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On hydromagnetic oscillations in a rotating cavity

  • Roger F. Gans (a1) (a2)

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The interior problem is shown to contain waves whose frequencies are of order ω, Aω and A2ω, where ω is the rotation rate of the cavity and A2 = B2/4πρωA2 [Lt ] 1 is the Alfvén number. B is an imposed magnetic field, ρ the fluid density and R the radius of the cavity. The first type of wave is a modification of the hydro-dynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spin-up, and the third is related to the MAC waves of Braginskiy (1967).

It is shown that the MAC waves must satisfy more than the usual normal boundary conditions and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. For normal liquid metals of small magnetic Prandtl number the MAC waves must satisfy full magnetic boundary conditions; only the no-slip conditions may be deferred to the boundary layers.

The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitude. The decay of the pseudo-geostrophic modes, essentially the spin-up problem, is discussed for a non-axisymmetric constraining field and non-zero container conductivity. Three regimes exist, depending on container conductivity.

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Benton, E. R. & Loper, D. E.1969 J. Fluid Mech. 39, 561-586.
Braginskiy, S. I.1967 Geomag. & Aeron. 7, 851859.
Braginskiy, S. I.1970 Geomag. & Aeron. 10, 172181.
Bullard, E. C.1949 Proc. Roy. Soc. A 197, 433-453.
Eckhardt, D., Larner, K. & Madden, T.1963 J. Geophys. Res. 68, 6279-6286.
Gans, R. F.1971 J. Fluid Mech. 45, 111-130.
Greenspan, H. P.1968 The Theory of Rotating Fluids. Cambridge University Press.
Hide, R.1966 Phil. Trans. Roy. Soc. A 259, 615-647.
Loper, D. E.1971 Phys. Earth Planet. Interiors, 4, 129137.
Loper, D. E. & Benton, E. R.1970 J. Fluid Mech. 43, 785-799.
Malkus, W. V. R.1967 J. Fluid Mech. 28, 793-802.
Munk, W. H. & MacDonald, G. J. F.1960 The Rotation of the Earth. Cambridge University Press.
Roberts, P. H.1967 An Introduction to Magnetohydrodynamics.New York: American Elsevier.
Smithells, C. J.1955 Metals Reference Book. Interscience.
Stacy, F. D.1967 Earth Planet. Sci. Letters, 3, 204206.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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