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Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface

Published online by Cambridge University Press:  26 April 2006

M. Brouillette  and
B. Sturtevant
M. Brouillette
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA Present address: Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1.
B. Sturtevant
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

We report on experiments to measure the shock-induced growth of sinusoidal perturbations on thick interfaces separating two gases of different densities. The results show that the growth rates are reduced as the interface thickness is increased. A model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface is proposed and good agreement is obtained with the experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 271 - 292
Copyright
© 1994 Cambridge University Press

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References

Afanas’ev, Yu. F., Basov, N. G., Gamalii, E. G., Krokhin, O. N. & Rozanov, V. B. 1976 Symmetry and stability of laser-drive compression thermonuclear targets. JETP Lett. 23, 566–569.Google Scholar
Andronov, V. A., Bakhrakh, S. M., Meshkov, E. E., Mokhov, V. N., Nikiforov, V. V., Pevnitskii, A. V. & Tolshmyakov, A. I. 1976 Turbulent mixing at contact surface accelerated by shock waves. Sov. Phys. JETP 44, 424–427.Google Scholar
Bellman, R. & Pennington, R. H. 1954 Effects of Surface Tension and Viscosity on Taylor Instability. Quart. Appl. Math. 12, 151–162.Google Scholar
Benjamin, R. F. & Fritz, J. N. 1987 Shock loading a rippled interface between liquids of different densities. Phys. Fluids 30, 331–336.Google Scholar
Benjamin, R. F., Trease, H. E. & Shaner, J. W. 1984 Coherent density gradients in water compressed by a modulated shock wave. Phys. Fluids 27, 2390–2393.Google Scholar
Bonazza, R. 1992 X-ray measurements of shock-induced mixing at an air/xenon interface. PhD thesis, California Institute of Technology.
Brouillette, M. 1989 On the interaction of shock waves with contact surfaces between gases of different densities. PhD thesis, California Institute of Technology.
Brouillette, M. & Sturtevant, B. 1989 Growth induced by multiple shock waves normally incident on plane gaseous interfaces. Physica D 37, 248–263.Google Scholar
Brouillette, M. & Sturtevant, B. 1993 Experiments on the Richtmyer—Meshkov instability: small-scale perturbations on a plane interface. Phys. Fluids A 5, 916–930.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Cole, R. H. 1948 Underwater Explosions. Princeton University Press.
Duff, R. E., Harlow, F. H. & Hirt, C. W. 1962 Effects of diffusion on interface instability between gases. Phys. Fluids 5, 417–425.Google Scholar
Emery, M. H., Gardner, J. H. & Boris, J. 1982 Rayleigh—Taylor and Kelvin—Helmoltz instability in targets accelerated by laser ablation. Phys. Rev. Lett. 48, 677–680.Google Scholar
Frost, D. L. 1988 Dynamics of explosive boiling of a droplet. Phys. Fluids 31, 2554–2561.Google Scholar
Grun, J., Emery, M. H., Kacenjar, S., Opal, C. B., McLean, E. A., Obenschain, S., Ripin, B. H. & Schmitt, A. 1984 Observation of the Rayleigh—Taylor instability in ablatively accelerated foils. Phys. Rev. Lett. 53, 1352–1355.Google Scholar
Kiang, R. L. 1969 Nonlinear Theory of inviscid Taylor instability near the cutoff wavenumber. Phys. Fluids 12, 1333–1339.Google Scholar
Kline, S. J. 1967 Observed structure features in turbulent and transitional boundary layers. In Fluid Mechanics of Internal Flow, pp. 27–68. Elsevier.
LeLevier, R., Lasher, G. J. & Bjorklund, F. 1955 Effect of a density gradient on Taylor instability. Rep. UCRL-4459. University of California Radiation Laboratory.Google Scholar
Lindl, J. D. & Mead, W. C. 1975 Two-dimensional simulation of fluid instability in laser-fusion pellet. Phys. Rev. Lett. 34, 1273–1276.Google Scholar
Marble, F. E., Hendricks, G. J. & Zukoski, E. E. 1987 Progress toward shock enhancement of supersonic combustion processes. AIAA paper 87-1880.Google Scholar
Markstein, G. H. 1957a A shock tube study of flame front—pressure wave interaction. In Sixth Symp. (Intl) on Combustion, pp. 387–390. Reinhold.
Markstein, G. H. 1957b Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave. J. Aero. Sci. 24, 238–239.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn. 4, 101–108.Google Scholar
Meyer, K. A. & Blewett, P. J. 1972 Numerical investigation of the stability of a shock accelerated interface between two fluids. Phys. Fluids 15, 753–757.Google Scholar
Mikaelian, K. O. 1985 Richtmyer—Meshkov instabilities in stratified fluids. Phys. Rev. A 31, 410–419.Google Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.Google Scholar
Rayleigh, Lord 1900 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. In Scientific Papers, Vol. 2, p. 200. Dover.
Read, K. I. 1984 Experimental investigation of turbulent mixing by Rayleigh—Taylor instability. Physica D 12, 45–58.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 8, 297–319.Google Scholar
Saffman, P. G. & Meiron, D. 1989 Kinetic energy generated by the incompressible Richtmyer—Meshkov instability in a continuously stratified fluid. Phys. Fluids A 1, 1767–1771.Google Scholar
Sharp, D. H. 1984 An overview of Rayleigh—Taylor instability. Physica D 12, 3–18.Google Scholar
Smarr, L., Wilson, J. R., Barton, R. T. & Bowers, R. L. 1981 Rayleigh—Taylor overturn in supernova core collapse. Astrophys. J. 246, 515–525.Google Scholar
Stalker, R. J. & Crane, K. C. A. 1978 Driver gas contamination in a high-enthalpy reflected shock tunnel. AIAA J. 16, 277–279.Google Scholar
Sturtevant, B. 1988 Rayleigh—Taylor instability in compressible fluids. In Shock Tubes and Waves (ed. H. GröNig), pp. 89–100. Wendheim: VCH.
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
Waitz, I. A., Marble, F. E. & Zukoski, E. E. 1991 An investigation of a contoured wall injector for hypervelocity mixing augmentation. AIAA paper 91-2265.Google Scholar