Symmetry-breaking convective dynamos in spherical shells

The convective dynamo is the generation of a magnetic field by the convecti ve motion of an electrically conducting fluid. We assume a spherical domain and spherically invariant basic equations and boundary conditions. The ini tial state of rest is then spherically symmetric. A first instability leads to purely convective flows, the pattern of which is selected according to the known classification of O(3)-symmetry-breaking bifurcation theory. A se cond instability can then lead to the dynamo effect. Computing this instabi lity is now a purely numerical problem, because the convective how is known only by its numerical approximation. However, since the convective how can still possess a nontrivial symmetry group G(0), this is again a symmetry-b reaking bifurcation problem. After having determined numerically the critic al linear magnetic modes, we determine the action of G(0) in the space of t hese critical modes. Applying methods of equivariant bifurcation theory, we can classify the pattern selection rules in the dynamo bifurcation. We con sider various aspect ratios of the spherical fluid domain, corresponding to different convective patterns, and we are able to describe the symmetry an d generic properties of the bifurcated magnetic fields.