- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Subcritical dynamos in rapidly rotating planar convection

R. G. Cooper*, P. J. Bushby, and C. Guervilly

  • School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK

  • *r.cooper4@newcastle.ac.uk
PDF

Phys. Rev. Fluids 5, 113702 – Published 30 November, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.113702

Abstract

We study dynamo action using numerical simulations of planar Boussinesq convection at rapid rotation (low Ekman numbers, Ek), focusing on subcritical dynamo action in which the dynamo is sustained for Rayleigh numbers, Ra, below the critical Rayleigh number for the onset of non-magnetic convection, Rac. These solutions are found by first investigating the supercritical regime, in which the dynamo is able to generate a large-scale magnetic field that significantly influences the convective motions, with an associated Elsasser number of order Ek1/3. Subcritical solutions are then found by tracking this solution branch into the subcritical regime, taking a supercritical solution and then gradually lowering the corresponding Rayleigh number. We show that decreasing the Ekman number leads to an extension of the subcritical range of Ra/Rac, down to an optimal value of Ek=10−5. For magnetic Prandtl numbers of order unity, subcriticality is then hampered by the emergence of a large-scale mode at lower Ekman numbers when the dynamo driven by the smaller scale convection generates relatively stronger large-scale magnetic field. The inability of the large-scale mode to sustain dynamo action leads to an intermittent behavior that appears to inhibit subcriticality. The subcritical solutions are also sensitive to the value of the magnetic Reynolds number (or equivalently, the magnetic Prandtl number, Pm), as values of the magnetic Reynolds number greater than 70 are required to produce dynamo action, but large values lead to fluctuations that are able to push the system too far from the subcritical branch and towards the trivial conducting state.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. G. Glatzmaier and P. H. Roberts, A three-dimensional self-consistent computer simulation of a geomagnetic field reversal, Nature 377, 203 (1995).
  2. U. R. Christensen, J. Aubert, and G. Hulot, Conditions for Earth-like geodynamo models, Earth Planet. Sci. Lett. 296, 487 (2010).
  3. U. R. Christensen and J. Wicht, Numerical dynamo simulations, in Treatise on Geophysics (Second Edition), Vol. 8, edited by G. Schubert (Elsevier, Amsterdam, 2015), pp. 245–277.
  4. N. Schaeffer, D. Jault, H.-C. Nataf, and A. Fournier, Turbulent geodynamo simulations: a leap towards Earth's core, Geophys. J. Int. 211, 1 (2017).
  5. J. Aubert, Approaching Earth's core conditions in high-resolution geodynamo simulations, Geophys. J. Int. 219, S137 (2019).
  6. U. R. Christensen and J. Aubert, Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields, Geophy. J. Int. 166, 97 (2006).
  7. Z. Stelzer and A. Jackson, Extracting scaling laws from numerical dynamo models, Geophys. J. Int. 193, 1265 (2013).
  8. E. M. King and B. A. Buffett, Flow speeds and length scales in geodynamo models: The role of viscosity, Earth Planet. Sci. Lett. 371, 156 (2013).
  9. L. Oruba and E. Dormy, Predictive scaling laws for spherical rotating dynamos, Geophys. J. Int. 198, 828 (2014).
  10. S. Chandrasekhar, The instability of a layer of fluid heated below and subject to Coriolis forces, Proc. R. Soc. Lond. A 217, 306 (1953).
  11. S. Childress and A. M. Soward, Convection-Driven Hydromagnetic Dynamo, Phys. Rev. Lett. 29, 837 (1972).
  12. A. M. Soward, A convection-driven dynamo: I. The weak field case, Phil. Trans. Royal Soc. London A 275, 611 (1974).
  13. Y. Fautrelle and S. Childress, Convective dynamos with intermediate and strong fields, Geophys. Astrophys. Fluid Dyn. 22, 235 (1982).
  14. M. St. Pierre, The Strong Field Branch of the Childress-Soward Dynamo, Solar Planet. Dynamos 295 (1993).
  15. C. A. Jones and P. H. Roberts, Convection-driven dynamos in a rotating plane layer, J. Fluid Mech. 404, 311 (2000).
  16. J. Rotvig and C. A. Jones, Rotating convection-driven dynamos at low Ekman number, Phys. Rev. E 66, 056308 (2002).
  17. S. Stellmach and U. Hansen, Cartesian convection driven dynamos at low Ekman number, Phys. Rev. E 70, 056312 (2004).
  18. B. Favier and M. R. E. Proctor, Kinematic dynamo action in square and hexagonal patterns, Phys. Rev. E 88, 053011 (2013).
