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On the hydrodynamic and hydromagnetic stability of swirling flows

Published online by Cambridge University Press:  28 March 2006

Louis N. Howard  and
A. S. Gupta
Louis N. Howard
Affiliation:
Mathematics Department, Massachusetts Institute of Technology
Both on leave during 1961-62 at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
A. S. Gupta
Affiliation:
Mathematics Department, Indian Institute of Technology, Kharagpur
Both on leave during 1961-62 at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
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Abstract

Some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current. In particular it is shown that the analogy between a rotating and a stratified fluid holds in this case, and that an important determinant of stability is a ‘Richardson number’ based on the analogue of the density gradient and the shear in the axial flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 3 , November 1962 , pp. 463 - 476
Copyright
© 1962 Cambridge University Press

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References

Chandrasekhar, S. 1960a The hydrodynamic stability of inviscid flow between coaxial cylinders. Proc. Nat. Acad. Sci., Wash., 46, 137.Google Scholar
Chandrasekhar, S. 1960b The stability of non-dissipative Couette flow in hydromagnetics. Proc. Nat. Acad. Sci., Wash., 46, 253.Google Scholar
Chandrasekhar, S. 1960c The stability of inviscid flow between rotating cylinders. J. Indian Math. Soc., 24, 211.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Drazin, P. G. 1958 The stability of a shear layer in an unbounded heterogeneous inviscid fluid. J. Fluid Mech. 4, 214.Google Scholar
Drazin, P. G. 1960 Stability of a broken-line jet in a parallel magnetic field. J. Math. Phys. 34, 49.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509.Google Scholar
Jain, R. K. 1961 On the stability of inviscid parallel flows in hydromagnetics. Appl. Sci. Res. B, 9, 85.Google Scholar
Ludwieg, H. 1960 Stabilität der Strömung in einem zylindrischen Ringraum. Z. Flugwiss, 8, 135.Google Scholar
Ludwieg, H. 1961a Ergänzung zu der Arbeit: Stabilität der Strömung in einem zylindrischen Ringraum. Z. Flugwiss, 9, 359.Google Scholar
Ludwieg, H. 1961b Rep. AVA/61 AO1, Aerodynamische Versuchsanstalt, Göttingen.
Michael, D. H. 1954 The stability of an incompressible electrically conducting fluid rotating about an axis when current flows parallel to the axis. Mathematika, 1, 45.Google Scholar
Michael, D. H. 1962 The stability of an incompressible jet with an aligned magnetic field. Unpublished.
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 509.Google Scholar
Rayleigh, J. W. S. 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 57 (also collected Sci. Papers, 1, 487) (see last paragraph).Google Scholar
Rayleigh, J. W. S. 1892 On the question of the stability of the flow of fluids. Phil. Mag. 34, 59 (also Sci. Papers, 3, 575).Google Scholar
Rayleigh, J. W. S. 1916 On the dynamics of revolving fluids. Proc. Roy. Soc. A, 93, 148 (also Sci. Papers, 6, 447).Google Scholar
Velikhov, E. P. 1959a Stability of a plane Poiseuille flow of an ideally conducting fluid in a longitudinal magnetic field. J. Exptl Theor. Phys. (U.S.S.R.), 36, 1192 (p. 848 in English trans.).Google Scholar
Velikhov, E. P. 1959b Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. J. Exptl Theor. Phys. (U.S.S.R.), 36, 1398 (p. 995 in English trans.).Google Scholar