Kinematic dynamo action in a sphere with weak differential rotation

Details Kinematic dynamo action in a sphere with weak differential rotation Kinematic dynamo action in a sphere with weak differential rotation

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009geoji.177...71g&link_type=abstract

Geophysical Journal International, Volume 177, Issue 8, pp. 71-80.

Astronomy and Astrophysics

Astronomy

1

Dynamo: Theories And Simulations, Geomagnetic Excursions, Reversals: Process, Time Scale, Magnetostratigraphy

Scientific paper

The geodynamo is controlled by two fundamental symmetries: reflection through the equator and change of sign of magnetic field. It may also be influenced by lower mantle anomalies, which have a dominant cos2φ longitude dependence; if so this would impart a further symmetry restriction of 180° rotation about the polar axis. Understanding these symmetry relations may help interpret magnetic observations and guide non-linear dynamic studies. This paper explores the kinematic dynamo action of a two-parameter class of steady flows with the four relevant spatial symmetries: axial and equatorial dipole and quadrupole, denoted Da, De, Qa, Qe, respectively. Previous work focussed on steady solutions and dynamo waves linked to the mean-field theory of Braginsky; here, we present some new steady solutions with Qe symmetry and new oscillatory solutions of all symmetries. All have only modest differential rotation and are unrelated to Braginsky theory. The results strengthen several previous findings: the vast majority of Da and Qa solutions are steady, in stark contrast to the findings of mean-field theory; differential rotation favours axial symmetry; symmetry is determined largely by the locations of flux concentration; and oscillatory solutions occur when radial and azimuthal components of field overlap. Some oscillatory solutions reverse by migration of flux in latitude, in similar fashion to those related to dynamo waves in mean-field theory, but others reverse by migration in longitude and yet more seem to reverse in place. The new dynamos raise the percentage of flows that generate magnetic field of any symmetry to 47 per cent. Many flows generate more than one symmetry and some generate all four symmetries; some flows generate two or three different symmetries at the same magnetic Reynolds number. About half the physically realizable symmetries (lowest critical magnetic Reynolds number) are Da, the remaining half being mainly Qa and De in equal proportion. Only 11 per cent of the dynamos are oscillatory, the rest are steady. This suggests steady flows favour steady magnetic fields, although for the Qe symmetry we find slightly more oscillatory solutions.

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