New Solutions of the Kinematic Dynamo Problem

Source abstract

The steady-state kinematic dynamo problem in a homogeneous 3-dimensional core is studied. The existence of a class of smooth solenoidal dynamos, satisfying a no-slip condition on the core boundary, is proved using perturbation theory. The dynamos are of the form q = q(1) + q(2) + q(3), where q(1) is spatially periodic on a sufficiently small scale of length, q(2) is zero except near the core boundary, and q(3) is an arbitrary sufficiently small motion. The term q(1) is also a spatially periodic dynamo in an appropriate sense for an infinite core. The last property allows a simple characterization of the bounded dynamos in terms of the admissible q(1).