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Spherical convective dynamos in the rapidly rotating asymptotic regime

Published online by Cambridge University Press:  20 January 2017

Julien Aubert ,
Thomas Gastine  and
Alexandre Fournier
Julien Aubert*
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, CNRS, 1 rue Jussieu, F-75005 Paris, France
Thomas Gastine
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, CNRS, 1 rue Jussieu, F-75005 Paris, France
Alexandre Fournier
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, CNRS, 1 rue Jussieu, F-75005 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$ . We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

JFM classification

MHD and Electrohydrodynamics: Dynamo theory Geophysical and Geological Flows: Geodynamo
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 558 - 593
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© 2017 Cambridge University Press 

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