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Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

Abstract

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1− 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm(E−1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.

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References

  1. Richtmyer R.D.: Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319 (1960)

    MathSciNet  Article  Google Scholar 

  2. Meshkov E.E.: Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104 (1972)

    Article  Google Scholar 

  3. Brouillette M.: The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468 (2002)

    MathSciNet  Article  Google Scholar 

  4. Kane J., Drake R.P., Remington B.A.: An evaluation of the Richtmyer–Meshkov instability in supernova remnant formation. Astrophys. J. 511, 335–340 (1999)

    Article  Google Scholar 

  5. Anderson M.H., Puranik B.P., Oakley J.G., Brooks P.W., Bonazza R.: Shock tube investigation of hydrodynamic issues related to inertial confinement fusion. Shock Waves 10, 377–387 (2000)

    Article  Google Scholar 

  6. Zabusky N.J.: Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the Rayleigh–Taylor and Richtmyer– Meshkov environments. Annu. Rev. Fluid Mech. 31, 495–536 (1999)

    MathSciNet  Article  Google Scholar 

  7. Krivets, V.V., Long, C.C., Jacobs, J.W., Greenough, J.A.: Shock tube experiments and numerical simulation of the single mode three-dimensional Richtmyer-Meshkov instability. In: 26th International Symposium on Shock Waves. pp. 1205–1210. Springer, Gottingen (2009)

  8. 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  Google Scholar 

  9. Chapman P.R., Jacobs J.W.: Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101 (2006)

    Article  Google Scholar 

  10. Ranjan D., Oakley J., Bonazza R.: Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140 (2011)

    MathSciNet  Article  Google Scholar 

  11. Ranjan D., Niederhaus J., Motl B., Anderson M., Oakley J., Bonazza R.: Experimental investigation of primary and secondary features in high-Mach-number shock-bubble interaction. Phys. Rev. Lett. 98, 024502 (2007)

    Article  Google Scholar 

  12. Ranjan D., Anderson M., Oakley J., Bonazza R.: Experimental investigation of a strongly shocked gas bubble. Phys. Rev. Lett. 94, 184507 (2005)

    Article  Google Scholar 

  13. Prestridge K., Vorobieff P., Rightley P.M., Benjamin R.F.: Validation of an instability growth model using particle image velocimetry measurements. Phys. Rev. Lett. 84, 4353–4356 (2000)

    Article  Google Scholar 

  14. Balakumar B.J., Orlicz G.C., Tomkins C.D., Prestridge K.P.: Particle-image velocimetry-planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock. Phys. Fluids 20, 124103 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Herrmann M., Moin P., Abarzhi S.I.: Nonlinear evolution of the Richtmyer–Meshkov instability. J. Fluid Mech. 612, 311–338 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  17. Gupta M.R., Roy S., Khan M., Pant H.C., Sarkar S., Srivastava M.K.: Effect of compressibility on the Rayleigh–Taylor and Richtmyer–Meshkov instability induced nonlinear structure at two fluid interface. Phys. Plasmas 16, 032303 (2009)

    Article  Google Scholar 

  18. Rikanati A., Oron D., Sadot O., Shvarts D.: High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability. Phys. Rev. E 67, 026307 (2003)

    Article  Google Scholar 

  19. Schilling O., Latini M.: High-order WENO simulations of three-dimensional reshocked Richtmyer-Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data. Acta Math. Sci. 30, 595–620 (2010)

    MathSciNet  MATH  Google Scholar 

  20. Thornber B., Drikakis D., Youngs D.L., Williams R.J.R.: The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability. J. Fluid Mech. 654, 99–139 (2010)

    MATH  Article  Google Scholar 

  21. Leinov E., Malamud G., Elbaz Y., Levin L.A., Ben-Dor G., Shvarts D., Sadot O.: Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449–475 (2009)

    MATH  Article  Google Scholar 

  22. Schilling, O., Latini, M., Don, W.: Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability. Phys. Rev. E 76(2007)

  23. Niederhaus, J.H.J., Ranjan, D., Oakley, J.G., Anderson, M.H., Greenough, J.A., Bonazza, R.: Computations in 3D for shock-induced distortion of a light spherical gas inhomogeneity. In: Shock waves, Part XVIII. Springer, Berlin, pp 1169–1174. doi:10.1007/978-3-540-85181-3_60

  24. Dimonte G., Ramaprabhu P.: Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104 (2010)

    Article  Google Scholar 

  25. McFarland J., Greenough J., Ranjan D.: Computational parametric study of a Richtmyer–Meshkov instability for an inclined interface. Phys. Rev. E 84, 026303 (2011)

    Article  Google Scholar 

  26. Aleshin A.N., Zaitsev S.G., Lazareva E.V.: Damping of perturbations at a shock front in the presence of a Richtmyer–Meshkov instability. Sov. Tech. Phys. Lett. 17, 493–496 (1991)

    Google Scholar 

  27. Aleshin, A.N., Chebotareve, E.I., Krivets, V.V., Lazareva, E.V., Sergeev, S.V., Titov, S.N., Zaytsev, S.: Investigation of Evolution of Interface After Its Interaction with Shock Waves. International Institute for Applied Physics and High Technology, Moscow (1996)

  28. Kolev T.V., Rieben R.N.: A tensor artificial viscosity using a finite element approach. J. Comput. Phys. 228, 8336–8366 (2009)

    MathSciNet  MATH  Article  Google Scholar 

  29. Sharp R.W., Barton R.T.: HEMP Advection Model. Lawrence Livermore Laboratory, Livermore (1981)

    Google Scholar 

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Correspondence to D. Ranjan.

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Communicated by R. Bonazza.

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Bailie, C., McFarland, J.A., Greenough, J.A. et al. Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave. Shock Waves 22, 511–519 (2012). https://doi.org/10.1007/s00193-012-0382-y

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  • DOI: https://doi.org/10.1007/s00193-012-0382-y

Keywords

  • Richtmyer–Meshkov instability
  • Shock wave refraction
  • Shock wave perturbation
  • Shock tube