Natural SciencesEarth SciencesPhysicsAtmospheric DynamicsGeomagnetismPlasma PhysicsMagnetohydrodynamicsPlanetary Magnetic FieldsPlanetary MagnetospheresSolar DynamoAlpha EffectEigenvaluesKinematic Dynamo ModelsMid-latitude CyclonesMidlatitude CyclonesPlanetary Dynamo TheorySolar Dynamo ProcessesSolar Dynamo Theory
Eigenvalues of the kinematic dynamo problem are obtained from a variational principle; the modes of free decay in an electrically conducting sphere are used as trial functions. This method is equivalent to an expansion method proposed earlier by Elsasser (l946a). An application to alpha omega - dynamos shows that a small number of trial functions often leads to quite accurate eigenvalues. The method is applied to Levy's (l972) dynamo model for the Earth. When the dynamo number is positive, this model favors indeed the steady dipolar field, as compared to oscillatory or quadrupolar fields. In the case of negative dynamo number the preferred field depends on the position of the cyclones (or alpha -effect''): High- and mid-latitude cyclones maintain predominartly oscillatory dipole fields, low-latitude cyclones favor steady quadrupole fields. For mid-latitude cyclones the field tends to oscillate when the inductive effects are confined to the outer third of the sphere (as it is the case in the Sun). (auth)