Dynamo action between two rotating discs

Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In absence of a magnetic field, various well-known self-similar flows arise, generalising that von Kármán. Magnetic field instabilities with same similarity structure are sought. kinematic eigenvalue problem found to have growing modes for Rem>Rc≃100. growth rate real and ferromagnetic cases, but complex insulating boundaries. As Rem→∞ it shown dynamo can fast slow, depending on flow structure. slow case, governed by boundary layer one saturates solution nonlinear problem. bifurcation subcritical dynamos Rem≳0.7Rc. Finally, flux energy large r examined, determine which solutions might generalise finite It tend inward flux, so unlikely realised practice. Slow outward found. suggested average rotation should non-zero