Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T21:53:18.465Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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. & 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