Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T10:47:38.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong-field spherical dynamos

Published online by Cambridge University Press:  22 January 2016

Emmanuel Dormy
Emmanuel Dormy*
Affiliation:
MAG (CNRS/IPGP/ENS), Ecole Normale Supérieure, 24 Rue Lhomond, 75005 Paris, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical models of the geodynamo are usually classified into two categories: dipolar modes, observed when the inertial term is small enough; and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution coexists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong-field branch, in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimising the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.

JFM classification

Geophysical and Geological Flows: Geodynamo Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 500 - 513
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aubert, J. 2005 Steady zonal flows in spherical shell dynamos. J. Fluid Mech. 542, 53–67.Google Scholar
Christensen, U. & Aubert, J. 2006 Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Intl 166, 1–97.CrossRefGoogle Scholar
Christensen, U., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G., Honkura, Y., Jones, C., Kono, M. et al. 2001 A numerical dynamo benchmark. Phys. Earth Planet. Inter. 128, 25–34.Google Scholar
Christensen, U., Olson, P. & Glatzmaier, G. 1999 Numerical modelling of the geodynamo: a systematic parameter study. Geophys. J. Intl 138, 393–409.Google Scholar
Dormy, E.1997 Modélisation numérique de la dynamo terrestre. PhD thesis, IPGP.Google Scholar
Dormy, E. & Soward, A. M.(Eds) 2007 Mathematical Aspects of Natural Dynamos. CRC.Google Scholar
Dormy, E. & Le Mouël, J.-L. 2008 Geomagnetism and the dynamo: where do we stand? C. R. Acad. Sci. Paris 9, 711–720.Google Scholar
Dormy, E. 2011 Stability and bifurcation of planetary dynamo models. J. Fluid Mech. 688, 1–4.Google Scholar
Fearn, D. R. 1979a Thermally driven hydromagnetic convection in a rapidly rotating sphere. Proc. R. Soc. Lond. A 369 (1737), 227–242.Google Scholar
Fearn, D. R. 1979b Thermal and magnetic instabilities in a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 14 (1), 103–126.Google Scholar
Fearn, D. R. 1998 Hydromagnetic flow in planetary cores. Rep. Prog. Phys. 61, 175–235.CrossRefGoogle Scholar
Fearn, D. R., Roberts, P. H. & Soward, A. M. 1986 Convection, stability and the dynamo. In Energy Stability and Convection (ed. Galdi, G. P.  & Straughan, B.), Proceedings of the Workshop, Capri, Longman Scientific & Technical.Google Scholar
Goudard, L. & Dormy, E. 2008 Relations between the dynamo region geometry and the magnetic behavior of stars and planets. Europhys. Lett. 83, 59001.Google Scholar
Gubbins, D., Willis, A. & Sreenivasan, B. 2007 Correlation of Earth’s magnetic field with lower mantle thermal and seismic structure. Phys. Earth Planet. Inter. 162, 256–260.Google Scholar
Jones, C. A. 2011 Planetary magnetic fields and fluid dynamos. Annu. Rev. Fluid Mech. 43, 583–614.CrossRefGoogle Scholar
Jones, C. A., Mussa, A. I. & Worland, S. J. 2003 Magnetoconvection in a rapidly rotating sphere: the weak-field case. Proc. R. Soc. Lond. A 459, 773–797.CrossRefGoogle Scholar
Kutzner, C. & Christensen, U. 2002 From stable dipolar towards reversing numerical dynamos. Phys. Earth Planet. Inter. 131, 29–45.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Morin, D. & Dormy, E. 2009 The dynamo bifurcation in rotating spherical shells. Intl J. Mod. Phys. B 23, 5467–5482.Google Scholar
Olson, P., Glatzmaier, G. & Coe, R. 2011 Complex polarity reversals in a geodynamo model. Earth Planet. Sci. Lett. 304, 168–179.Google Scholar
Oruba, L. & Dormy, E. 2014a Predictive scaling laws for spherical rotating dynamos. Geophys. J. Intl 198, 828–847.CrossRefGoogle Scholar
Oruba, L. & Dormy, E. 2014b Transition between viscous dipolar and inertial multipolar dynamos. Geophys. Res. Lett. 41 (20), 7115–7120.CrossRefGoogle Scholar
Proctor, M. R. E. 1994 Convection and magnetoconvection. In Lectures on Solar and Planetary Dynamos (ed. Proctor, M. R. E. & Gilberts, A. D.). Cambridge University Press.Google Scholar
Roberts, P. H. 1978 Magneto-convection in a rapidly rotating fluid. In Rotating Fluids in Geophysics (ed. Roberts, P. H. & Soward, A. M.). Academic.Google Scholar
Roberts, P. H. 1988 Future of geodynamo theory. Geophys. Astrophys. Fluid Dyn. 44, 3–31.CrossRefGoogle Scholar
Roberts, P. H. & Soward, A. M. 1992 Dynamo theory. Annu. Rev. Fluid Mech. 24, 459–512.Google Scholar
Schrinner, M., Petitdemange, L., Dormy, E. & Schrinner, M. 2012 Dipole collapse and dynamo waves in global direct numerical simulations. Astrophys. J. 752, 121.Google Scholar
Simitev, R. & Busse, F. 2009 Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells. Eur. Phys. Lett. 85, 19001.Google Scholar
Soward, A. M. S. 1979 Convection driven dynamos. Phys. Earth Planet. Inter. 20, 134–151.CrossRefGoogle Scholar
Sreenivasan, B. & Jones, C. A. 2011 Helicity generation and subcritical behaviour in rapidly rotating dynamos. J. Fluid Mech. 688, 5–30.Google Scholar
Sreenivasan, B., Sahoo, S. & Jones, C. A. 2014 The role of buoyancy in polarity reversals of the geodynamo. Geophys. J. Intl 199, 1698–1708.CrossRefGoogle Scholar