Properties of a nonlinear solar dynamo model
Abstract
A simple nonlinear model is developed for the solar dynamo, in which the real convective spherical shell is approximated by a thin flat slab, and only the back-reaction of the field B on the helicity is taken into account by choosing the simple law = (1-B2), where and are constants, to represent the decrease in generation coefficient with increasing field strength. Analytic expressions are obtained for the amplitude of the field oscillation and its period, T, as functions of the deviation d - dCT of a dynamo number d from its critical value dcr for regeneration. A symmetry is found for the case of oscillations of small constant amplitude: B(t+½T)= -B(t). A Landau equation is obtained that describes the transition to such oscillations.
- Publication:
-
Geophysical and Astrophysical Fluid Dynamics
- Pub Date:
- 1981
- DOI:
- 10.1080/03091928108243686
- Bibcode:
- 1981GApFD..17..281K
- Keywords:
-
- Dynamo Theory;
- Solar Cycles;
- Solar Magnetic Field;
- Solar Oscillations;
- Sunspots;
- Flat Plates;
- Landau-Ginzburg Equations;
- Mathematical Models;
- Nonlinear Equations;
- Slabs;
- Stochastic Processes;
- Time Dependence