The kinematic dynamo action of spiralling convective flows, Geophys

We consider the kinematic production of magnetic ¢elds in a sphere by velocity ¢elds dominated by di¡erential rotation and spiralling convective cells. The high magnetic Reynolds number limit of Braginsky (1964) is considered and formulae are derived allowing an a-e¡ect parametrization of such £ows to be easily calculated. This permits an axisymmetric system to be investigated in parallel with the direct 3-D numerical computations. Good agreement between the asymptotic and 3-D calculations is found. The `spiralling ' property typical of convective motion in rotating spheres is important in terms of dynamo action; the di¡erential rotation coexisting with this feature is also vital. Indeed, it is the presence of both features which allows the analysis of Braginsky to be employed. With £ows approximating the columnar form anticipated for rapidly rotating convection, dynamo action is relatively easily achieved for all azimuthal wavenumbers; modes of di¡ering wavenumbers interact almost by a simple superposition. With £ows of more complex latitudinal form, the mutual interactions between modes become more complicated. For columnar-type £ows, dipole magnetic ¢elds are favoured when the sense of outward spiralling is prograde and the zonal £ow is eastwards, as is physically preferred. Key words: kinematic dynamos, convection, geomagnetism.