Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T06:23:49.201Z Has data issue: false hasContentIssue false
  • English
  • Français

Ring vortices generated electromagnetically

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

If an electric current of uniform density j0 is passed axially through a stationary fluid between concentric cylinders of radii r1 and r2 (> r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line current J along the axis, sufficient conditions for stability being $J \le -\pi j _0(r^2_2 - r^2_1)$, or $\ge J\; \pi j _0r^2_1$

The values of J needed to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the case r2-r1 [Lt ] r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders if J and j0 have the same sign, and if J is not very small compared with πj0r2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 3 , April 1959 , pp. 436 - 444
Copyright
© 1959 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. 1954 The stability of viscous flow between rotating cylinders. Mathematika, 1, 5–13.Google Scholar
Lamb, H. 1945 Hydrodynamics. New York: Dover.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Pellew, A. & Southwell, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. Roy. Soc. A, 176, 312–343.Google Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Scientific Papers, 6, 447–453. Cambridge University Press.
Synge, J. L. 1938 On the stability of a viscous liquid between two rotating coaxial cylinders. Proc. Roy. Soc. A, 167, 250–256.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. A, 223, 289–343.Google Scholar
Yih, C.-S. 1959 Inhibition of hydrodynamic instability by an electric current. (To be published.)