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1.
  • Brandenburg, Axel, et al. (författare)
  • Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations
  • 2011
  • Ingår i: Astrophysical Journal, ISSN 0004-637X, EISSN 1538-4357. ; 740:2, s. L50-
  • Tidskriftsartikel (refereegranskat)abstract
    • We present the first numerical demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number. Our results support earlier mean-field calculations and analytic work that identified this instability. Applications to the formation of active regions in the Sun are discussed.
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2.
  • Brandenburg, Axel, 1959-, et al. (författare)
  • Dissipative magnetic structures and scales in small-scale dynamos
  • 2022
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press (OUP). - 0035-8711 .- 1365-2966. ; 518:4, s. 6367-6375
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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3.
  • Brandenburg, Axel, et al. (författare)
  • Magnetic concentrations in stratified turbulence : The negative effective magnetic pressure instability
  • 2016
  • Ingår i: New Journal of Physics. - : Institute of Physics Publishing (IOPP). - 1367-2630. ; 18:12
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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4.
  • Brandenburg, Axel, et al. (författare)
  • Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field
  • 2014
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 562
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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5.
  • Brandenburg, Axel, et al. (författare)
  • NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE
  • 2012
  • Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 749:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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6.
  • Brandenburg, Axel, et al. (författare)
  • NEW SCALING FOR THE ALPHA EFFECT IN SLOWLY ROTATING TURBULENCE
  • 2013
  • Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 762:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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7.
  • Brandenburg, Axel, et al. (författare)
  • SELF-ASSEMBLY OF SHALLOW MAGNETIC SPOTS THROUGH STRONGLY STRATIFIED TURBULENCE
  • 2013
  • Ingår i: Astrophysical Journal Letters. - 2041-8205 .- 2041-8213. ; 776:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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8.
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9.
  • Brandenburg, Axel, et al. (författare)
  • The Turbulent Chiral Magnetic Cascade in the Early Universe
  • 2017
  • Ingår i: Astrophysical Journal Letters. - : IOP PUBLISHING LTD. - 2041-8205 .- 2041-8213. ; 845:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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10.
  • Elperin, Tov, et al. (författare)
  • Clustering of aerosols in atmospheric turbulent flow
  • 2007
  • Ingår i: Environmental Fluid Mechanics. - : Springer Science and Business Media LLC. - 1567-7419 .- 1573-1510. ; 7:2, s. 173-193
  • Tidskriftsartikel (refereegranskat)abstract
    • A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of small-scale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.
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11.
  • Elperin, T., et al. (författare)
  • Tangling clustering instability for small particles in temperature stratified turbulence
  • 2013
  • Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 25:8, s. 085104-
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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12.
  • Haugen, Nils Erland L., et al. (författare)
  • Detection of turbulent thermal diffusion of particles in numerical simulations
  • 2012
  • Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 24:7
  • Tidskriftsartikel (refereegranskat)abstract
    • The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux (i.e., non-counter-gradient transport) of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the formation of inhomogeneities in the spatial distribution of inertial particles whose scale is large in comparison with the integral scale of the turbulence. The strength of this effect is maximum for Stokes numbers around unity, and decreases again for larger values. The dynamics of inertial particles is studied using Lagrangian modelling in forced temperature-stratified turbulence, whereas non-inertial particles and the fluid are described using DNS in an Eulerian framework.
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13.
  • Jabbari, Sarah, et al. (författare)
  • BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE
  • 2015
  • Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 805:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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14.
  • Jabbari, Sarah, et al. (författare)
  • Magnetic flux concentrations from dynamo-generated fields
  • 2014
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 568
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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15.
  • Jabbari, Sarah, et al. (författare)
  • Sharp magnetic structures from dynamos with density stratification
  • 2017
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : OXFORD UNIV PRESS. - 0035-8711 .- 1365-2966. ; 467:3, s. 2753-2765
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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16.
  • Jabbari, Sarah, et al. (författare)
  • Surface flux concentrations in a spherical alpha 2 dynamo
  • 2013
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 556
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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17.
  • Jabbari, Sarah, et al. (författare)
  • Turbulent reconnection of magnetic bipoles in stratified turbulence
  • 2016
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press. - 0035-8711 .- 1365-2966. ; 459:4, s. 4046-4056
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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18.
