Saturation and time dependence of geodynamo models

Abstract

In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo & Tobias (2009) and is closely related to the test field method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen & Aubert (2006). Dipolar dynamos with low Rossby number are kinematically stable whereas the tracer field grows exponentially in the multipolar dynamo regime. This difference in the saturation process for dynamos in both regimes comes along with differences in their time variability. Within our sample of 20 models, solely kinematically unstable dynamos show dipole reversals and large excursions. The complicated time behaviour of these dynamos presumably relates to the alternating growth of several competing dynamo modes. On the other hand, dynamos in the low Rossby number regime exhibit a rather simple time dependence and their saturation merely results in a fluctuation of the fundamental dynamo mode about its critical state.Comment: 6 pages, 8 figure

Geostrophic balance and reversals of the geomagnetic field

“…This regime is characterized by the frequent excursions of the field, when dipole intensity drops in three-five times and then recovers with the same sign. This regime satisfies to the criteria for the critical Rossby number Ro ∼ 0.12 introduced in [Christensen and Aubert, 2006], [Schrinner et al, 2010]. Accordingly to this estimate regimes with Ro < Ro correspond to the geostrophic states with the non-reversing magnetic dipole located in the Taylor cylinder.…”

Global dynamo models from direct numerical simulations and their mean-field counterparts

“…In addition, the growth rate of the leading eigenmode of D, λ = (σ), may be taken as a measure for the accuracy of the mean-field description. Ideally, it is 0, whereas all overtones are highly diffusive (Schrinner et al 2010a(Schrinner et al , 2011b. For numerical simulations, however, it is impossible to hit the critical point exactly.…”

“…The local Rossby number is always lower than 0.12 for the models considered here. They therefore belong to the regime of kinematically stable dynamos (Schrinner et al 2010a). To simplify the time averaging, models with low and fairly moderate Rm were chosen.…”

“…However, the class of chaotically time-dependent dynamos we considered is kinematically stable. Schrinner et al (2010a) identified a regime of rapidly rotating dynamos that are dominated by only one dipolar mode at marginal stability, whereas all overtones are highly diffusive. A saturated velocity field from this class of dynamos does not lead to exponential growth of the magnetic field in a corresponding kinematic calculation.…”

An efficient method for computing the eigenfunctions of the dynamo equation

“…The variability in time of the magnetic field of the direct numerical simulation is reflected in the variability of the expansion coefficients. More details are presented in Schrinner et al (2010).…”