THE WEAK TAYLOR STATE IN AN ALPHA-OMEGA-DYNAMO

A spherical alpha omega-dynamo is studied for small values of the visc ous coupling parameter epsilon similar to nu(1/2), paying attention pa rticularly to large dynamo numbers. The present study is a follow-up o f the work by Hollerbach er al. (1992) with their choice of alpha-effe ct and Archimedean wind including also the constraint of magnetic fiel d symmetry (or antisymmetry) due to equatorial plane. The magnetic fie ld scaled by epsilon(1/2) is independent of epsilon in the solutions f or dynamo numbers smaller than a certain value of D-b (the Ekman state ) which are represented by dynamo waves running from pole to equator o r vice-versa. However, for dynamo numbers larger than D-b the solution bifurcates and subsequently becomes dependent on epsilon. The bifurca tion is a consequence of a crucial role of the meridional convection i n the mechanism of magnetic field generation. Calculations suggest tha t the bifurcation appears near dynamo number about 33500 and the solut ions for larger dynamo numbers and epsilon = 0 become unstable and fai l, while the solutions for small but non-zero epsilon are characterize d by cylindrical layers of local maximum of magnetic field and sharp c hanges 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 spec ial structure of magnetic field. We rather obtained the solution in th e form of a ''weak'' Taylor state, where the Taylor constraint is sati sfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude an d structure are roughly fifty-fifty in our ''weak'' Taylor state solut ion and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynam o context.