  • Kemel, Koen, et al. (författare)
  • Active Region Formation through the Negative Effective Magnetic Pressure Instability
  • 2013
  • Ingår i: Solar Physics. - : Springer Science and Business Media LLC. - 0038-0938 .- 1573-093X. ; 287:1-2, s. 293-313
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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19.
  • Kemel, Koen, et al. (författare)
  • Non-uniformity effects in the negative effective magnetic pressure instability
  • 2013
  • Ingår i: Physica Scripta. - 0031-8949 .- 1402-4896. ; T155
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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20.
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21.
  • Kemel, Koen, et al. (författare)
  • Properties of the negative effective magnetic pressure instability
  • 2012
  • Ingår i: Astronomical Notes - Astronomische Nachrichten. - : Wiley. - 0004-6337 .- 1521-3994. ; 333:2, s. 95-100
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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22.
  • Kemel, Koen, et al. (författare)
  • Spontaneous formation of magnetic flux concentrations in stratified turbulence
  • 2012
  • Ingår i: Solar Physics. - : Springer Science and Business Media LLC. - 0038-0938 .- 1573-093X. ; 280:2, s. 321-333
  • Tidskriftsartikel (refereegranskat)abstract
    • 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
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23.
  • Kleeorin, Nathan, et al. (författare)
  • Energy and flux budget closure theory for passive scalar in stably stratified turbulence
  • 2021
  • Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 33:7
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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24.
  • Kleeorin, Nathan, et al. (författare)
  • Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity : mean-field theory
  • 2018
  • Ingår i: Journal of Plasma Physics. - : CAMBRIDGE UNIV PRESS. - 0022-3778 .- 1469-7807. ; 84:3
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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25.
  • Kleeorin, Nathan, et al. (författare)
  • Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows
  • 2019
  • Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 99:6
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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26.
  • Kleeorin, N., et al. (författare)
  • Magnetic fields of low-mass main sequences stars : non-linear dynamo theory and mean-field numerical simulations
  • 2023
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press (OUP). - 0035-8711 .- 1365-2966. ; 526:2, s. 1601-1612
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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27.
  • Kleeorin, Nathan, et al. (författare)
  • Nonlinear Mean-Field Dynamos With Magnetic Helicity Transport and Solar Activity: Sunspot Number and Tilt
  • 2023
  • Ingår i: Helicities in Geophysics, Astrophysics, and Beyond. - : Wiley. ; , s. 217-240
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
    • In this chapter, we discuss a mean field solar dynamo model with algebraic and dynamic nonlinearities, various mechanisms of sunspot formation, and prediction of solar activity. The algebraic nonlinearity describes the quenching of the alpha effect, turbulent magnetic diffusion, and the effective pumping velocity due to feedback from the growing large-scale magnetic field on the fluid motion. The dynamic nonlinearity is due to the evolution of the magnetic helicity of the small-scale magnetic field during the nonlinear stage of the dynamo; it is derived from conservation of the total (large-scale plus small-scale) magnetic helicity for very small microscopic magnetic diffusivity.We discuss observations of magnetic helicity in the Sun and their connection with the nonlinear mean field dynamo. We derive a budget equation for sunspot numbers taking into account sunspot formation mechanism due to the negative effective magnetic pressure instability. To predict solar activity, we use dynamo simulations as input to an artificial neural network that learns sunspot dynamics from available observations. Finally, we analyze the contribution of magnetic helicity transport to the formation of tilt in sunspot bipolar regions and compare the results with available observational data over the last 10 solar cycles (15-24).
  •  
28.
  • Kleeorin, Nathan, et al. (författare)
  • The mean tilt of sunspot bipolar regions : theory, simulations and comparison with observations
  • 2020
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : OXFORD UNIV PRESS. - 0035-8711 .- 1365-2966. ; 495:1, s. 238-248
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
29.
  • Kleeorin, N., et al. (författare)
  • Turbulent magnetic helicity fluxes in solar convective zone
  • 2022
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press (OUP). - 0035-8711 .- 1365-2966. ; 515:4, s. 5437-5448
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
30.
  • Kleeorin, Y., et al. (författare)
  • The dynamics of Wolf numbers based on nonlinear dynamos with magnetic helicity : comparisons with observations
  • 2016
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press. - 0035-8711 .- 1365-2966. ; 460:4, s. 3960-3967
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
31.
