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On hydromagnetic oscillations in a rotating cavity

Gans, Roger F. (1971) On hydromagnetic oscillations in a rotating cavity. Journal of Fluid Mechanics, 50 (3). pp. 449-467. ISSN 0022-1120. doi:10.1017/S0022112071002696.

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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 A^2ω where ω is the rotation rate of the cavity and A^2= B^2/4πρωA^2 ≪ 1 is the Alfvén number. B is an imposed magnetic field, p the fluid density and R the radius of the cavity. The first type of wave is a modification of the hydrodynamic 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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Additional Information:© 1971 Cambridge University Press. Published Online March 29 2006; Received February 1 1971; Revised July 20 1971. The comments of the referees regarding an earlier version of this paper are deeply appreciated. Support under the National Aeronautics and Space Administration Grant NGL-05-002-003 is gratefully acknowledged. This is contribution number 1975 of the Division of Geological and Planetary Sciences, California Institute of Technology.
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Caltech Division of Geological and Planetary Sciences1975
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Official Citation:Roger F. Gans (1971). On hydromagnetic oscillations in a rotating cavity. Journal of Fluid Mechanics, 50 , pp 449-467 doi:10.1017/S0022112071002696
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32871
Deposited On:02 Aug 2012 16:51
Last Modified:09 Nov 2021 21:30

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