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An overview of Rayleigh-Taylor instability. (English) Zbl 0577.76047
Summary: The aim of this talk is to survey Rayleigh-Taylor instability, describing the phenomenology that occurs at a Taylor unstable interface, and reviewing attempts to understand these phenomena quantitatively.

MSC:
76E15 Absolute and convective instability and stability in hydrodynamic stability
76T99 Multiphase and multicomponent flows
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[1] Rayleigh, Lord, (), 200
[2] Taylor, G.I., (), 192
[3] Smarr, L.; Wilson, J.R.; Barton, R.T.; Bowers, R.L., Ap. j., 246, 515, (1981)
[4] Norman, M.L.; Smarr, L.; Wilson, J.R.; Smith, M.D., Ap. j., 247, 52, (1981)
[5] Lindl, J.D.; Mead, W.C.; McCrory, R.L.; Montierth, L.; Morse, R.L.; Verdon, C.P.; Evans, R.G.; Bennett, A.J.; Pert, G.J.; Emery, M.H.; Gardner, J.H.; Boris, J.P., Phys. rev. lett., Phys. rev. lett., Phys. rev. lett., Phys. rev. lett., 48, 677, (1982), Some examples are:
[6] Gerwin, R.A.; Malone, R.C., Nucl. fusion, 19, 155, (1979)
[7] A more realistic description of the interaction of laser light with the surface of a fusion target is given in D.W. Forslund, “The Importance of Surface Physics in Laser-Plasma Interactions”.
[8] Lewis, D.J., (), 81
[9] Birkhoff, G., Taylor instability and laminar mixing, Los alamos national laboratory report LA-1862, Appendices A-H issued as report LA-1927, (1956)
[10] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, (1961), Oxford Univ. Press Oxford, Chap. X · Zbl 0142.44103
[11] Mitchner, M.; Landshoff, R.K.M., Phys. fluids, 7, 862, (1964) · Zbl 0127.42502
[12] Plesset, M.S.; Hsieh, D-Y., Phys. fluids, 7, 1099, (1964) · Zbl 0124.19803
[13] Wolf, G.H., Z. physik, 227, 291, (1969)
[14] Richtmyer, R.D., Comm. pure and appl. math., 13, 297, (1960)
[15] LeLevier, R.; Lasher, G.J.; Bjorklund, F., Effect of a density gradient on Taylor instability, Lawrence livermore laboratory report UCRL-4459, (1955)
[16] Hunt, J.N., Appl. sci. res. A, 10, 45, (1961) · Zbl 0096.41702
[17] Menikoff, R.; Mjolsness, R.C.; Sharp, D.H.; Zemach, C., Phys. fluids, 20, 2000, (1977) · Zbl 0379.76041
[18] Menikoff, R.; Mjolsness, R.C.; Sharp, D.H.; Zemach, C.; Doyle, B.J., Phys. fluids, 21, 1674, (1978) · Zbl 0431.76047
[19] Axford, R.A., Initial value problems of the Rayleigh-Taylor instability type, Los alamos national laboratory report LA-5378, (1974)
[20] Bell, G.I., Taylor instability on cylinders and spheres in the small amplitude approximation, Los alamos national laboratory report LA-1321, (1951)
[21] Birkhoff, G., Quart. appl. math., 12, 306, (1954)
[22] Plesset, M.S., J. appl. phys., 25, 96, (1954)
[23] Plesset, M.S.; Mitchell, T.P., Quart. appl. math., 13, 419, (1956)
[24] Birkhoff, G., Quart. appl. math., 13, 451, (1956)
[25] Fisher, H.N., Instabilities in converging compressible systems, (1982), unpublished, Los Alamos
[26] Ott, E., Phys. rev. lett., 29, 1429, (1972)
[27] Fermi, E.; Fermi, E.; von Neumann, J., Taylor instability at the boundary of two incompressible liquids, (), Document AECU-2979, vol. 2, 821, (1953), This article is also published in Fermi’s collected papers
[28] Baker, L.; Freeman, J.R., Heuristic model of the nonlinear Rayleigh-Taylor instability, Sandia national laboratories report sand80-0700J, (1980)
