Magnetic field reversals and secular variation in a bistable geodynamo model

Abstract

A method is described which enables the calculation of statistical properties of geodynamo models. The result is a Fokker–Planck equation for the probability distribution of the dipole moment. The method only requires a non-oscillatory, predominantly dipolar magnetic field and helicity fluctuations. 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 in a bistable potential with minima representing normal and reversed polarity, and occasional jumps between them. The shape of the potential is determined by supercritical dynamo excitation and nonlinear limitation of field growth. Application of the method to a mean-field dynamo model with random fluctuations of the helicity parameter α reproduces 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.