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.