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A Review of the Richtmyer-Meshkov Instability from an Experimental Perspective

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30th International Symposium on Shock Waves 1

Abstract

The events following the impulsive acceleration (e.g. by a shock wave) of the interface between gases of different acoustic impedance can be classified into two main categories: the refraction of the shock (involving a transmitted and a reflected shock and the distortion of their shapes) and the baroclinic generation of vorticity at the interface consequent to the non-zero cross product between the density gradient associated with the interface and the pressure gradient across the shock wave. The resulting flow field leads to the unbounded growth of any perturbations initially present on the interface, a phenomenon called the Richtmyer-Meshkov instability (RMI). Because it originates from baroclinic vorticity, the RMI can be interpreted as the “impulsive analog” of the Rayleigh-Taylor instability (RTI) which develops at an interface subjected to sustained acceleration.

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References

  1. Taylor, G.I: The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. Roy. Soc. A 201, 192 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  2. Richtmyer, R.D.: Taylor instability in shock acceleration of compressible fluids. Comm. Pure Appl. Math. 8, 297 (1960)

    Article  MathSciNet  Google Scholar 

  3. Meshkov, Y.Y.: Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101 (1969). [Izv. Akad. Nauk SSSR Mekh. Zhdik. Gaza 5, 151 (1969)]

    Google Scholar 

  4. Andronov, V.A., Bakhrakh, S.M., Meshkov, E.E., Mokhov, V.N., Nikiforov, V.V., Pevnitskii, A.V., Tolshmyakov, A.I.: Turbulent mixing at contact surface accelerated by shock waves. Sov. Phys. JETP 44 (2), 424 (1976)

    Google Scholar 

  5. Aleshin, A.N., Lazareva, E.V., Zaitsev, S.G., Rozanov, V.B., Gamalli, E.G., Lebo, I.G.: Linear, nonlinear, and transient stages in the development of the Richtmyer-Meshkov instability. Sov. Tech. Phys. Lett. 35 (2), 159 (1990)

    Google Scholar 

  6. Vetter, M., Sturtevant, B.: Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface. Shock Waves 4, 247 (1995)

    Article  Google Scholar 

  7. Nevmerzhitsky, N.V., Sotskov, E.A., Senkovsky, E.D., Razin, A.N., Ustinenko, V.A., Krivonos, O.L., Tochilina, L.V.: The influence of the Mach number of shock waves on turbulent mixing growth at an interface of gases. Phys. Scr. T142, 014016 (2010)

    Article  Google Scholar 

  8. Vanderboomgaerde, M., Souffland, D., Mariani, C., Biamino, L., Jourdan, G., Houas, L.: An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability. Phys. Fluids 24, 024109 (2014)

    Article  Google Scholar 

  9. Malamud, G., Leinov, E., Sadot, O., Elbaz, Y., Ben-Dor, G., Shvarts, D.: Reshocked Richtmyer-Meshkov instability: Numerical study and modeling of random multi-mode experiments. Phys. Fluids 26, 084107 (2014)

    Article  MATH  Google Scholar 

  10. Luo, X., Wang, X., Si, T.: The Richtmyer-Meshkov instability of a three-dimensional air/SF6 interface with a minimum-surface feature. J. Fluid Mech. 722, R2 (2013)

    Article  MATH  Google Scholar 

  11. Erez, L., Sadot, O., Oron, D., Erez, G., Levin, L.A., Shvarts, D., Ben-Dor, G.: Study of the membrane effect on turbulent mixing measurements in shock tubes. Shock Waves 10, 241–251 (2000)

    Article  Google Scholar 

  12. Jacobs, J.W., Jenkins, D.G., Klein, D.L., Benjamin, R.F.: Nonlinear growth of the shock-accelerated instability of a thin fluid layer. J. Fluid Mech. 295, 2342 (1995)

    Article  MathSciNet  Google Scholar 

  13. Orlicz, G.C., Balasubramanian, S., Prestridge, K.P.: Incident shock Mach number effects on Richtmyer-Meshkov mixing in a heavy gas layer. Phys. Fluids 25, 114101 (2013)

