TY - JOUR

T1 - Dynamo convergence tests, and application to a planar velocity dynamo

AU - Bachtiar, A. A.

AU - Jamesz, R. W.

N1 - Funding Information:
A.A. Bachtiar wishes to acknowledge the financial support from an Australian Development Scholarship at the University of Sydney, while on leave from the University of Indonesia.

PY - 2010/10

Y1 - 2010/10

N2 - 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 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, 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 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 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 has still not been achieved, and probably requires an alternative approach to the BIJ spectral representations.

AB - 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 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, 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 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 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 has still not been achieved, and probably requires an alternative approach to the BIJ spectral representations.

KW - Eigenproblem convergence

KW - Magnetic dynamo

KW - Planar velocity

UR - http://www.scopus.com/inward/record.url?scp=78449255266&partnerID=8YFLogxK

U2 - 10.1080/03091929.2010.510797

DO - 10.1080/03091929.2010.510797

M3 - Article

AN - SCOPUS:78449255266

VL - 104

SP - 531

EP - 543

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 5

ER -