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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, 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, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Schober, Jennifer
    Dissipative magnetic structures and scales in small-scale dynamos2023In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 518, no 4, p. 6367-6375Article in journal (Refereed)
    Abstract [en]

    Small-scale dynamos play important roles in modern astrophysics, especially on galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time-scale of galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values – contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the non-linearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime.

  • 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; 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.

  • 7.
    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.

  • 8. 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.

  • 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.
    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.

  • 10.
    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.

  • 11.
    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.

  • 12.
    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.

  • 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.
    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.
    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

  • 15.
    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.

  • 16.
    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.

  • 17. Kleeorin, N.
    et al.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Turbulent magnetic helicity fluxes in solar convective zone2022In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 515, no 4, p. 5437-5448Article in journal (Refereed)
    Abstract [en]

    Combined action of helical motions of plasma (the kinetic alpha effect) and non-uniform (differential) rotation is a key dynamo mechanism of solar and galactic large-scale magnetic fields. Dynamics of magnetic helicity of small-scale fields is a crucial mechanism in a non-linear dynamo saturation where turbulent magnetic helicity fluxes allow to avoid catastrophic quenching of the alpha effect. The convective zone of the Sun and solar-like stars, as well as galactic discs, are the source for production of turbulent magnetic helicity fluxes. In the framework of the mean-field approach and the spectral tau approximation, we derive turbulent magnetic helicity fluxes using the Coulomb gauge in a density-stratified turbulence. The turbulent magnetic helicity fluxes include non-gradient and gradient contributions. The non-gradient magnetic helicity flux is proportional to a non-linear effective velocity (which vanishes in the absence of the density stratification) multiplied by small-scale magnetic helicity, while the gradient contributions describe turbulent magnetic diffusion of the small-scale magnetic helicity. In addition, the turbulent magnetic helicity fluxes contain source terms proportional to the kinetic alpha effect or its gradients, and also contributions caused by the large-scale shear (solar differential rotation). We have demonstrated that the turbulent magnetic helicity fluxes due to the kinetic alpha effect and its radial derivative in combination with the non-linear magnetic diffusion of the small-scale magnetic helicity are dominant in the solar convective zone.

  • 18. Kleeorin, N.
    et al.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Safiullin, N.
    Gershberg, R.
    Porshnev, S.
    Magnetic fields of low-mass main sequences stars: non-linear dynamo theory and mean-field numerical simulations2023In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 526, no 2, p. 1601-1612Article in journal (Refereed)
    Abstract [en]

    Our theoretical and numerical analysis have suggested that for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, the generated large-scale magnetic field is caused by the mean-field alpha(2)Omega dynamo, whereby the alpha(2) dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the alpha(2)Omega and alpha(2) dynamos and a developed non-linear theory of alpha(2) dynamo. The applied MFS model was calibrated using turbulent parameters typical for the solar convective zone.

  • 19.
    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.

  • 20.
    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.

  • 21.
    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.
    Zilitinkevich, S.
    Energy and flux budget closure theory for passive scalar in stably stratified turbulence2021In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 33, no 7, article id 076601Article in journal (Refereed)
    Abstract [en]

    The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification, and it implies that turbulence is maintained by the velocity shear at any stratification. In a steady-state, expressions for the turbulent flux of the passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are derived, and universal flux Richardson number dependencies of the components of this tensor are obtained. The diagonal component in the vertical direction of the turbulent diffusion tensor is suppressed by strong stratification, while the diagonal components in the horizontal directions are not suppressed, but they are dominant in comparison with the other components of the turbulent diffusion tensor. This implies that any initially created strongly inhomogeneous particle cloud is evolved into a thin pancake in a horizontal plane with very slow increase in its thickness in the vertical direction. The turbulent Schmidt number (the ratio of the eddy viscosity and the vertical turbulent diffusivity of the passive scalar) linearly increases with the gradient Richardson number. The physics of such a behavior is related to the buoyancy force that causes a correlation between fluctuations of the potential temperature and the particle number density. This correlation that is proportional to the product of the vertical turbulent particle flux and the vertical gradient of the mean potential temperature reduces the vertical turbulent particle flux. Considering the applications of these results to the atmospheric boundary-layer turbulence, the theoretical relationships are derived, which allows us to determine the turbulent diffusion tensor as a function of the vertical coordinate measured in the units of the local Obukhov length scale. The obtained relations are potentially useful in modeling applications of particle dispersion in the atmospheric boundary-layer turbulence and free atmosphere turbulence.

  • 22.
    Kleeorin, Nathan
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Safiullin, N.
    Kuzanyan, K.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Tlatov, A.
    Porshnev, S.
    The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations2020In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 495, no 1, p. 238-248Article in journal (Refereed)
    Abstract [en]

    A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. Amechanism of formation of the mean tilt is related to the effect of the Coriolis force on meso-scale motions of supergranular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt, which can explain deviations from Joy's law for the sunspot bipolar regions at high latitudes. The theoretical results obtained and the results from numerical simulations based on the non-linear mean-field dynamo theory, which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15-24.

