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Interface coupling and growth rate measurements in multilayer Rayleigh-Taylor instabilities

Raymond Adkins1, Emily M. Shelton1, Marie-Charlotte Renoult2, Pierre Carles1,3,4, and Charles Rosenblatt1,*

  • 1Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA
  • 2Laboratoire CORIA, Normandie Université, UNIROUEN, CNRS, LOMC, F-76000 Rouen, France
  • 3Laboratoire FAST, Université Paris-Sud/CNRS, 23–25 rue Jean Rostand, Parc Club, F-91405 Orsay, France
  • 4Université Pierre et Marie Curie–Paris 06, 4, place Jussieu, F-75005 Paris, France

  • *rosenblatt@case.edu
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Phys. Rev. Fluids 2, 062001(R) – Published 19 June, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.062001

Abstract

Magnetic levitation was used to measure the growth rate Σ vs wave vector k of a Rayleigh-Taylor instability in a three-layer fluid system, a crucial step in the elucidation of interface coupling in finite-layer instabilities. For a three-layer (low-high-low density) system, the unstable mode growth rate decreases as both the height h of the middle layer and k are reduced, consistent with an interface coupling ∝e−kh. The ratios of the three-layer to the established two-layer growth rates are in good agreement with those of classic linear stability theory, which has long resisted verification in that configuration.

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Corrections

5 July, 2017

Erratum

Publisher's Note: Interface coupling and growth rate measurements in multilayer Rayleigh-Taylor instabilities [Phys. Rev. Fluids 2, 062001(R) (2017)]

Raymond Adkins, Emily M. Shelton, Marie-Charlotte Renoult, Pierre Carles, and Charles Rosenblatt
Phys. Rev. Fluids 2, 079901 (2017)

Article Text

References (28)

  1. G. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I, Proc. R. Soc. London, Ser. A 201, 192 (1950).
  2. D. Gueyffier and S. Zaleski, Formation de digitations lors de l'impact d'une goutte sur un film liquide, C. R. Acad. Sci. Paris, Ser. IIb 326, 839 (1998).
  3. D. Arnett, B. Fryxell, and E. Muller, An investigation of neutrino-driven convection and the core collapse supernova mechanism using multigroup neutrino transport, Astrophys. J. Lett. 341, L63 (1989).
  4. C. L. Fryer, A. L. Hungerford, and G. Rockefeller, Supernova explosions: Understanding mixing, Int. J. Mod. Phys. D 16, 941 (2007).
  5. J. L. Vinningland, O. Johnsen, E. G. Flekkoy, R. Toussaint, and K. J. Maloy, Granular Rayleigh-Taylor Instability: Experiments and Simulations, Phys. Rev. Lett. 99, 048001 (2007).
  6. M. Fermigier, L. Limat, J. E. Wesfreid, P. Boudinet, and C. Quilliet, Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer, J. Fluid Mech. 236, 349 (1992).
  7. M. H. Anderson, B. P. Puranik, J. G. Oakley, P. W. Brooks, and R. Bonazza, Shock tube investigation of hydrodynamic issues related to inertial confinement fusion, Shock Waves 10, 377 (2000).
  8. C. Boudesocque-Dubois, S. Gauthier, and J.-M. Clarisse, Self-similar solutions of unsteady ablation flows in inertial confinement fusion, J. Fluid Mech. 603, 151 (2008).
  9. V. Bychkov, M. Modestov, V. Akkerman, and L. E. Eriksson, The Rayleigh-Taylor instability in inertial fusion, astrophysical plasma and flames, Plasma Phys. Controlled Fusion 49, B513 (2007).
  10. See H. J. Kull, Theory of Rayleigh-Taylor instability, Phys. Rep. 206, 197 (1991), and references therein.
  11. D. J. Lewis, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II, Proc. R. Soc. London, Ser. A 202, 81 (1950).
  12. H. W. Emmons, C. T. Chang, and B. C. Watson, Taylor instability of finite surface waves, J. Fluid Mech. 7, 177 (1960).
  13. R. Bellman and R. H. Pennington, Effects of surface tension and viscosity on Taylor instability, Q. J. Appl. Math. 12, 151 (1954).
  14. R. L. Cole and R. S. Tankin, Experimental study of Taylor instability, Phys. Fluids 16, 1810 (1973).
  15. J. T. Waddell, C. E. Niederhaus, and J. W. Jacobs, Experimental study of Rayleigh-Taylor instability: Low Atwood number liquid systems with single-mode initial perturbations, Phys. Fluids 13, 1263 (2001).
  16. P. Carles, H. Huang, G. Carbone, and C. Rosenblatt, Rayleigh-Taylor Instability for Immiscible Fluids of Arbitrary Viscosities: A Magnetic Levitation Investigation and Theoretical Model, Phys. Rev. Lett. 96, 104501 (2006).
  17. K. O. Mikaelian, Time evolution of density perturbations in accelerating stratified fluids, Phys. Rev. A 28, 1637 (1983)
  18. K. O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities in multilayer fluids with surface tension, Phys. Rev. A 42, 7211 (1990).
  19. K. O. Mikaelian, Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension, Phys. Rev. E 54, 3676 (1996).
  20. K. O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells, Phys. Fluids 17, 094105 (2005).
  21. Y. Yang and Q. Zhang, General properties of a multilayer stratified fluids system, Phys. Fluids A 5, 1167 (1993).
  22. S. Parhi and G. Nath, A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow, Int. J. Eng. Sci. 29, 1439 (1991).
  23. J. W. Jacobs and S. B. Dalziel, Rayleigh-Taylor instability in complex stratifications, J. Fluid Mech. 542, 251 (2005).
  24. M. C. Renoult, R. G. Petschek, C. Rosenblatt, and P. Carles, Deforming static fluid interfaces with magnetic fields: Application to the Rayleigh-Taylor instability, Exp. Fluids 51, 1073 (2011).
  25. P. Carles (unpublished).
  26. M.C. Renoult, Étude non-linéaire de l'instabilité de Rayleigh-Taylor par lévitation magnétique: du contrôle des conditions initiales au developpement de nouveaux outils d'analyse, Ph.D. thesis, UPMC Paris 06, 2012.
  27. Measured using the pendant drop technique.
  28. J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell. 8, 679 (1986).

Outline

Information

Phys. Rev. Fluids 2, 062001(R)– Published 19 June, 2017
  • Received 2 December 2016
  • Corrected 5 July 2017
Article part of CHORUS

©2017 American Physical Society

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