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On the steady solutions of the problem of Rayleigh–Taylor instability

Published online by Cambridge University Press:  21 April 2006

M. J. Tan
M. J. Tan
Affiliation:
Centre d'Etudes Nucléaires de Grenoble, Service des Transferts Thermiques, 85 X, 38041 Grenoble, France Present address: Chemical Engineering Department, Northwestern University, Evanston, Illinois 60201.
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Abstract

The problem of Rayleigh–Taylor instability is reexamined within the framework of incompressible, inviscid and irrotational fluid flow in a bounded three-dimensional domain. A relation proposed by Pimbley (1976) between the slope and the amplitude of the interface at the rigid boundary is adopted as the interface boundary condition. Steady solutions are derived in approximate form by using bifurcation theory. It is shown that under the conditions given some of the steady solutions exhibit the features of the well-known bubbles-and-spikes configuration and can be stable to infinitesimal disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 339 - 353
Copyright
© 1986 Cambridge University Press

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References

Baker, L. & Freeman J. R.1981 Heuristic model of the nonlinear Rayleigh—Taylor instability. J. Appl. Phys. 52, 655–663.Google Scholar
Baker G. R., Meiron, D. I. & Orszag S. A.1980 Vortex simulation of the Rayleigh—Taylor instability. Phys. Fluids 23, 1485–1490.Google Scholar
Bauer L., Keller, H. B. & Reiss R. L.1975 Multiple eigenvalues lead to secondary bifurcation. SIAM Rev. 17, 101–122.Google Scholar
Bellman, R. & Pennington R. H.1954 Effects of surface tension and viscosity on Taylor instability. Q. Appl. Maths 12, 151–162.Google Scholar
Daly B. J.1969 Numerical study of the effect of surface tension on interface instability. Phys. Fluids 12, 1340–1354.Google Scholar
Dienes J. K.1978 Method of generalized coordinates and an application to Rayleigh—Taylor instability. Phys. Fluids 21, 736–744.Google Scholar
Dussan V, E. B. 1983 The moving contact line. In Waves on Fluid Interfaces (ed. R. E. Meyer), pp. 303–324. Academic.
Emmons H. W., Chang, C. T. & Watson B. C.1960 Taylor instability of finite surface waves. J. Fluid Mech. 7, 177–193.Google Scholar
Korn, G. A. & Korn T. M.1961 Mathematical Handbook for Scientists and Engineers, p. 509. McGraw-Hill.
Lewis D. J.1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, II Proc. R. Soc. Lond. A 202, 81–96.Google Scholar
Menikoff, R. & Zemach C.1983 Rayleigh—Taylor instability and the use of conformal maps for ideal fluid flow. J. Comp. Phys. 51, 28–64.Google Scholar
Miles, J. M. & Dienes J. K.1966 Taylor instability in a viscous liquid. Phys. Fluids 9, 2518–2519.Google Scholar
Morse, P. M. & Feshbach H.1953 Methods of Theoretical Physics. McGraw-Hill.
Pimbley G. H.1976 Stationary solutions of the problem of Rayleigh—Taylor instability. J. Math. Anal. Applics 55, 170–206.Google Scholar
Rayleigh Lord1900 In Scientific Papers, vol. II, pp. 200–227. Cambridge University Press.
Stakgold I.1971 Branching of solutions of nonlinear equations. SIAM Rev. 13, 289–332.Google Scholar
Stakgold I.1979 Green's Functions and Boundary Value Problems, p. 201. Wiley.
Taylor G. I.1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, I Proc. R. Soc. Lond. A 201, 192–196.Google Scholar