### The geodynamo as a bistable oscillator - magnetic field reversals,
secular variation and stochastic resonance

**
Dieter Schmitt, Max-Planck-Institut für Aeronomie, Katlenburg-Lindau
**

The geodynamo is modeled as a bistable oscillator by means of a
mean-field alpha-Omega dynamo. The model requires a non-oscillatory,
predominantly dipolar magnetic field and stochastic helicity
fluctuations (multiplicative noise). The fluctuations perturb the
fundamental dynamo mode and lead to the excitation of higher modes.
This results in stochastic oscillations of the dipole field amplitude
(secular variation) in a bistable potential with minima representing
normal and reversed polarity, and occasional jumps between them
(reversals). The shape of the potential is determined by supercritical
dynamo excitation and nonlinear limitation of field growth. The
observed relation between the secular variation and the reversal rate
of the geomagnetic field as well as the amplitude distribution of the
dipole field inferred from the Sint-800 record are reproduced.

A periodic signal with a period of 100 kyr in the distribution of
residence times between reversals of the geomagnetic field has
recently been suggested as signature of stochastic resonance. This
period has also been found in other geomagnetic quantities. By adding
a weak periodic component either to the dynamo effects (multiplicative
periodic term) or as a source term to the dynamo equation (additive
periodic term) we demonstrate the signatures of stochastic resonance
in the distribution of residence times. Depending on the
multiplicative (additive) character of the periodic term, we find
peaks at integer (half-integer) values of the applied period,
superposed the otherwise Poissonian distribution, demonstrating the
increased reversal rates at the resonance frequencies. Especially the
optimum resonance conditions for various mean times between reversals
and various periodicities are derived. The periodic terms need to be
about 0.1 in amplitude compared to the other terms in the dynamo
equation to show the observed signatures of the magnetic field of the
Earth. A sharp peak at the forcing frequency in the power spectrum of
the dipole amplitude is only found in the additive case. As such a
peak is absent in the Earth data, this rules for the multiplicative
case. It is yet unclear what may cause such an effect to the
geodynamo.