Dynamo in a spherical shell, controlled by Poincare operator eigenmodes

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   In the study of the mechanisms of planetary dynamo, various options for
   the problem of conducting fluid convection in a rotating spherical shell
   appear. Application of spectral methods for the solution of these problems
   raises the question on the choice of the basis to present the fields of
   velocity, temperature and magnetic field. The paper suggests to apply
   Poincare operator eigenmode approximations as the basis for velocity. The
   geometrical structure of these modes corresponds to free oscillations of
   ideal rotating fluid and seems to be the most natural from all the
   considered problems.

   In this work the large-scale approximations of Poincare modes and low-mode
   models of convection in conducting rotating shells are proposed. The
   models present velocity as an approximation of one of Poincare modes by
   spherical harmonics, the temperature field and magnetic field are
   specified by spherical harmonics structurally consistent with the
   velocity. It is shown that dipole magnetic field is generated in this type
   of modes.

   It is shown, that inhomogeneities in the Earth's liquid core density may
   geometrically correspond to one of Poincare modes, according to the
   splitting-functions of its free oscillations.