A Three‐dimensional Multilayered Spherical Dynamic Interface Dynamo Using the Malkus‐Proctor Formulation

Abstract

We investigate a fully three-dimensional and multilayered spherical dynamic interface dynamo using a finite-element method based on the three-dimensional tetrahedralization of the whole spherical system. The dynamic interface dynamo model consists of four magnetically coupled zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a turbulent convection envelope, and a nearly insulating exterior. In the thin tachocline at the base of the convection zone, a differential rotation, similar to that of the observed solar differential rotation, is imposed. In the convection zone, the Malkus-Proctor formulation with a prescribed α-effect is employed while the fully three-dimensional dynamic feedback of Lorentz forces is taken into account. Our numerical simulations of the dynamic interface dynamo are focused on the Taylor number -->Ta = 105 with a unity magnetic Prandtl number. It is shown that the dynamic interface dynamo, depending on the size of the magnetic Reynolds number -->Rem based on the differential rotation, can be either nonaxisymmetric or axisymmetric. When -->Rem is small or moderate, the dynamic dynamo is characterized by quasi-periodic and nonaxisymmetric azimuthally traveling waves. When -->Rem is sufficiently large, the dynamo is characterized by a strong toroidal magnetic field, axisymmetric or nearly axisymmetric, that selects dipolar symmetry and propagates equatorward. Implications of our dynamic interface dynamo for the solar dynamo are also discussed.