  • Kuzanyan, K. M., et al. (författare)
  • Large-Scale Properties of the Tilt of Sunspot Groups and Joy's Law Near the Solar Equator
  • 2019
  • Ingår i: ASTROPHYSICS. - : Springer Nature. - 0571-7256 .- 1573-8191. ; 62:2, s. 261-275
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
32.
  • Käpylä, Petri J., et al. (författare)
  • Flux concentrations in turbulent convection
  • 2012
  • Ingår i: Proceedings of the International Astronomical Union. - : Cambridge University Press. - 9781107033832 ; , s. 283-288
  • Konferensbidrag (refereegranskat)abstract
    • 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.
  •  
33.
  • Käpylä, Petri, et al. (författare)
  • Magnetic flux concentrations from turbulent stratified convection
  • 2016
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 588
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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34.
  • Li, Xiang-Yu, et al. (författare)
  • Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment
  • 2020
  • Ingår i: Journal of the Atmospheric Sciences. - : AMER METEOROLOGICAL SOC. - 0022-4928 .- 1520-0469. ; 77:1, s. 337-353
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
35.
  • Li, X. Y., et al. (författare)
  • Effect of Turbulence on Collisional Growth of Cloud Droplets
  • 2018
  • Ingår i: Journal of the Atmospheric Sciences. - : American Meteorological Society. - 0022-4928 .- 1520-0469. ; 75:10, s. 3469-3487
  • Tidskriftsartikel (refereegranskat)abstract
    • Weinvestigate the effect of turbulence on the collisional growth of micrometer-sized droplets through highresolution numerical simulations with well-resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate <<, but only weakly on the Reynolds number. This can be explained through the << dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as << 1/ 2 even when coalescence is invoked. The size distribution exhibits power-law behavior with a slope of 23.7 from a maximum at approximately 10 up to about 40 mm. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is because turbulence enhances the collisional growth between similar-sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.
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36.
  • Liberman, Michael A., et al. (författare)
  • Multipoint radiation induced ignition of dust explosions : turbulent clustering of particles and increased transparency
  • 2018
  • Ingår i: Combustion theory and modelling. - : Informa UK Limited. - 1364-7830 .- 1741-3559. ; 22:6, s. 1084-1102
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
37.
  • Liberman, Michael, et al. (författare)
  • Mechanism of unconfined dust explosions : Turbulent clustering and radiation-induced ignition
  • 2017
  • Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 95:5
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
38.
  • Mitra, Dhrubaditya, et al. (författare)
  • Intense bipolar structures from stratified helical dynamos
  • 2014
  • Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press (OUP). - 0035-8711 .- 1365-2966. ; 445:1, s. 761-769
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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39.
  • Mitra, Dhrubaditya, et al. (författare)
  • Turbophoresis in forced inhomogeneous turbulence
  • 2018
  • Ingår i: The European Physical Journal Plus. - : SPRINGER HEIDELBERG. - 2190-5444. ; 133:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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40.
  • Rivero Losada, Illa, et al. (författare)
  • Competition of rotation and stratification in flux concentrations
  • 2013
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 556
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
41.
  • Rivero Losada, Illa, et al. (författare)
  • Magnetic bipoles in rotating turbulence with coronal envelope
  • 2019
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 621
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
42.
  • Rivero Losada, Illa, et al. (författare)
  • Magnetic flux concentrations in a polytropic atmosphere
  • 2014
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 564
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
43.
  • Rivero Losada, Illa, et al. (författare)
  • Rotational effects on the negative magnetic pressure instability
  • 2012
  • Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 548
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
44.
  • Rogachevskii, Igor, et al. (författare)
  • Compressibility effects in turbulent transport of the temperature field
  • 2021
  • Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 103:1
  • Tidskriftsartikel (refereegranskat)abstract
    • Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Peclet numbers and the spectral tau approach for large Peclet 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.
  •  
45.
  • Rogachevskii, Igor, et al. (författare)
  • COSMIC-RAY CURRENT-DRIVEN TURBULENCE AND MEAN-FIELD DYNAMO EFFECT
  • 2012
  • Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 753:1
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
  •  
46.
  • Rogachevskii, Igor, et al. (författare)
  • Effects of MHD turbulence on mean magnetic pressure and formation of magnetic structures
  • 2020
  • Ingår i: ETC 2013 - 14th European Turbulence Conference. - : Zakon Group LLC.
