Solution of one class of magnetohydrodynamic equations with magnetic field amplification

Solution of magnetohydrodynamic equations applied to solar magnetic fiel

Doubts about the crucial role of the rising-tube mechanism in the formation of sunspot groups

Some preliminary processing results are presented for a dataset obtained with the Solar Optical Telescope on the Hinode satellite. The idea of the project is to record, nearly simultaneously, the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a photospheric level. Our ultimate aim is to elaborate observational criteria to distinguish between the manifestations of two mechanisms of sunspot-group formation --- the rising of an Omega-shaped flux tube of a strong magnetic field and the in situ amplification and structuring of magnetic field by convection (the convective mechanism is briefly described). Observations of a young bipolar subregion developing within AR 11313 were carried out on 9--10 October 2011. Based on the series of filtergrams, the trajectories of corks are computed, using a technique similar to but more reliable than local correlation tracking (LCT), and compared with the magnetic maps. At this stage of the investigation, only the vertical magnetic field and the horizontal flows are used for a qualitative analysis. According to our preliminary findings, the velocity pattern in the growing active region has nothing to do with a spreading flow on the scale of the entire bipolar region, which could be expected if a tube of strong magnetic field emerged. No violent spreading flows on the scale of the entire growing magnetic region can be identified. Instead, normal mesogranular and supergranular flows are preserved. The observed scenario of evolution seems to agree with Bumba's inference that the development of an active region does not entail the destruction of the existing convective-velocity field. The convective mechanism appears to be better compatible with observations than the rising-tube mechanism.Comment: 13 pages, 5 figure

Do quasi-regular structures really exist in the solar photosphere? I. Observational evidence

Two series of solar-granulation images -- the La Palma series of 5 June 1993 and the SOHO MDI series of 17--18 January 1997 -- are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt (2002)), which no longer appear unusual in images averaged over 1--2-h time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips (``ridges'' and ``trenches'' in the brightness distributions). In some cases, rings are combined with radial ``spokes'' and can thus form ``web'' patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules -- overheated blobs -- may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (2002) on the original paper by Getling and Brandt (2002) can be dismissed.Comment: 21 page, 8 figures; accepted by "Solar Physics

Space-Time Distribution of G-Band and Ca II H-Line Intensity Oscillations in Hinode/SOT-FG Observations

We study the space-time distributions of intensity fluctuations in 2 - 3 hour sequences of multi-spectral, high-resolution, high-cadence broad-band filtergram images (BFI) made by the SOT-FG system aboard the Hinode spacecraft. In the frequency range 5.5 < f < 8.0 mHz both G-band and Ca II H-line oscillations are suppressed in the presence of magnetic fields, but the suppression disappears for f > 10 mHz. By looking at G-band frequencies above 10 mHz we find that the oscillatory power, both at these frequencies and at lower frequencies too, lies in a mesh pattern with cell scale 2 - 3 Mm, clearly larger than normal granulation, and with correlation times on the order of hours. The mesh pattern lies in the dark lanes between stable cells found in time-integrated G-band intensity images. It also underlies part of the bright pattern in time-integrated H-line emission. This discovery may reflect dynamical constraints on the sizes of rising granular convection cells together with the turbulence created in strong intercellular downflows.Comment: 24 pages, 15 figure

Instability of small-amplitude convective flows in a rotating layer with stress-free boundaries

We consider stability of steady convective flows in a horizontal layer with stress-free boundaries, heated below and rotating about the vertical axis, in the Boussinesq approximation (the Rayleigh-Benard convection). The flows under consideration are convective rolls or square cells, the latter being asymptotically equal to the sum of two orthogonal rolls of the same wave number k. We assume, that the Rayleigh number R is close to the critical one, R_c(k), for the onset of convective flows of this wave number: R=R_c(k)+epsilon^2; the amplitude of the flows is of the order of epsilon. We show that the flows are always unstable to perturbations, which are a sum of a large-scale mode not involving small scales, and two large-scale modes, modulated by the original rolls rotated by equal small angles in the opposite directions. The maximal growth rate of the instability is of the order of max(epsilon^{8/5},(k-k_c)^2), where k_c is the critical wave number for the onset of convection.Comment: Latex, 12 pp., 15 refs. An improved version of the manuscript submitted to "Mechanics of fluid and gas", 2006 (in Russian; English translation "Fluid Dynamics"