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Rayleigh-Taylor instability of fluid layers

Published online by Cambridge University Press:  21 April 2006

G. R. Baker ,
R. L. Mccrory ,
C. P. Verdon  and
S. A. Orszag
G. R. Baker
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
R. L. Mccrory
Affiliation:
Laboratory for Laser Energetics, University of Rochester, NY 14627, USA
C. P. Verdon
Affiliation:
Laboratory for Laser Energetics, University of Rochester, NY 14627, USA
S. A. Orszag
Affiliation:
Applied and Computational Mathematics, Princeton University, NJ 08540, USA
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Abstract

It is shown that the Rayleigh-Taylor instability of an accelerating incompressible, inviscid fluid layer is the result of pressure gradients, not gravitational acceleration. As in the classical Rayleigh-Taylor instability of a semi-infinite layer, finite fluid layers form long thin spikes whose structure is essentially independent of the initial thickness of the layer. A pressure maximum develops above the spike that effectively uncouples the flow in the spike from the rest of the fluid. Interspersed between the spikes are rising bubbles. The bubble motion is seriously affected by the thickness of the layer. For thin layers, the bubbles accelerate upwards exponentially in time and the layer thins so rapidly that it may disrupt at finite times.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 161 - 175
Copyright
© 1987 Cambridge University Press

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References

Baker, G. R. 1983 Generalized vortex methods for free-surface flows. In Waves on Fluid Interfaces (ed. R. E. Meyer), pp. 53–81. MCK, University of Wisconsin, Madison.
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1980 Vortex simulations of the Rayleigh-Taylor instability. Phys. Fluids 23, 1485–1490.Google Scholar
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477–501.Google Scholar
Baker, G. R. & Shelley, M. 1986 Boundary integral methods for multi-connected domains. J. Comp. Phys. 64, 112–132.Google Scholar
Dagan, G. 1975 Taylor instability of a non-uniform free-surface flow. J. Fluid Mech. 67, 113–123.Google Scholar
Daly, B. J. 1967 Numerical study of two fluid Rayleigh-Taylor instability. Phys. Fluids 10, 297–307.Google Scholar
Fraley, G., Gula, W., Henderson, D., McCrory, R., Malone, R., Mason, R. & Morse, R. 1974 Implosion, stability and burn at multi-shell fusion pellets. In Plasma Physics and Controlled Nuclear Fusion Research, vol. 2, pp. 543–549. Tokyo, Japan. (international Atomic Energy Agency, Vienna, Austria).
Maskew, B. 1977 Subvortex technique for the close approach to a discretized vortex sheet. J. Aircraft 14, 188–196.Google Scholar
Mason, R. J. 1975 The calculated performance of structured laser fusion pellets. Nuclear Fusion 15, 1031–1044.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
Pullin, D. I. 1982 Numerical studies of surface-tension effects in nonlinear Kelvin-Helmholtz and Rayleigh-Taylor instabilities. J. Fluid Mech. 119, 507–532.Google Scholar
Sharp, D. H. 1984 An overview of Rayleigh-Taylor instability. Physica 12, 31–18.Google Scholar
Shelley, M. J. & Baker, G. R. 1987 Order preserving approximations to successive derivatives of periodic functions by iterated splines. SIAM J. Num. Anal. (In press).Google Scholar
Verdon, C. P., McCrory, R. L., Morse, R. L., Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Nonlinear effects of multi-frequency hydrodynamic instabilities on ablatively accelerating thin shells. Phys. Fluids 25, 1653–1673.Google Scholar