Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T08:39:08.890Z Has data issue: false hasContentIssue false
  • English
  • Français

Fast and furious dynamo action in the anisotropic dynamo

Published online by Cambridge University Press:  11 May 2022

Franck Plunian Open the ORCID record for Franck Plunian [Opens in a new window]  and
Thierry Alboussière Open the ORCID record for Thierry Alboussière [Opens in a new window]
Franck Plunian*
Affiliation:
Université Grenoble Alpes, University of Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, ISTerre, 38000 Grenoble, France
Thierry Alboussière
Affiliation:
Université Lyon 1, ENS de Lyon, CNRS, Laboratoire de Géologie de Lyon, Lyon 69622, France
*
†Email address for correspondence: Franck.Plunian@univ-grenoble-alpes.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

In the limit of large magnetic Reynolds numbers, it is shown that a smooth differential rotation can lead to fast dynamo action, provided that the electrical conductivity or magnetic permeability is anisotropic. If the shear is infinite, for example between two rotating solid bodies, the anisotropic dynamo becomes furious, meaning that the magnetic growth rate increases toward infinity with an increasing magnetic Reynolds number.

JFM classification

Geophysical and Geological Flows: Geodynamo MHD and Electrohydrodynamics: Dynamo theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A66
Check for updates
Copyright
© The Author(s), 2022. Published by 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

