@ARTICLE{10.3389/feart.2016.00038,
AUTHOR={Meduri, Domenico G. and Wicht, Johannes},
TITLE={A Simple Stochastic Model for Dipole Moment Fluctuations in Numerical Dynamo Simulations},
JOURNAL={Frontiers in Earth Science},
VOLUME={4},
PAGES={38},
YEAR={2016},
URL={https://www.frontiersin.org/article/10.3389/feart.2016.00038},
DOI={10.3389/feart.2016.00038},
ISSN={2296-6463},
ABSTRACT={Earth's axial dipole field changes in a complex fashion on many different
time scales ranging from less than a year to tens of million years.
Documenting, analysing, and replicating this intricate signal
is a challenge for data acquisition, theoretical interpretation,
and dynamo modelling alike. Here we explore whether axial dipole variations
can be described by the superposition of a slow deterministic drift
and fast stochastic fluctuations, i.e. by a Langevin-type system.
The drift term describes the time averaged behaviour of the axial dipole variations,
whereas the stochastic part mimics complex flow interactions over convective time scales.
The statistical behaviour of the system is described by a Fokker-Planck equation which
allows useful predictions, including the average rates of dipole reversals and excursions.
We analyse several numerical dynamo simulations, most of which have
been integrated particularly long in time, and also the palaeomagnetic
model PADM2M which covers the past 2 Myr.
The results show that the Langevin description provides a viable statistical model
of the axial dipole variations on time scales longer than about 1 kyr.
For example, the axial dipole probability distribution and the average reversal
rate are successfully predicted.
The exception is PADM2M where the stochastic model reversal rate seems too low.
The dependence of the drift on the axial dipole
moment reveals the nonlinear interactions that establish the
dynamo balance. A separate analysis of inductive and diffusive magnetic effects
in three dynamo simulations suggests that the classical quadratic
quenching of induction predicted by mean-field theory seems at work.}
}