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Kelvin–Helmholtz instability of finite amplitude

Published online by Cambridge University Press:  29 March 2006

P. G. Drazin
Affiliation:
University of Bristol

Abstract

Non-linear Kelvin–Helmholtz instability, of two parallel horizontal streams of inviscid incompressible fluids under the action of gravity, is studied theoretically. The lower stream is denser and there is surface tension between the streams. Some progressing waves of finite amplitude are found as the development of a slightly unstable wave of infinitesimal amplitude. In particular, the non-linear elevation of the interface between the fluids is calculated. The finite amplitude of the waves does not equilibrate to a constant after a long time, but varies periodically with time. In practice, slight dissipation should lead to equilibration at an amplitude close to a value given by the present theory.

Type
Research Article
Copyright
© 1970 Cambridge University Press

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References

Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Drazin, P. G. & Howard, L. N. 1966 Advanc. Appl. Mech. 9, 1.
Landau, L. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon.
Miles, J. W. 1959 J. Fluid Mech. 6, 58.
Palm, E. 1960 J. Fluid Mech. 8, 18.
Stuart, J. T. 1960 J. Fluid Mech. 9, 35.
Thorpe, S. A. 1968 J. Fluid Mech. 32, 69.
Thorpe, S. A. 1969 J. Fluid Mech. 39, 2.
Watson, J. 1960 J. Fluid Mech. 9, 37.
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