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Stability of the parallel flow of a fluid over a slightly heavier fluid

Published online by Cambridge University Press:  28 March 2006

Robin E. Esch
Robin E. Esch
Affiliation:
Computation Laboratory, Harvard University
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Abstract

The incompressible, inviscid, parallel flow of a layer of fluid over a slightly denser fluid, in the presence of gravity, is investigated for stability. Two idealized piece-wise-linear steady velocity profiles are examined analytically, and a comparison with related experimental results is made.

The dimensionless parameter U/(gh)½, where U is flow velocity, g the acceleration of gravity, and h the thickness of the upper layer, appears to have a critical value between 0.2 and 0.7, below which stable flows can persist. At the onset of instability disturbances of wavelength about h or 2h are predicted, with more violent disturbances of longer wavelength occurring at higher values of U/(gh)½ For continuous steady velocity profiles this instability phenomenon is found to be relatively insensitive to the ratio of the densities of the two fluids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 2 , February 1962 , pp. 192 - 208
Copyright
© 1962 Cambridge University Press

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