Dynamo theory for the interface between the convection zone and the radiative interior of a star

This thesis examines the possibility that the solar dynamo operates in a thin overshoot region between the convection zone and the radiative interior. Model equations are derived in Cartesian geometry that contain the essential physics for the dynamo, presenting both analytic and numerical solutions. In the model momentum, magnetic induction, and continuity equations are solved for axisymmetric large scale magnetic and velocity fields in the presence of cyclonic turbulence. A family of exact, force-free solutions to the nonlinear equations were found when there is no imposed velocity shear. When the induced velocity fields are large, the exact solutions are unstable. The induced velocities control the location of the peak in the magnetic energy spectrum and the slope of the spectrum at high wave numbers. The amplitude of the induced velocity field varies greatly with variations in the free parameters: the magnetic diffusivity, the viscous diffusivity, and the total magnetic energy. In all cases, solutions with no imposed velocity shear show no oscillatory or dynamo wave character