DOI QR코드

DOI QR Code

LARGE AMPLITUDE THEORY OF A SHOCK-ACCELERATED INSTABILITY IN COMPRESSIBLE FLUIDS

  • Sohn, Sung-Ik (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2011.04.25
  • Accepted : 2011.06.20
  • Published : 2011.06.30

Abstract

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

Keywords

References

  1. R. D. Richtmyer, Taylor instability in shock acceleration of compressible fluids, Comm. Pure Appl. Math. 13 (1960), 297-319. https://doi.org/10.1002/cpa.3160130207
  2. D. Sharp, An overview of Rayleigh-Taylor instability, Physica D 12 (1984), 3-10. https://doi.org/10.1016/0167-2789(84)90510-4
  3. Y. Yang, Q. Zhang and D. H. Sharp, Small amplitude theory of Richtmyer-Meshkov instability, Phys. Fluids A 6 (1994), 1856-1873. https://doi.org/10.1063/1.868245
  4. Q. Zhang and S.-I. Sohn, Nonlinear theory of unstable fluid mixing driven by shock waves, Phys. Fluids 9 (1997), 1106-1124. https://doi.org/10.1063/1.869202
  5. Q. Zhang and S.-I. Sohn, Quantitative theory of Richtmyer-Meshkov instability in three dimensions, Zeit. angew. Math. Phys. 50 (1999), 1-46. https://doi.org/10.1007/s000330050137
  6. S.-I. Sohn, Computation and analysis of mathematical model for moving free boundary flows, J. Korean Math. Soc. 37 (2000), 779-791.
  7. B. Cheng, J. Glimm and D. H. Sharp, Dynamic evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts, Phys. Rev. E 66 (2002), 036312: 1-7.
  8. S.-I. Sohn, Density dependence of a Zufiria-type model for Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts, Phys. Rev. E 70 (2004), 045301: 1-4.
  9. S.-I. Sohn, Analytic solutions of unstable interfaces for all density ratios in axisymmetric flows, J. Comput. Appl. Math. 177 (2005), 367-374. https://doi.org/10.1016/j.cam.2004.09.026
  10. M. Vandenboomgaerde, S. Gauthier and C. Mugler, Nonlinear regime of a multimode Richtmyer.Meshkov instability: A simplified perturbation theory, Phys. Fluids 14 (2002), 1111-1122. https://doi.org/10.1063/1.1447914
  11. M. Vandenboomgaerde, C. Cherfils, D. Galmiche, S. Gauthier and P. A. Raviart, Efficient perturbation methods for Richtmyer-Meshkov and Rayleigh-Taylor instabilities: Weakly nonlinear stage and beyond, Laser Part. Beams 21 (2003), 321-325.
  12. J. Grove, Applications of front tracking to the simulations of shock refractions and unstable mixing, Appl. Numer. Math. 14 (1994), 213-237. https://doi.org/10.1016/0168-9274(94)90027-2
  13. R. L. Holmes, J. W. Grove and D. H. Sharp, A numerical investigation of Richtmyer-Meshkov instability using front tracking, J. Fluid Mech. 301 (1995), 51-64. https://doi.org/10.1017/S002211209500379X
  14. S.-I. Sohn, Analycal and numerical study of mode interactions in shock-induced interfacial instability, Commun. Korean Math. Soc. 15 (2000), 155-172.
  15. S.-I. Sohn, Vortex simulations of impulsively accelerated unstable interface, Math. Comput. Modelling 04 (2004), 627-636.
  16. R. Courant and K. O. Friedrich, Supersonic flow and shock waves, Springer, New York, 1976.