[29] D. Levermore, private communication, 1983. · Zbl 0184.53705
[30] Davies, R.M.; Taylor, G.I., (), 375
[31] Layzer, D., Ap. j., 122, 1, (1955)
[32] Birkhoff, G.; Carter, D., J. math. mech., 6, 769, (1957)
[33] Garabedian, P.R., (), 423
[34] Menikoff, R.; Zemach, C., J. comp. phys., 36, 366, (1980)
[35] Menikoff, R.; Zemach, C., Rayleigh-Taylor instability and the use of conformal maps for ideal fluid flow, J. comp. phys., (1983), in press · Zbl 0563.76024
[36] Baker, G.R.; Meiron, D.I.; Orszag, S.A., Phys. fluids, 23, 1485, (1980)
[37] Verdon, C.P.; McCrory, R.L.; Morse, R.L.; Baker, G.R.; Meiron, D.I.; Orszag, S.A., Phys. fluids, 25, 1653, (1982)
[38] Harlow, F.H.; Welch, J.E., Phys. fluids, 9, 842, (1966)
[39] Daly, B.J., Phys. fluids, 10, 297, (1967)
[40] Daly, B.J., Phys. fluids, 12, 1340, (1969)
[41] Freeman, J.R.; Clauser, M.J.; Thompson, S.L., Nucl. fusion, 17, 223, (1977)
[42] Meyer, K.A.; Blewett, P.J., Some preliminary numerical studies of Taylor instability which include effects of material strength, Los alamos national laboratory report LA-4754-MS, (1971)
[43] Meyer, K.A.; Blewett, P.J., Phys. fluids, 15, 753, (1972)
[44] Glimm, J.; McBryan, O.; Menikoff, R.; Sharp, D.H., Front tracking applied to Rayleigh-Taylor instability, (1983), in preparation · Zbl 0582.76107
[45] O. McBryan, “Computing Discontinuous Flows”, these proceedings.
[46] D.L. Youngs, private communication, 1983.
[47] Sharp, D.H.; Wheeler, J.A., Late stage of Rayleigh-Taylor instability, Institute for defense analyses, (1961), Unpublished report
[48] Birkhoff, G.; Zarantonello, E.H., Jets, wakes and cavities, (1957), Academic Press New York, chap. XV · Zbl 0077.18703
[49] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, (1961), Oxford Univ. Press Oxford, chap. XII · Zbl 0142.44103
[50] Rayleigh, Lord, (), 361
[51] Read, K.I.; Youngs, D.L., Experimental investigation of turbulent mixing by Rayleigh-Taylor instability, AWRE report no. 011/83, (1983)
[52] Youngs, D.L., Turbulent mixing by Rayleigh-Taylor instability, Physica, 12D, 32, (1984), these Proceedings
[53] Reitz, R.D.; Bracco, F.V., Phys. fluids, 25, 1730, (1982)
[54] Wallis, G.B., One-dimensional two-phase flow, (1969), McGraw-Hill New York, chap. 12
[55] Allred, J.C.; Blount, G.H., Experimental studies of Taylor instability, Los alamos national laboratory report LA-1600, (1953)
[56] Duff, R.E.; Harlow, F.H.; Hirt, C.W., Phys. fluids, 5, 417, (1962)
[57] Emmons, H.W.; Chang, C.T.; Watson, B.C., J. fluid mech., 7, 177, (1960)
[58] Ratafia, M., Phys. fluids, 16, 1207, (1973)
[59] Cole, R.L.; Tankin, R.S., Phys. fluids, 16, 1810, (1973)
[60] Popil, R.; Curzon, F.L., Rev. sci. instr., 50, 1291, (1979)
[61] Barnes, J.F.; Blewett, P.J.; McQueen, R.G.; Meyer, K.A.; Venable, D., J. appl. phys., 45, 727, (1974)
[62] Barnes, J.F.; Janney, D.H.; London, R.K.; Meyer, K.A.; Sharp, D.H., J. appl. phys., 51, 4678, (1980)
[63] Orszag, S.A., Generalized vortex methods in 3-dimensional Rayleigh-Taylor instability, Physica, 12D, 19, (1984), these Proceedings
[64] This suggestion was formulated in conversations with J. Glimm and H.A. Rose.
[65] Mandelbrot, B., J. fluid mech., 62, 331, (1974)
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