61 research outputs found
Solution of one class of magnetohydrodynamic equations with magnetic field amplification
Solution of magnetohydrodynamic equations applied to solar magnetic fiel
Limitations of the background field method applied to Rayleigh-Bénard convection
We consider Rayleigh-Bénard convection as modeled by the Boussinesq equations, in case of infinite Prandtl number and with no-slip boundary condition. There is a broad interest in bounds of the upwards heat flux, as given by the Nusselt number , in terms of the forcing via the imposed temperature difference, as given by the Rayleigh number in the turbulent regime . In several works, the background field method applied to the temperature field has been used to provide upper bounds on in terms of . In these applications, the background field method comes in form of a variational problem where one optimizes a stratified temperature profile subject to a certain stability condition; the method is believed to capture marginal stability of the boundary layer. The best available upper bound via this method is . it proceeds via the construction of a stable temperature background
profile that increases logarithmically in the bulk. In this paper, we show that the background temperature field method cannot provide a tighter upper bound in terms of the power of the logarithm. However, by another method one does obtain the tighter upper bound , so that the result of this paper implies that the background temperature field method is unphysical in the sense that it cannot provide the optimal bound
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
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