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MULTI-HARMONIC MODELS FOR BUBBLE EVOLUTION IN THE RAYLEIGH-TAYLOR INSTABILITY

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초록

We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.

Abstract

We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.

참고문헌 (26)

  1. S. I. Abarzhi, "Stable steady flows in Rayleigh-Taylor instability", Phys. Rev. Lett, 81, pp.337~340 (1998)
  2. S. I. Abarzhi, "Review of theoretical modelling approaches of Rayleigh-Taylor instabilities and turbulent mixing", Phil. Trans. R. Soc. A, 368, pp.1809~1828 (2010)
  3. S. I. Abarzhi, "Dynamics of two-dimensional Rayleigh-Taylor bubbles for fluids with a finite density contrast", Phys. Fluids, 15(8), pp.2190~2197 (2003)
  4. S. I. Abarzhi, "Rayleigh-Taylor and Richtmyer-Meshkov instabilities for fluids with a finite density ratio", Phys. Lett. A, 317, pp.470~476 (2003)
  5. S. I. Abarzhi, "Multiscale character of the nonlinear coher-ent dynamics in the Rayleigh-Taylor instability", Phys. Rev. E, 73, pp.036310~ (2006)
  6. G. Birkhoff, "Rising plane bubbles", J. Math. Mech, 6, pp.769~779 (1957)
  7. Y. G. Cao, "Effect of viscosity on the growth of Rayleigh-Taylor instability", J. Phys. A, 44(27), pp.8~ (2011)
  8. P. R. Garabedian, "On steady-state bubbles generated by Taylor instability", Proc. R. Soc. London Ser. A, 241, pp.423~431 (1957)
  9. J. Glimm, "New directions for Rayleigh-Taylor mixing", Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci, 371(2003), pp.19~ (2013)
  10. V. N. Goncharov, "Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers", Phys. Rev. Lett, 88, pp.134502~ (2002)
  11. J. Hecht, "Potential flow models of Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts", Phys. Fluids, 6, pp.4019~4030 (1994)
  12. H. Jin, "Rayleigh-Taylor mixing rates for compressible flow", Phys. Fluids, 17, pp.024104~ (2005)
  13. D. Layzer, "On the instability of superposed fluids in a gravitational field", Astrophys. J, 122, pp.1~12 (1955)
  14. K. O. Mikaelian, "Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers", Phys. Rev. E, 67, pp.026319~ (2003)
  15. K. O. Mikaelian, "Limitations and failures of the Layzer model for hydrodynamic instabilities", Phys. Rev. E, 78, pp.015303~ (2008)
  16. P. Ramaprabhu, "Single-mode dynamics of the Rayleigh-Taylor insta-bility at any density ratio", Phys. Rev. E, 71, pp.036314~ (2005)
  17. L. Rayleigh, "Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density", Proc. London Math. Soc, 14, pp.170~177 (1883)
  18. B. Rollin, "Mathematical model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for viscoelastic fluids", Phys. Rev. E, 83, pp.046317~ (2011)
  19. D. Sharp, "An overview of Rayleigh-Taylor instability", Phys. D, 12, pp.3~10 (1984)
  20. S.-I. Sohn, "Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities", Phys. Rev. E, 69, pp.036703~ (2004)
  21. S.-I. Sohn, "Density dependence of a Zufiria-type model for Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts", Phys. Rev. E, 70, pp.045301~ (2004)
  22. S.-I. Sohn, "Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities", Phys. Rev. E, 80, pp.055302~ (2009)
  23. S.-I. Sohn, "Asymptotic bubble evolutions of the Rayleigh-Taylor instability", Commun. Non-linear Sci. Numer. Simul, 17(11), pp.4017~4022 (2012)
  24. J. P. Wilkinson, "Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability", Phys. Fluids, 19, pp.124102~ (2007)
  25. Q. Zhang, "Analytical solutions of Layzer-type approach to unstable interfacial fluid mix-ing", Phys. Rev. Lett, 81, pp.3391~3394 (1998)
  26. Y. B. Zudin, "Analytical solution of the problem of the rise of a Taylor bubble", Phys. Fluids, 25, pp.053302~ (2013)

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