Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-28T09:37:16.766Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the westward drift of the earth's magnetic field

Published online by Cambridge University Press:  12 April 2006

W. W. Wood
W. W. Wood
Affiliation:
Department of Mathematics, University of Melbourne Parkville, Victoria 3052, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A model of the earth's liquid core is assumed in which the underlying magnetic field and velocity are zonal and axially symmetric. Alfvén waves that vary as ei(kϕ−σt) are considered, where ϕ is the angle of longitude. Buoyancy and Coriolis forces Ω × U are included.

For a wide class of basic states and regions of flow, it is shown that roughly as many of the waves with a given k [ges ] 2 propagate eastwards as propagate westwards. All these waves are neutrally stable. The class of basic states is restricted by certain inequalities involving their velocity, magnetic field and entropy gradient.

it is observed that the known equivalence (Malkus 1967) between Alfvén waves with frequencies σ [Lt ] Ω and inertial waves with frequencies σp which are O(Ω) still holds when buoyancy forces are present. The equivalence requires σp2 to be real. If σp is pure imaginary, as is possible (though perhaps uncommon) in an unstably stratified medium, then the corresponding Alfvén wave is not neutrally stable and travels westwards.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 2 , 7 September 1977 , pp. 389 - 400
Copyright
© 1977 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

Acheson, D. J. 1972 On the hydromagnetic stability of a rotating fluid annulus. J. Fluid Mech. 52, 529.Google Scholar
Acheson, D. J. 1973 Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid. J. Fluid Mech. 61, 609.Google Scholar
Acheson, D. J. & Hide, R. 1973 Hydromagnetics of rotating fluids. Rep. Prog. Phys. 36, 159.Google Scholar
Braginskií, S. I. 1967 Magnetic waves in the earth's core. Geomag. Aero. 7, 851.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.
Frieman, E. & Rotenberg, M. 1960 On hydromagnetic stability of stationary equilibria. Rev. Mod. Phys. 32, 898.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Gubbins, D. 1974 Theories of the geomagnetic and solar dynamos. Rev. Geophys. Space Phys. 12, 137.Google Scholar
Hide, R. 1966 Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation. Phil. Trans. A 259, 615.Google Scholar
Hide, R. 1971 Viscosity of the earth's core. Nature 233, 100.Google Scholar
Malkus, W. V. R. 1967 Hydromagnetic planetary waves. J. Fluid Mech. 28, 793.Google Scholar
Poincaré, H. 1910 Sur la précession des corps déformables. Bull. Astron. 27, 321.Google Scholar
Roberts, P. H. & Soward, A. M. 1972 Magnetohydrodynamics of the earth's core. Ann. Rev. Fluid Mech. 4, 117.Google Scholar
Stacey, F. D. 1969 Physics of the Earth. Wiley.
Stewartson, K. 1967 Slow oscillations of fluid in a rotating cavity in the presence of a toroidal magnetic field. Proc. Roy. Soc. A 299, 173.Google Scholar