  19. M. A. Calkins, K. Julien, S. M. Tobias, and J. M. Aurnou, A multiscale dynamo model driven by quasi-geostrophic convection, J. Fluid Mech. 780, 143 (2015).
  20. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961).
  21. I. A. Eltayeb, Hydromagnetic convection in a rapidly rotating fluid layer, Proc. R. Soc. Lond. A 326, 229 (1972).
  22. N. Gillet, D. Jault, E. Canet, and A. Fournier, Fast torsional waves and strong magnetic field within the Earth's core, Nature 465, 74 (2010).
  23. V. Morin and E. Dormy, The dynamo bifurcation in rotating spherical shells, Int. J. Mod. Phys. B 23, 5467 (2009).
  24. B. Sreenivasan and C. A. Jones, Helicity generation and subcritical behavior in rapidly rotating dynamos, J. Fluid Mech. 688, 5 (2011).
  25. E. Dormy, Strong-field spherical dynamos, J. Fluid Mech. 789, 500 (2016).
  26. W. Kuang, W. Jiang, and T. Wang, Sudden termination of martian dynamo?: Implications from subcritical dynamo simulations., Geophys. Res. Lett. 35, 1 (2008).
  27. K. Hori and J. Wicht, Subcritical dynamos in the early Mars' core: Implications for cessation of the past Martian dynamo, Phys. Earth Planet. Inter. 219, 21 (2013).
  28. F. Cattaneo, T. Emonet, and N. O. Weiss, On the interaction between convection and magnetic fields, Astrophys. J. 588, 1183 (2003).
  29. C. Guervilly, D. W. Hughes, and C. A. Jones, Large-scale vortices in rapidly rotating Rayleigh-Bénard convection, J. Fluid Mech. 758, 407 (2014).
  30. F. Cattaneo, D. W. Hughes, and N. O. Weiss, What is a stellar dynamo? Mon. Not. R. Astron. Soc. 253, 479 (1991).
  31. B. Favier and P. J. Bushby, Small-scale dynamo action in rotating compressible convection, J. Fluid Mech. 690, 262 (2011).
  32. K. M. Soderlund, E. M. King, and J. M. Aurnou, The influence of magnetic fields in planetary dynamo models, Earth Planet. Sci. Lett. 333, 9 (2012).
  33. A. Courvoisier, D. W. Hughes, and S. M. Tobias, Mean induction and diffusion: the influence of spatial coherence, J. Fluid Mech. 627, 403 (2009).
  34. A. Tilgner, Transitions in Rapidly Rotating Convection Driven Dynamos, Phys. Rev. Lett. 109, 248501 (2012).
  35. C. Guervilly, D. W. Hughes, and C. A. Jones, Generation of magnetic fields by large-scale vortices in rotating convection, Phys. Rev. E 91, 041001(R) (2015).
  36. P. J. Bushby, P. J. Käpylä, Y. Masada, A. Brandenburg, B. Favier, C. Guervilly, and M. J. Käpylä, Large-scale dynamos in rapidly rotating plane layer convection, Astron. Astrophys. 612, A97 (2018).
  37. F. Cattaneo and D. W. Hughes, Dynamo action in rapidly rotating Rayleigh-Bénard convection at infinite Prandtl number, J. Fluid Mech. 825, 385 (2017).
  38. T. Schwaiger, T. Gastine, and J. Aubert, Force balance in numerical geodynamo simulations: A systematic study, Geophys. J. Int 219, S101 (2019).
  39. C. Guervilly, D. W. Hughes, and C. A. Jones, Large-scale-vortex dynamos in planar rotating convection, J. Fluid Mech. 815, 333 (2017).
  40. A. van Kan, T. Nemoto, and A. Alexakis, Rare transitions to thin-layer turbulent condensates, J. Fluid Mech. 878, 356 (2019).
  41. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (University Press, Cambridge, 1978).
  42. F. Cattaneo and D. W. Hughes, Dynamo action in a rotating convective layer, J. Fluid Mech. 553, 401 (2006).
  43. D. W. Hughes and F. Cattaneo, The alpha-effect in rotating convection: size matters, J. Fluid Mech. 594, 445 (2008).
  44. K. Julien, A. M. Rubio, I. Grooms, and E. Knobloch, Statistical and physical balances in low Rossby number Rayleigh–Bénard convection, Geophys. Astrophys. Fluid Dyn. 106, 392 (2012).
  45. B. Favier, L. J. Silvers, and M. R. E. Proctor, Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection, Phys. Fluids 26, 096605 (2014).
  46. Y. Masada and T. Sano, Mean-field modeling of an α2 dynamo coupled with direct numerical simulations of rigidly rotating convection, Astrophys. J. Lett. 794, L6 (2014).
  47. P. J. Käpylä, M. J. Mantere, and A. Brandenburg, Oscillatory large-scale dynamos from cartesian convection simulations, Geophys. Astrophys. Fluid Dyn. 107, 244 (2013).
  48. B. Favier and P. J. Bushby, On the problem of large-scale magnetic field generation in rotating compressible convection, J. Fluid Mech. 723, 529 (2013).
  49. www.dirac.ac.uk.

Outline

Information

Phys. Rev. Fluids 5, 113702– Published 30 November, 2020
  • Received 14 February 2020
  • Accepted 27 October 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation