Subharmonic Dynamo Action in the Roberts Flow
Abstract
The paper deals with the dynamo action of the Roberts flow, that is, a flow depending periodically on two cartesian coordinates, X and Y, but being independent of the third one, Z. In particular the case is considered in which the magnetic fields, which are periodic in X, Y and Z, have period lengths in the XYplane being integer multiples of that of the flow. Two approaches are used. Firstly, the equations governing the magnetic field are reduced to a matrix eigenvalue problem, which is solved numerically. Secondly, a mean magnetic field is defined by averaging over proper areas in the XYplane, corresponding equations are derived, in which the induction effect of the flow occurs as an anisotropic feffect, and analytic solutions are given. The results are of particular interest for the Karlsruhe dynamo experiment, which works with a Roberts type flow consisting of 52 cells inside a cylindrical volume. In order to check the reliability of predictions concerning selfexcitation based on the meanfield approach, analogous predictions are derived for a rectangular box containing 50 cells, and are compared with results obtained with the help of direct solutions of the eigenvalue problem mentioned. It turns out that the simple meanfield approach in general underestimates the requirements for selfexcitation. The corresponding results agree with those obtained in the subharmonic approach only if the side length L of the box, its height H and the edge length l of a spin generator satisfy L ≫ H ≫ l . In Appendix B, some comments on previous results concerning cal {ABC} dynamos are made in the light of the subharmonic formalism used in the paper.
 Publication:

Geophysical and Astrophysical Fluid Dynamics
 Pub Date:
 February 2002
 DOI:
 10.1080/03091920290004506
 Bibcode:
 2002GApFD..96..115P