THE WEAK TAYLOR STATE IN AN ALPHA-OMEGA-DYNAMO

A spherical alpha omega-dynamo is studied for small values of the viscous coupling parameter epsilon similar to nu(1/2), paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach er al. (1992) with their choice of alpha-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by epsilon(1/2) is independent of epsilon in the solutions for dynamo numbers smaller than a certain value of D-b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D-b the solution bifurcates and subsequently becomes dependent on epsilon. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and epsilon = 0 become unstable and fail, while the solutions for small but non-zero epsilon are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a ''weak'' Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our ''weak'' Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.