A Three-dimensional Spherical Nonlinear Interface Dynamo

A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo is investigated using a finite-element method based on the three-dimensional tetrahedralization of the spherical system. The spherical interface dynamo model consists of four zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a uniformly rotating turbulent convection envelope, and a nearly insulating exterior. The four regions are coupled magnetically through matching conditions at the interfaces. Without the effect of a tachocline, the conventional nonlinear 2 dynamo is always stationary, axisymmetric, and equatorially antisymmetric even though numerical simulations are always fully threedimensional and time dependent. When there is no tachocline, the azimuthal field is confined to the convection zone while the poloidal magnetic field penetrates into the radiative core. The effects of an interface dynamo with a tachocline having a purely axisymmetric toroidal velocity field are as follows: (1) the action of the steady tachocline always gives rise to an oscillatory dynamo with a period of about 2 magnetic diffusion units, or about 20 yr if the magnetic diffusivity in the convection zone is 108 m2 s 1; (2) the interface dynamo solution is always axisymmetric, selects dipolar symmetry, and propagates equatorward (for the assumed form of ) although the simulation is fully three-dimensional; (3) the generated magnetic field mainly concentrates in the vicinity of the interface between the tachocline and the convection zone; and (4) the strength of the toroidal magnetic field is dramatically amplified by the effect of the tachocline. Extensions of Cowling’s theorem and the toroidal flow theorem to multilayer spherical shell regions with radially discontinuous magnetic diffusivities are presented. Subject heading: Sun: magnetic fields