REFERENCES

Abramowitz, M. & Stegun, I.A. 1968 Handbook of Mathematical Functions with Formulas, Graphs and Mathemarical Tables. Dover Publications.Google Scholar
Alboussière, T., Drif, K. & Plunian, F. 2020 Dynamo action in sliding plates of anisotropic electrical conductivity. Phys. Rev. E 101, 033107.CrossRefGoogle ScholarPubMed
Braginskii, S.I. 1965 Transport processes in a plasma. Rev. Plasma Phys. 1, 205.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1–4), 1–209.CrossRefGoogle Scholar
Childress, S. & Gilbert, A.D. 1995 Stretch, Twist, Fold: The Fast Dynamo. Springer.Google Scholar
Cowling, T.G. 1934 The magnetic field of sunspots. Mon. Not. R. Astron. Soc. 94, 39–48.CrossRefGoogle Scholar
Deuss, A. 2014 Heterogeneity and anisotropy of earth's inner core. Annu. Rev. Earth Planet. Sci. 42 (1), 103–126.CrossRefGoogle Scholar
Favier, B. & Proctor, M.R.E. 2013 Growth rate degeneracies in kinematic dynamos. Phys. Rev. E 88, 031001.CrossRefGoogle ScholarPubMed
Gallet, B., Pétrélis, F. & Fauve, S. 2012 Dynamo action due to spatially dependent magnetic permeability. Europhys. Lett. 97 (6), 69001.CrossRefGoogle Scholar
Gallet, B., Pétrélis, F. & Fauve, S. 2013 Spatial variations of magnetic permeability as a source of dynamo action. J. Fluid Mech. 727, 161–190.CrossRefGoogle Scholar
Gilbert, A.D. 1988 Fast dynamo action in the ponomarenko dynamo. Geophys. Astrophys. Fluid Dyn. 44 (1-4), 241–258.CrossRefGoogle Scholar
Gilbert, A.D. 2003 Chapter 9 - Dynamo theory. In Handbook of Mathematical Fluid Dynamics, vol. 2, pp. 355–441. North-Holland.CrossRefGoogle Scholar
Kreuzahler, S., Ponty, Y., Plihon, N., Homann, H. & Grauer, R. 2017 Dynamo enhancement and mode selection triggered by high magnetic permeability. Phys. Rev. Lett. 119, 234501.CrossRefGoogle ScholarPubMed
Lortz, D. 1989 Axisymmetric dynamo solutions. Z. Naturforsch. 44a, 1041–1045.CrossRefGoogle Scholar
Lowes, F.J. & Wilkinson, I. 1963 Geomagnetic dynamo: a laboratory model. Nature 198, 1158–1160.CrossRefGoogle Scholar
Lowes, F.J. & Wilkinson, I. 1968 Geomagnetic dynamo: an improved laboratory model. Nature 219, 717–718.CrossRefGoogle Scholar
Marcotte, F., Gallet, B., Pétrélis, F. & Gissinger, C. 2021 Enhanced dynamo growth in nonhomogeneous conducting fluids. Phys. Rev. E 104, 015110.CrossRefGoogle ScholarPubMed
Miralles, S., Bonnefoy, N., Bourgoin, M., Odier, P., Pinton, J.-F., Plihon, N., Verhille, G., Boisson, J., Daviaud, F. & Dubrulle, B. 2013 Dynamo threshold detection in the von Kármán sodium experiment. Phys. Rev. E 88, 013002.CrossRefGoogle ScholarPubMed
Nore, C., Castanon Quiroz, D., Cappanera, L. & Guermond, J.-L. 2018 Numerical simulation of the von Kármán sodium dynamo experiment. J. Fluid Mech. 854, 164–195.CrossRefGoogle Scholar
Ohta, K., Nishihara, Y., Sato, Y., Hirose, K., Yagi, T., Kawaguchi, S.I., Hirao, N. & Ohishi, Y. 2018 An experimental examination of thermal conductivity anisotropy in HCP iron. Front. Earth Sci. 6, 176.CrossRefGoogle Scholar
Pétrélis, F., Alexakis, A. & Gissinger, C. 2016 Fluctuations of electrical conductivity: A new source for astrophysical magnetic fields. Phys. Rev. Lett. 116, 161102.CrossRefGoogle ScholarPubMed
Plunian, F. & Alboussière, T. 2020 Axisymmetric dynamo action is possible with anisotropic conductivity. Phys. Rev. Res. 2, 013321.CrossRefGoogle Scholar
Plunian, F. & Alboussière, T. 2021 Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability. J. Plasma Phys. 87 (1), 905870110.CrossRefGoogle Scholar
Ponomarenko, Y.B. 1973 On the theory of hydromagnetic dynamos. Zh. Prikl. Mekh. Tekh. Fiz. 6, 47–51.Google Scholar
Rincon, F. 2019 Dynamo theories. J. Plasma Phys. 85 (4), 205850401.CrossRefGoogle Scholar
Roberts, G.O. 1972 Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 271, 411–454.Google Scholar
Ruderman, M.S. & Ruzmaikin, A.A. 1984 Magnetic field generation in an anisotropically conducting fluid. Geophys. Astrophys. Fluid Dyn. 28 (1), 77–88.CrossRefGoogle Scholar
Ruzmaikin, A., Sokoloff, D. & Shukurov, A. 1988 Hydromagnetic screw dynamo. J. Fluid Mech. 197, 39–56.CrossRefGoogle Scholar
Soward, A.M. 1987 Fast dynamo action in a steady flow. J. Fluid Mech. 180, 267–295.CrossRefGoogle Scholar
Soward, A.M. 1994 Fast dynamos. In Lectures on Solar and Planetary Dynamos (ed. M.R.E. Proctor & A.D. Gilbert), pp. 181–217, Cambridge University Press.CrossRefGoogle Scholar
Tobias, S.M. 2021 The turbulent dynamo. J. Fluid Mech. 912, P1.CrossRefGoogle ScholarPubMed
Vainshtein, S.I. & Zel'dovich, Y.B. 1972 Origin of magnetic fields in astrophysics. Usp. Fiz. Nauk 106, 431–457 [English transl.: Sov. Phys. Usp., Vol. 15, p. 159-172, 1972].CrossRefGoogle Scholar
Zel'dovich, Y.B. 1957 The magnetic field in the two-dimensional motion of a conducting turbulent liquid. J. Expl Theor. Phys. 4, 460 [Russian original - ZhETF, Vol. 31, No. 3, p. 154, 1957].Google Scholar