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The character of the equilibrium of an incompressible heavy viscous fluid of variable density

Published online by Cambridge University Press:  24 October 2008

S. Chandrasekhar
S. Chandrasekhar
Affiliation:
Yerkes Observatory and Institute for Nuclear StudiesUniversity of Chicago
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Abstract

This paper is devoted to a consideration of the following problem: Given a static state in which an incompressible viscous fluid is arranged in horizontal strata and the density is a function of the vertical coordinate only, to determine the initial manner of development of an infinitesimal disturbance. The mathematical problem is reduced to one in characteristic values in a fourth-order differential equation and a variational principle characterizing the solution is enunciated. The particular case of two uniform fluids of different densities (but the same kinematic viscosity) separated by a horizontal boundary is considered in some detail. The mode of maximum instability in case the upper fluid is more dense and the manner of decay in case the lower fluid is more dense are determined; and the results of the calculations are illustrated graphically. Gravity waves (obtained in the limit when the density of the upper fluid is zero) are also treated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 162 - 178
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Chandrasekhar, S.Quart. J. Mech. (in the Press).Google Scholar
(2)Harrison, W. J.Proc. Lond. math. Soc. 6 (1908), 396–405.CrossRefGoogle Scholar
(3)Hide, R.Proc. Camb. phil. Soc. 51 (1955), 179–201.CrossRefGoogle Scholar
(4)Lamb, H.Hydrodynamics, 6th ed. (Cambridge, 1931).Google Scholar
(5)Lewis, W. J.Proc. roy. Soc. A, 202 (1950), 81–98.Google Scholar
(6)Rayleigh, Lord. Proc. Lond. math. Soc. 14 (1883), 170–77Google Scholar
Rayleigh, Lord. also, Scientific Papers, vol. 2, pp. 200–207.Google Scholar
(7)Taylor, G. I.Proc. roy. Soc. A, 201 (1950), 192–96.Google Scholar