Losada, I. R.
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rotational effects on the negative magnetic pressure instability2012In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 548, p. A49-Article 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.

  • 20.
    Losada, I. R.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, Stockholm University, SE-10691 Stockholm, Sweden; Nordic Optical Telescope, Apartado 474, E-38700 Santa Cruz de La Palma, Spain; Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, D-79104, Freiburg, Germany.
    Warnecke, J.
    Glogowski, K.
    Roth, M.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, Stockholm University, SE-10691 Stockholm, Sweden; ;.
    Kleeorin, N.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Mechanical Engineering, Ben-Gurion University of the Negev, POB 653, Beer-Sheva 84105, Israel.
    Rogachevskii, I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Mechanical Engineering, Ben-Gurion University of the Negev, POB 653, Beer-Sheva 84105, Israel.
    A new look at sunspot formation using theory and observations2016In: Proceedings of the International Astronomical Union, Cambridge University Press , 2016, p. 46-59Conference paper (Refereed)
    Abstract [en]

    Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are the origin of the bipolar sunspot structure seen on the solar surface. However, this theory has been challenged, in particular recently by new surface observation, helioseismic inversions, and numerical models of convective dynamos. In this article we discuss another theoretical approach to the formation of sunspots: the negative effective magnetic pressure instability. This is a large-scale instability, in which the total (kinetic plus magnetic) turbulent pressure can be suppressed in the presence of a weak large-scale magnetic field, leading to a converging downflow, which eventually concentrates the magnetic field within it. Numerical simulations of forced stratified turbulence have been able to produce strong superequipartition flux concentrations, similar to sunspots at the solar surface. In this framework, sunspots would only form close to the surface due to the instability constraints on stratification and rotation. Additionally, we present some ideas from local helioseismology, where we plan to use the Hankel analysis to study the pre-emergence phase of a sunspot and to constrain its deep structure and formation mechanism. 

  • 21.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel; NI Lobachevsky State Univ Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel; NI Lobachevsky State Univ Nizhny Novgorod, Russia.
    Intense bipolar structures from stratified helical dynamos2014In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 445, no 1, p. 761-769Article in journal (Refereed)
    Abstract [en]

    We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to delta spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of 10.

  • 22.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Haugen, Nils Erland L.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.

  • 23.
    Rivero Losada, Illa
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Competition of rotation and stratification in flux concentrations2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, p. A83-Article 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.

  • 24.
    Rivero Losada, Illa
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Magnetic flux concentrations in a polytropic atmosphere2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 564, p. A2-Article 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.

  • 25.
    Rogachevskii, Igor
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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.

  • 26.
    Rogachevskii, Igor
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    KTH, Centres, 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, no 5, 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 Fs=σus, where σ 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, Fc=T σ us , of the fluid internal energy, where T 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, in the limits of small and large Péclet numbers, using the quasi-linear approach and the spectral τ approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.

  • 27.
    Rogachevskii, Igor
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, 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, p. 6-Article in journal (Refereed)
    Abstract [en]

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

  • 28.
    Rogachevskii, Igor
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Ruchayskiy, Oleg
    Boyarsky, Alexey
    Frohlich, Jurg
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Schober, Jennifer
    KTH, Centres, 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.

  • 29.
    Singh, Nishant K.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 850, no 1, article id L8Article in journal (Refereed)
    Abstract [en]

    Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate gamma of the SSD and the turbulent rms velocity u(rms) with shear rate S that are independent of the magnetic Prandtl number: gamma proportional to vertical bar S vertical bar and u(rms) proportional to vertical bar S vertical bar(2/3). For large fluid and magnetic Reynolds numbers, gamma, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, (gamma) over tilde proportional to vertical bar S vertical bar(2/3), arising solely from the induction equation for a given velocity field.

  • 30.
    Warnecke, Jörn
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Losada, Illa R.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Bipolar magnetic structures driven by stratified turbulence with a coronal envelope2013In: Astrophysical Journal Letters, ISSN 2041-8205, Vol. 777, no 2, p. L37-Article 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.

  • 31.
    Warnecke, Jörn
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rivero Losada, Illa
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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 - 31 of 31
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