Other
Scientific paper
Jul 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001gapfd..94..263h&link_type=abstract
GApFD, 94, 263
Other
20
Geodynamo, Reversals, Secular Variation, Dynamo Theory, Helicity Fluctuations, Stochastic Processes, Bistable Oscillator
Scientific paper
Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating alpha reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ~(1-a^2)^2, subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2-3)x10^5years, is shown to imply a secular variation of the dipole moment of ~15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.
Hoyng Peter
Ossendrijver A. J. H. M.
Schmitt Denis
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