Kinematic Dynamo Theory

Kinematic dynamo theory is concerned with solutions of the induction equation (7.8), which we rewrite here in the form 8.1a$$ \frac{{\partial B}} {{\partial t}} - \eta \nabla ^2 B = B \cdot \nabla u - u \cdot \nabla B, $$ for a given velocity field u(r,t). In its broadest sense, the theory seeks to discover, among some classes of admissible u, those functions which lead to “dynamo action”, as discussed in Section 7.3. The precise meaning of dynamo action will generally depend upon the nature of the admissible functions u.