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Richtmyer-Meshkov instability of an interface between two media due to passage of two successive shocks

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Abstract

The instability of a free surface of aluminum after passage of two shocks that follow one after the other at a certain time interval is studied numerically. The first shock is rather strong (the postshock pressure is about 75 GPa). It is shown that if at the moment when the second shock arrives at the free surface, the perturbation evolution is nonlinear, then, in contrast to the linear stage, the change in the growth rate of the amplitude depends weakly on the wavelength of the initial perturbation. A formula is proposed which describes the effect of the second shock on the amplitude growth rate and in which the main structure of Richtmyer's formula is preserved. It is demonstrated that the parameters of the second shock that ensure freezing of the instability can be determined using only the growth rate of the amplitude.

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References

  1. R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,”Comm. Pure Appl. Math.,13, No. 2, 297–319 (1960).

    MathSciNet  Google Scholar 

  2. E. E. Meshkov, “Instability of an interface between two gases accelerated by a shock,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 151–157 (1969).

    Google Scholar 

  3. K. A. Meyer and P. J. Blewett, “Numerical investigation of the stability of a shock-accelerated interface between two fluids,”Phys. Fluids,15, No. 5, 753–759 (1972).

    Article  Google Scholar 

  4. N. N. Anuchina, S. M. Bakhrakh, A. V. Zabrodin, et al., “Hydrodynamic instability of an interface between two media,” in:Investigation of Hydrodynamic Stability Using Computers [in Russian], Inst. of Appl. Math., USSR Acad. of Sci., Moscow (1981), pp. 108–162.

    Google Scholar 

  5. A. N. Aleshin, V. E. Lazareva, S. G. Zaitsev, et al., “Linear, nonlinear, and intermediate stages of development of Richtmyer-Meshkov instability,”Dokl. Akad. Nauk SSSR,310, No. 5, 1105–1108 (1990).

    Google Scholar 

  6. V. E. Neuvazhaev, “Development of turbulent mixing due to Richtmyer-Meshkov instability,”Mat. Model.,3, No. 7, 10–28 (1991).

    MathSciNet  Google Scholar 

  7. I. G. Lebo, V. V. Nikishin, V. B. Rozanov, and V. F. Tishkin, “On the influence of boundary conditions on the development of contact surface instability due to arrival of a shock,”Krat. Soobshch. Fiz., Nos. 1/2, 48–57 (1997).

    Google Scholar 

  8. G. Dimonte, C. E. Frerking, M. Schneider, and B. Remington, “Richtmyer-Meshkov instability with strong radiatively driven shocks,”Phys. Plasmas,3, No. 2, 614–630 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  9. K. O. Mekaélian, “Richtmyer-Meshkov instabilities in stratified fluids,”Phys. Rev. A,31, No. 1, 410–419 (1985).

    Article  ADS  Google Scholar 

  10. A. A. Charakhch'an, “Stability of shaped-charge jets generated by pulsed action on conical targets,”Prikl. Mekh. Tekh. Fiz.,38, No. 3, 10–13 (1997).

    Google Scholar 

  11. V. E. Meshkov, “Results of experimental studies of gravitational instability on an interface between media with different densities,” in:Investigation of Hydrodynamical Stability Using Computers [in Russian], Inst. of Appl. Math., USSR Acad. of Sci., Moscow (1981), pp. 162–190.

    Google Scholar 

  12. A. V. Bushman, G. I. Kanel', A. L. Ni, and V. E. Fortov,Thermophysics and Dynamics of Intense Impulsive Impacts [in Russian], Inst for Chem. Phys., Chernogolovka (1988).

    Google Scholar 

  13. Ya. B. Zel'dovich and Yu. P. Raizer,Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, New York (1967).

    Google Scholar 

  14. S. A. Ivanenko and A. A. Charakhch'an, “Curvilinear meshes with convex quadrangular cells,”Zh. Vychisl. Mat. Mat. Fiz.,28, No. 4, 503–514 (1988).

    MATH  Google Scholar 

  15. A. A. Charakhch'an, “Elliptic generator of meshes based on quasi-one-dimensional meshes,”Zh. Vychisl. Mat. Mat. Fiz.,39, No. 5, 832–837 (1999).

    MathSciNet  Google Scholar 

  16. D. L. Youngs, “Modeling turbulent mixing by Rayleigh-Taylor instabilities,”Physica D,37, Nos. 1/3 270–287 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  17. Yu. A. Kucherenko, V. E. Neuvazhaev, and A. P. Pylaev, “Behavior of a gravitational mixing region under conditions leading to separation,”Dokl. Ross. Akad. Nauk,334, No. 4, 445–448 (1994).

    Google Scholar 

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Authors
  1. A. A. Charakhch'an
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Computing Center, Russian Academy of Sciences, Moscow 117967. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 28–37, January–February, 2000.

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Charakhch'an, A.A. Richtmyer-Meshkov instability of an interface between two media due to passage of two successive shocks. J Appl Mech Tech Phys 41, 23–31 (2000). https://doi.org/10.1007/BF02465232

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  • DOI: https://doi.org/10.1007/BF02465232

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