Динамо в сферической оболочке, управляемое собственными модами оператора Пуанкаре

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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 Poincar ́e 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 Poincar ́e modes and low-mode models of convection in conducting rotating shells are proposed. The models present velocity as an approximation of one of Poincar ́e 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 Poincar ́e modes, according to the splitting-functions of its free oscillations.

Водинчар Г.М., Фещенко Л.К. – Динамо в сферической оболочке, управляемое собственными модами оператора Пуанкаре. // СОЛНЕЧНО-ЗЕМНЫЕ СВЯЗИ И ФИЗИКА ПРЕДВЕСТНИКОВ ЗЕМЛЕТРЯСЕНИЙ Сборник докладов VI международной конференции. Ответственный редактор Б.М. Шевцов. - 2013. - С. 255-259.