Abstract
Bachtiar, Ivers and James (2006, BIJ), showed that the proof of the long standing planar velocity antidynamo theorem fails when the volume of the conducting fluid is a finite sphere. BIJ also found a planar velocity that appeared to support growth of the magnetic field B, but an unequivocal conclusion was prevented by inadequate convergence of the growth rate λ near the critical magnetic Reynolds number. This follow-up article revisits the BIJ model, with a revised numerical code, attaining much higher truncation levels [J, N]. Given the convergence difficulties, we are led to compare various tests of convergence based on normalized differences of λ, its poloidal-toroidal eigenvector (S, T), the vector B and surface and volume root mean square (SRMS, VRMS) averages of B. We have ranked these tests with respect to sensitivity to changes in [J, N], by applying them to various established kinematic dynamos. Contrary to expectations, we find that λ is more sensitive than S, T, and often even more sensitive than B. The SRMS test is more convenient and usually more sensitive than the S, T test, but is not as sensitive as λ or B. The VRMS test is least sensitive. All these tests imply conclusively that the BIJ planar flow does support growing magnetic fields. However, because of its sensitivity, high accuracy for λ has still not been achieved, and probably requires an alternative approach to the BIJ spectral representations.
Published Version
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