Spherical Oscillatory alpha2 Dynamo Induced by Magnetic Coupling between a Fluid Shell and an Inner Electrically Conducting Core: Relevance to the Solar Dynamo.

A two-layer spherical alpha2 dynamo model consisting of an inner electrically conducting core (magnetic diffusivity lambdai and radius ri) with alpha=0 surrounded by an electrically conducting spherical shell (magnetic diffusivity lambdao and radius ro) with a constant alpha is shown to exhibit oscillatory behavior for values of beta=lambdai&solm0;lambdao and ri&solm0;ro relevant to the solar dynamo. Time-dependent dynamo solutions require ri&solm0;ro>/=0.55 and beta</=O&parl0;1&parr0;. For the Sun, ri&solm0;ro is about 0.8 and beta approximately 10-3. The timescale of the oscillations matches the 22 yr period of the sunspot cycle for lambda0=O(102 km2 s-1). It is unnecessary to hypothesize an alpha-omega dynamo to obtain oscillatory dynamo solutions; an alpha2 dynamo suffices provided the spherical shell region of dynamo action lies above a large, less magnetically diffusive core, as is the case for the solar dynamo.