Skip to main content Accessibility help
×
Home

Force balance in convectively driven dynamos with no inertia

  • David W. Hughes (a1) and Fausto Cattaneo (a2)

Abstract

We study dynamo action in rotating, plane layer Boussinesq convection in the absence of inertia. This allows a decomposition of the velocity into a thermal part driven by buoyancy, and a magnetic part driven by the Lorentz force. We have identified three families of solutions, defined in terms of what is the dominant contribution to the velocity. In weak field dynamos the dominant contribution is the thermal component, in super strong field dynamos the dominant contribution is magnetic and in strong field dynamos the two components are comparable. For each of these solutions we investigate the force balance in the momentum equation to determine the relative importance of the viscous, buoyancy, Coriolis and magnetic forces. We do this by extracting the solenoidal part of the individual terms in the momentum equation, thereby removing their pressure contributions. This is numerically preferable to the more common practice of taking the curl of the momentum equation, which introduces an extra derivative. We find that, irrespective of the type of dynamo solution, the dynamics is controlled by the horizontal forces (in projection). Furthermore, in the progression from weak to strong to super strong dynamos, we find that the viscous forces in the thermal equation become negligible, thereby leading to a balance between buoyancy and Coriolis forces. On the other hand, no corresponding trend is observed in the magnetic part of the momentum equation: the viscous stresses always remain significant. This can be attributed to the different degrees of smoothness of the Coriolis and Lorentz forces, the latter having contributions from strong, filamentary structures. We discuss how our findings relate to dynamo solutions in which viscosity plays no role whatsoever – so-called Taylor states.

Copyright

Corresponding author

Email address for correspondence: d.w.hughes@leeds.ac.uk

References

Hide All
Aubert, J., Gastine, T. & Fournier, A. 2017 Spherical convective dynamos in the rapidly rotating asymptotic regime. J. Fluid Mech. 813, 558593.
Cattaneo, F. 1999 On the origin of magnetic fields in the quiet photosphere. Astrophys. J. 515, L39L42.
Cattaneo, F., Emonet, T. & Weiss, N. 2003 On the interaction between convection and magnetic fields. Astrophys. J. 588, 11831198.
Cattaneo, F. & Hughes, D. W. 2006 Dynamo action in a rotating convective layer. J. Fluid Mech. 553, 401418.
Cattaneo, F. & Hughes, D. W. 2017 Dynamo action in rapidly rotating Rayleigh–Bénard convection at infinite Prandtl number. J. Fluid Mech. 825, 385411.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Dormy, E. 2016 Strong-field spherical dynamos. J. Fluid Mech. 789, 500513.
Eltayeb, I. A. 1972 Hydromagnetic convection in a rapidly rotating fluid layer. Proc. R. Soc. Lond. A 326, 229254.
Eltayeb, I. A. & Roberts, P. H. 1970 Note: on the hydromagnetics of rotating fluids. Astrophys. J. 162, 699.
Hughes, D. W. & Cattaneo, F. 2016 Strong-field dynamo action in rapidly rotating convection with no inertia. Phys. Rev. E 93, 061101.
Jones, C. A. & Roberts, P. H. 2000 Convection-driven dynamos in a rotating plane layer. J. Fluid Mech. 404, 311343.
Roberts, P. H. 1978 Magneto-convection in a rapidly rotating fluid. In Rotating Fluids in Geophysics (ed. Roberts, P. H. & Soward, A. M.). Academic.
Roberts, P. H. & Soward, A. M. 1992 Dynamo theory. Annu. Rev. Fluid Mech. 24, 459512.
Rotvig, J. & Jones, C. A. 2002 Rotating convection-driven dynamos at low Ekman number. Phys. Rev. E 66, 056308.
Schaeffer, N., Jault, D., Nataf, H.-C. & Fournier, A. 2017 Turbulent geodynamo simulations: a leap towards Earth’s core. Geophys. J. Intl 211, 129.
Taylor, J. B. 1963 The magneto-hydrodynamics of a rotating fluid and the Earth’s dynamo problem. Proc. R. Soc. Lond. A 274, 274283.
Yadav, R. K., Gastine, T., Christensen, U. R., Wolk, S. J. & Poppenhaeger, K. 2016 Approaching a realistic force balance in geodynamo simulations. Proc. Natl Acad. Sci. 113, 1206512070.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Force balance in convectively driven dynamos with no inertia

  • David W. Hughes (a1) and Fausto Cattaneo (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.