Summary
The authors consider the case of two compressible, non-viscous fluids, one above the other, and investigate the stability of their equilibrium under the action of gravity. It is found that the equilibrium is stable if and only if the density of the upper fluid in the immediate vicinity of the interface is less than that of the lower.
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References
G. Stokes,On the Theory of Oscillatory Waves, « Camb. Trans. », vii (1847) (Pages i, 212).
S. Chandrasekhar,The character of the equilibrium of an incompressible heavy viscous fluid of variable density, « Proc. Camb. Phil. Soc. », 51 (1955), 162–178.
R. Hide,The character of the equilibrium of an incompressible heavy viscous fluid of variable density in an approximate theory, « Proc. Camb. Phil. Soc. », 51 (1955), 179–201.
Cf.E. T. Whittaker andG. N. Watson,Modern Analysis, Cambridge (1940). p. 337.
Cf.H. Lamb,Hydrodynamics, Cambridge (1932), p. 370.
Cf.Whittaker andWatson,op. cit., p. 343.
Cf.Lamb,op. cit., p. 371.
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To Mauro Picone on his 70th birthday.
Work was cosponsored by the Office of Naval Research and the U. S. Army under Contract No. N-7-ONR-38801 and Contract No. DA-36-034-ORD-1646, respectively.
On leave from the Weizmann Institute of Science, Rehovoth, Israel.
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Goldstine, H.H., Gillis, J. On the stability of two superposed compressible fluids. Annali di Matematica 40, 261–267 (1955). https://doi.org/10.1007/BF02416537
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DOI: https://doi.org/10.1007/BF02416537