Instability of non-linear α2-dynamos

D. R. Fearn, M. M. Rahman

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α0, the strength of α. Above some critical value of α0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B̄ with α0.

Original languageEnglish
Pages (from-to)101-112
Number of pages12
JournalPhysics of the Earth and Planetary Interiors
Volume142
Issue number1-2
DOIs
Publication statusPublished - May 12 2004

Fingerprint

rotating generators
magnetic field
core (planetary)
rotating fluid
planetary cores
magnetic fields
rotating fluids
magnetic induction
spherical shells
Lorentz force
momentum
planet
shell

Keywords

  • Earth's core
  • Magnetic instability
  • Non-linear dynamo

ASJC Scopus subject areas

  • Geophysics
  • Space and Planetary Science

Cite this

Instability of non-linear α2-dynamos. / Fearn, D. R.; Rahman, M. M.

In: Physics of the Earth and Planetary Interiors, Vol. 142, No. 1-2, 12.05.2004, p. 101-112.

Research output: Contribution to journalArticle

@article{ed377fadcd9b4e8d8b6dfe3e016e1cf1,
title = "Instability of non-linear α2-dynamos",
abstract = "Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α0, the strength of α. Above some critical value of α0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B̄ with α0.",
keywords = "Earth's core, Magnetic instability, Non-linear dynamo",
author = "Fearn, {D. R.} and Rahman, {M. M.}",
year = "2004",
month = "5",
day = "12",
doi = "10.1016/j.pepi.2003.12.010",
language = "English",
volume = "142",
pages = "101--112",
journal = "Physics of the Earth and Planetary Interiors",
issn = "0031-9201",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Instability of non-linear α2-dynamos

AU - Fearn, D. R.

AU - Rahman, M. M.

PY - 2004/5/12

Y1 - 2004/5/12

N2 - Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α0, the strength of α. Above some critical value of α0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B̄ with α0.

AB - Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α0, the strength of α. Above some critical value of α0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B̄ with α0.

KW - Earth's core

KW - Magnetic instability

KW - Non-linear dynamo

UR - http://www.scopus.com/inward/record.url?scp=1842420479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842420479&partnerID=8YFLogxK

U2 - 10.1016/j.pepi.2003.12.010

DO - 10.1016/j.pepi.2003.12.010

M3 - Article

VL - 142

SP - 101

EP - 112

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 1-2

ER -