    Article  Google Scholar 

  14. Brouillette, M., Sturtevant, B.: Experiments on the Richtmyer-Meshkov instability: Small scale perturbations on a plane interface. Phys. Fluids A 5 (4), 916–930 (1993)

    Article  Google Scholar 

  15. Brouillette, B., Sturtevant, B.: Experiments on the Richtmyer-Meshkov instability: single scale perturbations on a continuous interface. J. Fluid Mech. 263, 271–292 (1994)

    Article  Google Scholar 

  16. Bonazza, R., Sturtevant, B.: X-ray measurements of growth rates at a gas interface accelerated by shock waves. Phys. Fluids 8 (9), 2496–2512 (1996)

    Article  Google Scholar 

  17. Jones, M.A., Jacobs, J.W.: A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface. Phys. Fluids 9 (10), 3078–3085 (1997)

    Article  Google Scholar 

  18. Jacobs, J.W., Krivets, V.V., Tsiklashvili, V., Likhachev, O.A.: Experiments on the Richtmyer-Meshkov instability with an imposed, random initial perturbation. Shock Waves 23, 407–413 (2013)

    Article  Google Scholar 

  19. Morgan, R.V., Aure, R., Stockero, J.D., Greenough, J.A., Cabot, W., Likhachev, O.A., Jacobs, J.W.: On the late-time growth of the two-dimensional Richtmyer-Meshkov instability in shock tube experiments. J. Fluid Mech. 712, 354–383 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Motl, B., Oakley, J., Ranjan, D., Weber, C., Anderson, M., Bonazza, R.: Experimental validation of a Richtmyer-Meshkov scaling law over large density ratio and shock strength ranges. Phys. Fluids 21, 126102 (2009)

    Article  MATH  Google Scholar 

  21. Weber, C., Haehn, N., Oakley, J., Anderson, M., Bonazza, R.: Richtmyer-Meshkov instability on a low Atwood number interface after reshock. Shock Waves 22, 317–325 (2012)

    Article  Google Scholar 

  22. Weber, C., Haehn, N., Oakley, J., Rothamer, D., Bonazza, R.: Turbulent mixing measurements in the Richtmyer-Meshkov instability. Phys. Fluids 24, 074105 (2012)

    Article  Google Scholar 

  23. Weber, C, Haehn, N., Oakley, J., Rothamer, D., Bonazza, R.: An experimental investigation of the turbulent mixing transition in the Richtmyer-Meshkov instbility. J. Fluid Mech. 748, 457–487 (2014)

    Article  Google Scholar 

  24. Mikaelian, K.O.: Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E 67, 026319 (2003)

    Article  Google Scholar 

  25. Oron, D., Arazi, L., Kartoon, D., Rikanati, A., Alon, U., Shvarts, D.: Dimensionality dependence of the Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws. Phys. Plasmas 8, 2108–2115 (2001)

    Article  Google Scholar 

  26. Zhang, Q., Sohn, S.I.: Padé approximation to an interfacial fluid mixing problem. Appl. Math. Lett. 10, 121–127 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L.A., Erez, G., Ben-Dor, G., Shvarts, D.: Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability. Phys. Rev. Lett. 80, 1654–1657 (1988)

    Article  Google Scholar 

  28. Mikaelian, K.O.: Testing an analytic model for Richtmyer-Meshkov turbulent mixing widths. Shock Waves 25, 35–45 (2015)

    Article  Google Scholar 

  29. Tritschler, V.K., Hickel, S., Hu, X.Y., Adams, N.A.: On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability. Phys. Fluids 25, 071701 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Physics, University of Wisconsin, 1500 Engineering Drive, 53706, Madison, WI, USA

    R. Bonazza

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  1. R. Bonazza
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Correspondence to R. Bonazza .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel

    Gabi Ben-Dor

  2. Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Oren Sadot

  3. Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel

    Ozer Igra

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Bonazza, R. (2017). A Review of the Richtmyer-Meshkov Instability from an Experimental Perspective. In: Ben-Dor, G., Sadot, O., Igra, O. (eds) 30th International Symposium on Shock Waves 1. Springer, Cham. https://doi.org/10.1007/978-3-319-46213-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-46213-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46211-0

  • Online ISBN: 978-3-319-46213-4

  • eBook Packages: EngineeringEngineering (R0)

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