[2] The original motivation of this study was suggested by the problems of solar physics. Although the results obtained at this stage cannot be interpreted to represent the specifically solar dynamo process, we should give a brief exposition of the previous investigation that led us to the formulation of the problem considered here.
[3] Observations of the solar magnetic fields reveal a bewildering variety of structures and activities. It is remarkable that solar processes vary in scale from sizes comparable to the solar radius to the limit of present resolution and in duration from tens of years to minutes [see, e.g., Schrijver and Zwaan, 2000].
[4] Mean-field electrodynamics [Krause and Rädler, 1980; Moffatt, 1978] has clarified many issues concerning the generation of the global magnetic fields of cosmic bodies. However, such problems as the formation of local magnetic fields and their relationship to the global fields fall completely beyond the scope of mean-field theories. Meanwhile, the phenomenon of solar and stellar magnetism could be adequately understood only if the dynamics of the interplay between structures in the velocity field and magnetic field is comprehensively studied over a wide range of spatial scales. Dynamo models that are aimed at a unified description of the global and local processes and that deal with local, instantaneous quantities rather than averaged ones can naturally be referred to as "deterministic" models. They describe the structural elements present in the flow and in the magnetic field instead of considering the averaged parameters of the turbulent flow (in particular, the statistical predominance of one sign of the velocity field helicity or another).
[5] The idea that convection cells in the solar subphotospheric zone could be a connecting link between global and local magnetic fields traces back to the mid-1960s. Tverskoy [1966] represented the convection cell by a toroidal eddy and demonstrated, in the framework of a kinematic approach, that such a model convection cell can amplify the magnetic field and produce characteristic bipolar magnetic configurations. This approach was also used by Getling and Tverskoy [1971a, 1971b] to construct a kinematic model of the global dynamo in which toroidal eddies distributed over a spherical shell, acting jointly with the differential rotation of the shell, maintain a sign-alternating global magnetic field. If a poloidal magnetic field is present, the differential rotation produces a toroidal component of the global magnetic field.
[6] If the local magnetic configuration produced by an eddy interacting with the large-scale toroidal field is rotated through some angle about the axis of the eddy, this configuration contributes to the regeneration of the poloidal component of the global magnetic field.
[7] Thus a cell locally interacting with the magnetic field serves in this model as a building block of the global dynamo, and the latter can in this case be called the "cellular" dynamo. The rotation of the local magnetic field pattern can be expected if the system rotates as a whole and the flow is affected by the Coriolis force.
[8] In recent years, after the advent of suitable computing facilities, some steps have been made to verify these ideas by means of numerical simulation. Getling [2001] and Getling and Ovchinnikov [2002] obtained numerical solutions to the three-dimensional nonlinear problem of magnetoconvection in a plane horizontal layer of incompressible fluid, heated from below, and found that hexagonal convection cells interacting with a weak initial ("seed"), horizontal magnetic field can produce various structures of the strongly amplified magnetic field, with a predominant bipolar component. Dobler and Getling [2004] extended this numerical analysis to compressible fluids and obtained similar results.
[9] Modern computing resources make it possible to approach the development of numerical cellular-dynamo models that could provide a parallel description of both the global and local magnetic fields. However, even today, numerical schemes can hardly be used to simulate flows and magnetic fields over scale ranges covering two or more orders of magnitude. Only the largest convection cells, of sizes comparable to the depth of the convection zone (such as solar "giant" cells, for which little observational evidence exists), can be simulated in the framework of global models. If we assume that the principal features of the process should be similar for convection on different scales, such global models would help us to verify our qualitative notion and provide guidelines for the elaboration of a more detailed description.
[10] Here, we use numerical simulations to investigate the properties of cellular dynamos in rotating spherical shells, which could operate in stars under certain conditions. Although there are reasons to believe that the solar dynamo is also of a cellular type, we do not directly associate the presently obtained results with solar processes, since the computed patterns of magnetic-filed evolution bear only limited similarity to the pattern observed on the Sun. We merely note some remarkable features of the cellular dynamos, which may be of interest from the standpoint of stellar magnetohydrodynamics.
Powered by TeXWeb (Win32, v.2.0).