  • 23. 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.

  • 24. Kuzanyan, K.
    et al.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Sokoloff, D.
    Zhang, H.
    Estimates of Current Helicity and Tilt of Solar Active Regions and Joy's Law2020In: Geomagnetism and Aeronomy, ISSN 0016-7932, E-ISSN 1555-645X, Vol. 60, no 8, p. 1032-1037Article in journal (Refereed)
    Abstract [en]

    The tilt angle, current helicity and twist of solar magnetic fields can be observed in solar active regions. We carried out estimates of these parameters by two ways. Firstly, we consider the model of turbulent convective cells (super-granules) which have a loop floating structure towards the surface of the Sun. Their helical properties are attained during the rising process in the rotating stratified convective zone. The other estimate is obtained from a simple mean-field dynamo model that accounts magnetic helicity conservation. The both values are shown to be capable to give important contributions to the observable tilt, helicity and twist.

  • 25. 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.

  • 26.
    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.

  • 27.
    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.

  • 28.
    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.

  • 29.
    Losada, Illa Rivero
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Warnecke, Jörn
    Max-Planck Insitute for Solar system Research.
    Glogowski, Kolja
    Kiepenheuer-Institu für Sonnenphysik.
    Roth, Markus
    Kiepenheuer-Institu für Sonnenphysik.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    A new look at sunspot formation using theory and observations2017In: Proceedings of the International Astronomical Union, 2017, Vol. 327, 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 super-equipartition 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.

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  • 30.
    Mitra, Dhrubaditya
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    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.
    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.

  • 31.
    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, 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.

  • 32. 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.

  • 33.
    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.

  • 34.
    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.

  • 35.
    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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  • 36.
    Rogachevskii, Igor
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, N.
    Semi-organized structures and turbulence in the atmospheric convection2024In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 36, no 2, article id 026610Article in journal (Refereed)
    Abstract [en]

    The atmospheric convective boundary layer (CBL) consists of three basic parts: (1) the surface layer unstably stratified and dominated by small-scale turbulence of very complex nature; (2) the CBL core dominated by the energy-, momentum-, and mass-transport of semi-organized structures (large-scale circulations), with a small contribution from small-scale turbulence produced by local structural shears; and (3) turbulent entrainment layer at the upper boundary, characterized by essentially stable stratification with negative (downward) turbulent flux of potential temperature. The energy- and flux budget theory developed previously for atmospheric stably-stratified turbulence and the surface layer in atmospheric convective turbulence is extended to the CBL core using budget equations for turbulent energies and turbulent fluxes of buoyancy and momentum. For the CBL core, we determine global turbulent characteristics (averaged over the entire volume of the semi-organized structure) as well as kinetic and thermal energies of the semi-organized structures as the functions of the aspect ratio of the semi-organized structure, the scale separation parameter between the vertical size of the structures and the integral scale of turbulence and the degree of thermal anisotropy characterized the form of plumes. The obtained theoretical relationships are potentially useful in modeling applications in the atmospheric convective boundary-layer and analysis of laboratory and field experiments, direct numerical simulations, and large-eddy simulations of convective turbulence with large-scale semi-organized structures.

  • 37.
    Rogachevskii, Igor
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Kleeorin, N.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of Negev, Israel.
    Turbulent transport of radiation in the solar convective zone2021In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 508, no 1, p. 1296-1304Article in journal (Refereed)
    Abstract [en]

    A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases 2.5 times in the vicinity of the solar surface. The main reasons for this are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation.

  • 38.
    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).
    Compressibility effects in turbulent transport of the temperature field2021In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 103, no 1, article id 013107Article in journal (Refereed)
    Abstract [en]

    Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Péclet numbers and the spectral τ approach for large Péclet numbers. The compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for the particle number density and magnetic field. However, expressions for the turbulent diffusion coefficient for the mean temperature field in a compressible turbulence are different from those for the mean particle number density and the mean magnetic field. The combined effect of compressibility and inhomogeneity of turbulence causes an increase of the mean temperature in the regions with more intense velocity fluctuations due to a turbulent pumping. Formally, this effect is similar to a phenomenon of compressible turbophoresis found previously [J. Plasma Phys. 84, 735840502 (2018)] for noninertial particles or gaseous admixtures. The gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to the turbulent barodiffusion of particles and gaseous admixtures. The compressibility of a fluid flow also causes a turbulent cooling of the surrounding fluid due to an additional sink term in the equation for the mean temperature field. There is no analog of this effect for particles.

  • 39.
    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.

  • 40.
    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.

  • 41.
    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.

  • 42.
    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.

  • 43.
    Rogachevskii, Igor
    et al.