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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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References

Bellman, R. & Pennington, R. H. 1954 Effects of surface tension and viscosity on Taylor instability. Quart. appl. Math. 12, 151.Google Scholar
Bjerknes, V., Bjerknes, J., Solberg, H. & Bergeron, T. 1933 Physikalische Hydrodynamik. Berlin: Springer.
Drazin, P. G. 1958 The stability of a shear layer in an unbound heterogeneous inviscid fluid. J. Fluid Mech. 4, 214.Google Scholar
Esch, R. E. 1957 The instability of a shear layer between two parallel streams. J. Fluid Mech. 3, 289.Google Scholar
Godske, C. L., Bergeron, T., Bjerknes, J. & Bundgaard, R. C. 1957 Dynamic Meteorology and Weather Forecasting. Boston, American Meteorological Society, and Washington, Carnegie Institute of Washington.
Goldstein, S. 1931 On the stability of superposed streams of fluids of different densities. Proc. Roy. Soc. A, 132, 524.Google Scholar
Kunz, K. S. 1957 Numerical Analysis. New York: McGraw-Hill.
Lamb, H. 1945 Hydrodynamics. Cambridge University Press.
Lin, C. C. 1955 Theory of Hydrodynamic Stability. Cambridge University Press.
Menkes, J. 1959 On the stability of a shear layer. J. Fluid Mech. 6, 518.Google Scholar
Rayleigh, Lord 1945 Theory of Sound. New York: Dover.
Taylor, G. I. 1931 Effect of variation in density on the stability of superposed streams of fluid. Proc. Roy. Soc. A, 132, 499.Google Scholar