Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T22:53:33.088Z Has data issue: false hasContentIssue false

On the hydromagnetic stability of an unsteady Kelvin-Helmholtz flow

Published online by Cambridge University Press:  29 March 2006

B. Roberts
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland

Abstract

An analysis is made of the stability of an unsteady basic flow of a conducting fluid in the presence of a parallel magnetic field. The particular profile investigated is the classical Kelvin–Helmholtz profile modified by the addition of an oscillatory component. Two cases are considered in detail: that of a perfectly conducting fluid and that of a poorly conducting fluid. The investigation leads, in both cases, to an equation of the Hill type. It is concluded that the magnetic field has a stabilizing influence but is nevertheless unable to suppress the Kelvin–Helmholtz instability in an unsteady (basic) flow.

Type
Research Article
Copyright
© 1973 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. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Conrad, P. W. & Criminale, W. O. 1965 Z. angew. Math. Phys. 16, 233.
Drazin, P. G. 1960 J. Fluid Mech. 8, 130.
Drazin, P. G. 1961 J. Fluid Mech. 10, 571.
Drazin, P. G. 1967 Quart. J. Mech. Appl. Math. 20, 201.
Greenspan, H. P. & Benney, D. J. 1963 J. Fluid Mech. 15, 133.
Hains, F. D. 1965 Phys. Fluids, 8, 2014.
Hill, G. W. 1886 Acta. Math. 8, 1.
Kelly, R. E. 1965 J. Fluid Mech. 22, 547.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Mclachlan, N. W. 1947 Theory and Application of Mathieu Functions. Oxford University Press.
Shen, S. F. 1961 J. Aerospace Sci. 28, 397.
Stoker, J. J. 1950 Nonlinear Vibrations. Interscience.
Stuart, J. T. 1954 Proc. Roy. Soc. A, 221, 189.
Whittaker, E. T. & Watson, G. N. 1969 A Course of Modern Analysis. Cambridge University Press.