Dynamo theory for the interface between the convection zone and the radiative interior of a star: Part ii. numerical solutions of the nonlinear equations

We discuss numerical solutions of nonlinear equations that model magnetic field generation in a thin layer beneath the convection zone of a late type star. The model equations were derived previously in Paper I (DeLuca and Gilman, 1986b). Three main results are found: first, the oscillating, dynamo wave solutions discussed in DeLuca and Gilman (1986a) are shown to be a result of the severe truncation used in those calculations; second, the induced velocity feld is shown to have an important role in determining the spatial structure of the magnetic field solutions; time dependent solutions have been found. These are not wavelike solutions, rather the amplitude of different horizontal wave modes vary in time. Further, we show that the exact solutions found in Paper I are generally unstable, with the exception of those that are independent of ŷ (latitude in our Cartesian geometry), which are stable if the transient induced velocity field remains small. We conclude that the induced velocity fields are an important ingredient in any model of dynamo action below the solar convection zone.