  • Konferensbidrag (refereegranskat)abstract
    • A review of analytical and numerical results on effects of developed magnetohydrodynamic (MHD) turbulence on mean magnetic pressure and formation of magnetic structures is presented. Suppression of turbulent hydromagnetic pressure (the isotropic part of combined Reynolds and Maxwell stresses) by the mean large-scale magnetic field is related to an effective mechanism for the formation of magnetic inhomogeneous structures in MHD turbulence. At large Reynolds numbers and for sub-equipartition mean magnetic fields, the resulting negative turbulent contribution can be enough large so that the effective mean magnetic pressure (the sum of turbulent and non-turbulent contributions) appears negative. We also investigated the effect of mean current density on the turbulent hydromagnetic pressure reduction, and demonstrated that an enhanced mean current density increases the suppression of the turbulent pressure. Such currents are associated with sharp gradients of the growing magnetic structures. The negative effective mean magnetic pressure was found in direct numerical simulation (DNS) in both, stably stratified forced turbulence and turbulent convection. This phenomenon causes the excitation of the negative effective magnetic pressure instability (NEMPI). By the action of this instability, an initially uniform magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. This instability has been recently detected in DNS of forced stratified MHD turbulence that requires enough large scale separation between the forcing scale and the size of the box (e.g., the number of turbulent eddies in the computational domain is about 30). Strong spontaneous formation of large-scale magnetic structures caused by NEMPI, is seen even without performing any spatial averaging. The characteristic time of the instability is comparable to the turbulent diffusion time. We also demonstrated that the magnetic energy of the forming large-scale inhomogeneous magnetic structures is only weakly dependent on the magnetic Reynolds number, provided its value is large enough for the excitation of NEMPI. Our DNS results support mean-field calculations and analytical results which identified this instability. For example, for an isothermal layer the onset of the instability occurs at the same depth that increases with increasing field strength, the growth rate of NEMPI is independent of the field strength, provided the magnetic structures are fully contained within the domain. NEMPI may play a crucial role in the formation of sunspots and active regions in the upper part of convective zones of Sun and stars. 
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47.
  • Rogachevskii, Igor, et al. (författare)
  • Energy- and flux-budget theory for surface layers in atmospheric convective turbulence
  • 2022
  • Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 34:11
  • Tidskriftsartikel (refereegranskat)abstract
    • The energy- and flux-budget (EFB) theory developed previously for atmospheric stably stratified turbulence is extended to the surface layer in atmospheric convective turbulence. This theory is based on budget equations for turbulent energies and fluxes in the Boussinesq approximation. In the lower part of the surface layer in the atmospheric convective boundary layer, the rate of turbulence production of the turbulent kinetic energy (TKE) caused by the surface shear is much larger than that caused by the buoyancy, which results in three-dimensional turbulence of very complex nature. In the upper part of the surface layer, the rate of turbulence production of TKE due to the shear is much smaller than that caused by the buoyancy, which causes unusual strongly anisotropic buoyancy-driven turbulence. Considering the applications of the obtained results to the atmospheric convective boundary-layer turbulence, the theoretical relationships potentially useful in modeling applications have been derived. The developed EFB theory allows us to obtain a smooth transition between a stably stratified turbulence to a convective turbulence. The EFB theory for the surface layer in a convective turbulence provides an analytical expression for the entire surface layer including the transition range between the lower and upper parts of the surface layer, and it allows us to determine the vertical profiles for all turbulent characteristics, including TKE, the intensity of turbulent potential temperature fluctuations, the vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature), the integral turbulence scale, the turbulence anisotropy, the turbulent Prandtl number, and the flux Richardson number.
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48.
  • Rogachevskii, Igor, et al. (författare)
  • Generation of a large-scale vorticity in a fast-rotating density-stratified turbulence or turbulent convection
  • 2019
  • Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 100:6
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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49.
  • Rogachevskii, Igor, et al. (författare)
  • Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory
  • 2017
  • Ingår i: Astrophysical Journal. - : Institute of Physics (IOP). - 0004-637X .- 1538-4357. ; 846:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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50.
  • Rogachevskii, Igor, et al. (författare)
  • Mean-field theory of differential rotation in density stratified turbulent convection
  • 2018
  • Ingår i: Journal of Plasma Physics. - : CAMBRIDGE UNIV PRESS. - 0022-3778 .- 1469-7807. ; 84:2
  • Tidskriftsartikel (refereegranskat)abstract
    • 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.
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