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Hydromagnetic edge waves in a rotating stratified fluid

Published online by Cambridge University Press:  29 March 2006

D. G. Andrews  and
R. Hide
D. G. Andrews
Affiliation:
Department of Geophysics, Reading University, Reading, Berkshire, England
R. Hide
Affiliation:
Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire, England
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Abstract

The properties of edge waves confined by the interaction of buoyancy and Coriolis forces to the vicinity of a rigid plane boundary in a rotating, stratified, electrically conducting fluid pervaded by a magnetic field are established in some simple cases. The background shear is taken to be zero, the basic Alfvén velocity V and Brunt–Väisälä frequency N are assumed uniform, and all dissipative effects are taken to be vanishingly small. It is shown that waves trapped against the bounding wall can occur only if V is parallel to the wall. When the basic rotation vector Ω is also parallel to the wall, the hydromagnetic edge waves have a higher frequency and smaller spatial extent perpendicular to the wall than their non-hydromagnetic counterparts, but more complex behaviour is found when Ω possesses a component normal to the wall. There are conditions under which edge waves may exist even when the basic density stratification is top-heavy (i.e. when N2 < 0).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 593 - 603
Copyright
© 1975 Cambridge University Press

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References

Acheson, D. J. & Hide, R. 1973 Hydromagnetics of rotating fluids. Rep. Prog. Phys. 36, 159–221.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Hide, R. 1966 Free hydromagnetic oscillations of the Earth's core and the theory of the geomagnetic secular variation. Phil. Trans. A 259, 615–647.Google Scholar
Hide, R. 1969a On hydromagnetic waves in a stratified rotating incompressible fluid. J. Fluid Mech. 39, 283–287.Google Scholar
Hide, R. 1969b The viscous boundary layer at the rigid bounding surface of an electrically-conducting rotating fluid in the presence of a magnetic field. J. Atmos. Sci. 26, 847–853.Google Scholar
Hide, R. & Stewartson, K. 1972 Hydromagnetic oscillations of the Earth's core. Rev. Geophys. Space Phys. 10, 579–598.Google Scholar
Rhines, P. B. 1970 Edge-, bottom-, and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn. 1, 273–302.Google Scholar
Roberts, P. H. 1967 An Introduction to Magnetohydrodynamics. Longmans.
Roberts, P. H. & Soward, A. 1972 Magnetohydrodynamics of the Earth's core. Ann. Rev. Fluid Mech. 4, 117–153.Google Scholar
Skiles, D. D. 1972 On the transmission of energy in an incompressible magnetohydrodynamic wave into a conducting solid. Phys. Earth Planet. Interiors, 5, 99–109.Google Scholar
Stewartson, K. 1960 On the motion of a non-conducting body through a perfectly-conducting fluid. J. Fluid Mech. 8, 82–96.Google Scholar