PERIODIC, CHAOTIC AND STEADY SOLUTIONS IN ALPHA-OMEGA-DYNAMOS

Nonlinear alphaomega dynamo models in a duct geometry are considered. The rapid rotation approximation, in which inertial terms are neglected and viscosity is only significant in boundary layers, is used. The nonlinearities that arise in the model are the magnetically driven geostrophic flow and meridional circulation. The numerical method used is a two-dimensional, time-stepping spectral code. Just after the critical dynamo number is exceeded, the field is weak, limited by the weak core-mantle coupling. The circumstances under which strong magnetic fields satisfying Taylor's constraint can arise is investigated: these strong fields are of the same order of magnitude as those believed, to occur in the Earth's core. The question of whether steady alphaomega dynamos of this type can be constructed is also addressed. Two models are examined in detail, with differing alpha distributions. In the first model, oscillatory dynamos were found, with intervals of quasiperiodicity and chaos. The weak field regime is terminated by a subcritical Hopf bifurcation into chaotic solutions, as found in some spherical models. This model has no clear-cut Taylor state, and reverses much more frequently than the geodynamo. The second model investigated has an alpha-distribution which changes sign radially as well as about the equator. This model has the feature that steady modes onset just prior to oscillatory modes. Taylor states are found, and this model has non-reversing regimes, as well as reversing ones. The dynamical behaviour of this second model fits in better with the observed behaviour of the geodynamo.