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Simple Dynamical Fast Dynamos

Published online by Cambridge University Press:  11 May 2010

A.D. Gilbert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St., Cambridge, CB3 9EW UK
N.F. Otani
Affiliation:
School of Electrical Engineering, Cornell University, Ithaca, NY 14853 USA
S. Childress
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA
M. R. E. Proctor
Affiliation:
University of Cambridge
P. C. Matthews
Affiliation:
University of Cambridge
A. M. Rucklidge
Affiliation:
University of Cambridge
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Summary

Fast dynamo saturation is explored numerically using a simplified model. The magnetic field has many degrees of freedom and allows the generation of fine structure at large Rm. The velocity field is constrained, containing two Fourier modes and so eight degrees of freedom; the Lorentz force is projected onto these modes. Numerical simulations at varying Rm are discussed.

Fast dynamo instabilities are the subject of intense research (reviewed in Childress 1992), through numerical simulations and analytical studies of simple models. However little is known about how a fast dynamo instability might saturate and what the resulting spatial structure and temporal behaviour of the field might be. Does a fast dynamo saturate by suppressing the flow field until the effective magnetic Reynolds number is reduced to a value of order unity or by modifying transport effects of the flow (Vainshtein et al. 1993)? Is the saturated magnetic energy in equipartition with the kinetic energy and how is the magnetic energy distributed; in particular how much energy is stored in large-scale field components (Vainshtein & Cattaneo 1992)? Does the field contain the fine structure typical of kinematic fast dynamo instabilities and is it intermittent in time? The difficulty in answering these questions is that dynamo action only allows growth of 3-d magnetic fields and through the Lorentz force this leads to all the complexities of 3-d MHD turbulence. Numerical studies are computationally expensive and only moderate values of Rm have been achieved (see, for example, Gilman 1983, Glatzmaier 1985, Meneguzzi & Pouquet 1989, Nordlund et al 1991 and Galanti et al 1992).

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Publisher: Cambridge University Press
Print publication year: 1994

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  • Simple Dynamical Fast Dynamos
    • By A.D. Gilbert, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St., Cambridge, CB3 9EW UK, N.F. Otani, School of Electrical Engineering, Cornell University, Ithaca, NY 14853 USA, S. Childress, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA
  • Edited by M. R. E. Proctor, University of Cambridge, P. C. Matthews, University of Cambridge, A. M. Rucklidge, University of Cambridge
  • Book: Solar and Planetary Dynamos
  • Online publication: 11 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511662874.018
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  • Simple Dynamical Fast Dynamos
    • By A.D. Gilbert, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St., Cambridge, CB3 9EW UK, N.F. Otani, School of Electrical Engineering, Cornell University, Ithaca, NY 14853 USA, S. Childress, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA
  • Edited by M. R. E. Proctor, University of Cambridge, P. C. Matthews, University of Cambridge, A. M. Rucklidge, University of Cambridge
  • Book: Solar and Planetary Dynamos
  • Online publication: 11 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511662874.018
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Simple Dynamical Fast Dynamos
    • By A.D. Gilbert, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St., Cambridge, CB3 9EW UK, N.F. Otani, School of Electrical Engineering, Cornell University, Ithaca, NY 14853 USA, S. Childress, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA
  • Edited by M. R. E. Proctor, University of Cambridge, P. C. Matthews, University of Cambridge, A. M. Rucklidge, University of Cambridge
  • Book: Solar and Planetary Dynamos
  • Online publication: 11 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511662874.018
Available formats
×