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Kelvin-Helmholtz instability of a slowly varying flow

Published online by Cambridge University Press:  29 March 2006

P. G. Drazin
P. G. Drazin
Affiliation:
Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado
Permanent address: School of Mathematics, University of Bristol, England.
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Abstract

The linear stability of a basic flow of two homogeneous inviscid incompressible fluids under the action of gravity is treated mathematically. In the basic state, one fluid is at rest below a horizontal plane z = 0; and the other flows above in the x direction, its speed varying slowly with the lateral co-ordinate y. The eigenvalue problem for normal modes is derived; its equation is a partial differential one, the co-ordinates y and z not being separable. The problem is solved approximately by taking the modes locally as if the basic velocity were independent of y, though the lateral wavenumber is allowed to vary slowly with y. This leads to an ordinary differential equation in y which is solved by the JWKB method. Detailed calculations are made for a parabolic profile, representing the blowing of air over water in a wide channel, and for other profiles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 4 , 2 October 1974 , pp. 781 - 797
Copyright
© 1974 Cambridge University Press

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References

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