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On large-amplitude magnetohydrodynamics

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih*
Affiliation:
Department of Engineering Mechanics, University of Michigan, Ann Arbor, Michigan
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Extract

Three results on the flow of an infinitely conducting and inviscid fluid are presented in this paper. The first result is that all steady flows with magnetic lines coincident with streamlines are reducible to flows without a magnetic field. The second result is on the establishment of a steady irrotational and current-free flow with coincident streamlines and magnetic lines. It throws some light on the controversy between Stewartson (1960) and Sears & Resler (1959) concerning the possibility of such a flow. The third result concerns the flow of a fluid through a circular cylinder of radius R into a point sink with strength m when the fluid carries a current of density j0 at infinity. It is shown that the condition of uniform flow at infinity is impossible to maintain if a dimensionless number (kR)2 involving the current density j0 exceeds the value (3·831)2, and that the current has the effect of concentrating the flow near the centre line and of producing ring eddies which become longer and longer as (kR)2 is increased.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 2 , October 1965 , pp. 261 - 271
Copyright
Copyright © Cambridge University Press 1965

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References

Debler, W. R. 1959 J. Engng Mech. Div., Proc. A.S.C.E. 85, 51–65.Google Scholar
Goldsworthy, F. A. 1961 J. Fluid Mech. 11, 519.CrossRefGoogle Scholar
Grad, H. 1960 Rev. Mod. Phys. 32, 830–47. See especially p. 836.CrossRefGoogle Scholar
Long, R. R. 1956 Quart. J. Mech. Appl. Math. 9, 385–93.CrossRefGoogle Scholar
Long, R. R. 1958 Quart. J. Roy. Met. Soc. 84, 159–61.CrossRefGoogle Scholar
Long, R. R. 1960 J. Fluid Mech. 7, 108–114.CrossRefGoogle Scholar
Sears, W. R. 1961 Astro. Acta, 1, 223–36.Google Scholar
Sears, W. R. & Resler, E. L. 1959 J. Fluid Mech. 5, 257–73.CrossRefGoogle Scholar
Stewartson, K. 1960 J. Fluid Mech. 8, 82–96.CrossRefGoogle Scholar
Stewartson, K. 1963 Proc. Roy. Soc. A, 275, 70.Google Scholar
Yih, C.-S. 1959 Quart. Appl. Math. 16, 409–15.CrossRefGoogle Scholar
Yih, C.-S. 1960 J. Fluid Mech. 9, 161–74.CrossRefGoogle Scholar
Yih, C.-S. 1957 La Houille Blanche, no. 3, 439–50.Google Scholar
Yih, C.-S. 1958 On the flow of a stratified fluid. Proc. Third U.S. National Congress of Appl. Mech. pp. 857–61.Google Scholar