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51.
John V. Shebalin 《地球物理与天体物理流体动力学》2013,107(4):411-466
Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B o?=?0 and weakly broken when B o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects. 相似文献
52.
We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based
on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of
one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The
constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse
magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one
at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test
cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.
235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set
of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse
scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field
solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss
the potential usefulness of our method and its limitations. 相似文献
53.
Xing Wei 《地球物理与天体物理流体动力学》2014,108(2):213-221
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear stability analysis, i.e. the length scale of the imposed field is much larger than the wavelength of perturbations. The dispersion relationship is derived and then simplified to give the criteria for the onset of the magnetic instability in three cases of imposed field, namely, the axial dependence, the radial dependence and the mixed case. The orientation of rotation, imposed field and imposed current is important for this instability. 相似文献
54.
The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the
effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the
effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003 相似文献
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We explore an accretion model for low luminosity AGN (LLAGN) that attributes the low radiative output to a low mass accretion
rate,
, rather than a low radiative efficiency. In this model, electrons are assumed to drain energy from the ions as a result of
collisionless plasma microinstabilities. Consequently, the accreting gas collapses to form a geometrically thin disk at small
radii and is able to cool before reaching the black hole. The accretion disk is not a standard disk, however, because the
radial disk structure is modified by a magnetic torque which drives a jet and which is primarily responsible for angular momentum
transport. We also include relativistic effects. We apply this model to the well known LLAGN M87 and calculate the combined
disk-jet steady-state broadband spectrum. A comparison between predicted and observed spectra indicates that M87 may be a
maximally spinning black hole accreting at a rate of ∼10−3
M
⊙ yr−1. This is about 6 orders of magnitude below the Eddington rate for the same radiative efficiency. Furthermore, the total jet
power inferred by our model is in remarkably good agreement with the value independently deduced from observations of the
M87 jet on kiloparsec scales.
* This paper has previously been published in Astrophysics and Space Science, vol. 310:3–4. 相似文献
58.
S. Servidio V. Carbone L. Primavera P. Veltri K. Stasiewicz 《Planetary and Space Science》2007,55(15):2239-2243
By direct numerical simulations we investigate the nonlinear dynamics of a compressible Hall Magnetohydrodynamic (MHD) plasma. At small scales, where the Hall effect dominates, we found an increase of the compressibility of the system and the breakdown of the strong link between velocity and magnetic fields, typical of usual MHD. Moreover, we find that small-scale fluctuations are characterized by an anti-correlation between density and magnetic field intensity. These features characterize the excitation of a quasi-perpendicular magnetosonic turbulence that can be interpreted as the small-scale signature of the break-down of the MHD nonlinear energy cascade due to Hall effect. Fluctuations with the same properties, based on measurements by Cluster spacecraft in space plasma turbulence during different magnetopause crossings, have been recently observed. 相似文献
59.
Linear and nonlinear dynamo action is investigated for square patterns in nonrotating and weakly rotating Boussinesq Rayleigh-Bénard convection in a plane horizontal layer. The square-pattern solutions may or may not be symmetric to up-down reflections. Vertically symmetric solutions correspond to checkerboard patterns. They do not possess a net kinetic helicity and are found to be incapable of kinematic dynamo action at least up to magnetic Reynolds numbers of , 12 000. There also exist vertically asymmetric squares, characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, among them such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures. Without rotation these dynamos are, however, always only kinematic, not nonlinear dynamos since the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where stationary asymmetric squares are also nonlinear dynamos. These nonlinear dynamos are characterized by a subtle balance between the Coriolis and Lorentz forces. In some parameter regions also nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls are found. 相似文献
60.
An experimental investigation was made of the upstream influence in front of two‐dimensional obstacles when they were towed in a linearly stratified fluid. The experiments were performed in a plexiglas channel 30.5 feet long, 2 feet high and 14 inches wide filled with a linearly stratified salt solution. Velocity measurements and flow visualization were obtained by neutrally buoyant liquid droplets and dye lines. Density measurements were made by a salinity probe. The existence of unattenuated upstream influence in front of an obstacle was quantitatively documented for the first time. It occurred in the form of multiple unattenuated horizontal jets when there was a separated open wake behind the obstacle. These jets were identified to be the super‐position of “columnar disturbance modes”. The total number of columnar modes was determined solely by the Froude number of the flow and was equal to the number of lee‐wave modes excited. The drag due to upstream columnar modes was estimated and found to be lower than the drag due to the lee wave modes: 相似文献