Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T22:44:06.524Z Has data issue: false hasContentIssue false

Hydromagnetic stability of dissipative flow between rotating permeable cylinders

Published online by Cambridge University Press:  28 March 2006

Tien Sun Chang
Affiliation:
Oak Ridge National Laboratory, Oak Ridge, Tennessee Present address: Virginia Polytechnic Institute, Blacksburg, Virginia.
Walter K. Sartory
Affiliation:
Oak Ridge National Laboratory, Oak Ridge, Tennessee

Abstract

The theory of stability of the flow of a viscous, electrically conducting fluid between rotating cylinders in the presence of an axial magnetic field is extended to the case where the cylinders are permeable and the primary flow includes a radial component. Numerical results pertaining to the stationary axially symmetric modes are presented, and the asymptotic stability behaviour for large values of the radial Reynolds number is derived.

Type
Research Article
Copyright
© 1967 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

Chandrasekhar, S. 1953 The stability of the viscous flow between rotating cylinders in the presence of a magnetic field. Proc. Roy. Soc. A, 216, 293.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chang, T. S. & Sartory, W. K. 1965a Hydromagnetic stability of vortex-like flow. Oak Ridge National Laboratory, USAEC Rep. no. ORNL-3707.Google Scholar
Chang, T. S. & Sartory, W. K. 1965b Transition from stationary to oscillatory modes of instability in magnetohydrodynamic Couette flow. Presented at the 1965 Divisional Meeting of Fluid Dynamics, American Physical Society in Cleveland, Ohio. Oak Ridge National Laboratory, USAEC Rep. no. ORNL-TM-1404.Google Scholar
Chang, T. S. & Sartory, W. K. 1965c Hydromagnetic stability of dissipative vortex flow Phys. Fluids, 8, 235.Google Scholar
HÄMMERLIN, G. 1955 Über das Eigenwertproblem der dreidimensionalen Instabilität laminarer Grenzschichten an konkaven Wänden J. Ratl. Mech. Anal. 4, 279.Google Scholar
Hazlehurst, J. 1963 Are spiral flows stable? Astrophys. J. 137, 126.Google Scholar
Kerrebrock, J. L. & Megreblian, R. V. 1961 Vortex containment for the gaseous fission rocket J. Aero. Sci. 28, 710.Google Scholar
Kurzweg, U. H. 1963 The stability of couette flow in the presence of an axial magnetic field J. Fluid Mech. 17, 52.Google Scholar
Lewellen, W. S. 1960 Magnetohydrodynamically driven vortices. Proc. Heat Trans. and Fluid Mech. Inst. p. 1. Stanford University Press.
Niblett, E. R. 1958 The stability of couette flow in an axial magnetic field Canad. J. Phys. 36, 1509.Google Scholar
Rayleigh, J. W. S. 1918 On the dynamics of revolving fluids Proc. Roy. Soc. A, 93, 148.Google Scholar
Roberts, P. H. 1964 The stability of hydromagnetic couette flow Proc. Camb. Phil. Soc. 60, 635.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. A, 223, 289.Google Scholar
Walowit, J., Tsao, S. & Diprima, R. C. 1964 Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient. J. Appl. Mech. E, 31, 585.Google Scholar