Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T15:25:59.802Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study of bubble competition and spike competition in Richtmyer–Meshkov flows

Published online by Cambridge University Press:  21 September 2022

Yu Liang Open the ORCID record for Yu Liang [Opens in a new window] ,
Lili Liu  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi 129188, UAE
Lili Liu
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi 129188, UAE
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: xluo@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Shock-tube experiments on various two-bubble and two-spike interfaces are performed to examine the dependence of bubble competition and spike competition on the initial spectra and density ratio of the interface. The differences in the influences of bubble competition and spike competition on the Richtmyer–Meshkov instability are highlighted for the first time. The bubble-competition effect is mainly dependent on the initial spectra of the two-bubble configuration. In contrast, the spike-competition effect is determined by both the initial spectra and density ratio. The extended buoyancy–drag model is adopted to explain the variation of the drag force imposed on the long-wavelength and short-wavelength structures as the initial conditions change. Based on the spectrum analysis, it is found that the constituent modes of two-bubble and two-spike interfaces have different contributions to the long-wavelength and short-wavelength perturbation growths. A generalised, nonlinear, analytical model is then established to quantify the bubble-competition effect and spike-competition effect considering arbitrary initial spectra and density ratio. The bubble-competition effect is believed to be stronger than the spike-competition effect at a high density ratio because it suppresses the high-frequency perturbation growth more evidently.

JFM classification

Compressible Flows: Shock waves Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A3
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abarzhi, S.I. 2008 Coherent structures and pattern formation in Rayleigh–Taylor turbulent mixing. Phys. Scr. 78 (1), 015401.CrossRefGoogle Scholar
Abarzhi, S.I. 2010 Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing. Phil. Trans. R. Soc. A 368 (1916), 1809–1828.CrossRefGoogle ScholarPubMed
Alon, U., Hecht, J., Mukamel, D. & Shvarts, D. 1994 Scale invariant mixing rates of hydrodynamically unstable interface. Phys. Rev. Lett. 72, 2867–2870.CrossRefGoogle Scholar
Alon, U., Hecht, J., Ofer, D. & Shvarts, D. 1995 Power laws and similarity of Rayleigh–Taylor and Richtmyer-Meshkov mixing fronts. Phys. Rev. Lett. 74, 534–537.CrossRefGoogle ScholarPubMed
Balasubramanian, S., Orlicz, G.C. & Prestridge, K.P. 2013 Experimental study of initial condition dependence on turbulent mixing in shock-accelerated Richtmyer-Meshkov fluid layers. J. Turbul. 14 (3), 170–196.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer-Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Cao, Y.G., Chow, W.K. & Fong, N.K. 2011 Solutions to buoyancy-drag equation for dynamical evolution of Rayleigh–Taylor and Richtmyer-Meshkov mixing zone. Commun. Theor. Phys. 56 (4), 751–755.CrossRefGoogle Scholar
Cheng, B., Glimm, J. & Sharp, D.H. 2000 Density dependence of Rayleigh–Taylor and Richtmyer-Meshkov mixing fronts. Phys. Lett. A 268, 366–374.CrossRefGoogle Scholar
Cheng, B., Glimm, J. & Sharp, D.H. 2002 Dynamical evolution of Rayleigh–Taylor and Richtmyer-Meshkov mixing fronts. Phys. Rev. E 66, 036312.CrossRefGoogle ScholarPubMed
Cheng, B., Glimm, J. & Sharp, D.H. 2020 The $\alpha _s$ and $\theta _s$ in Rayleigh–Taylor and Richtmyer-Meshkov instabilities. Physica D 404, 132356.CrossRefGoogle Scholar
Di Stefano, C.A., Malamud, G., Kuranz, C.C., Klein, S.R. & Drake, R.P. 2015 a Measurement of Richtmyer-Meshkov mode coupling under steady shock conditions and at high energy density. High Energy Density Phys. 17, 263–269.CrossRefGoogle Scholar
Di Stefano, C.A., Malamud, G., Kuranz, C.C., Klein, S.R., Stoeckl, C. & Drake, R.P. 2015 b Richtmyer-Meshkov evolution under steady shock conditions in the high-energy-density regime. Appl. Phys. Lett. 106 (11), 114103.CrossRefGoogle Scholar
Dimonte, G. 2000 Spanwise homogeneous buoyancy-drag model for Rayleigh–Taylor mixing and experimental evaluation. Phys. Plasmas 7, 2255–2269.CrossRefGoogle Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer-Meshkov instability. Phys. Fluids 22, 014104.CrossRefGoogle Scholar
Dimonte, G. & Schneider, M. 2000 Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321.CrossRefGoogle Scholar
Dimonte, G., Youngs, D.L., Dimits, A., Weber, S. & Zingale, M. 2004 A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: the alpha-group collaboration. Phys. Fluids 16 (5), 1668–1693.CrossRefGoogle Scholar
Drake, R.P. 2018 High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics. Springer.CrossRefGoogle Scholar
Elbaz, Y. & Shvarts, D. 2018 Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh–Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions. Phys. Plasmas 25 (6), 062126.CrossRefGoogle Scholar
Groom, M. & Thornber, B. 2020 The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer-Meshkov instability. Physica D 407, 132463.CrossRefGoogle Scholar
Guo, X., Zhai, Z., Si, T. & Luo, X. 2019 Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface. Phys. Rev. Fluids 4 (9), 092001.CrossRefGoogle Scholar
Haan, S.W. 1991 Weakly nonlinear hydrodynamic instabilities in inertial fusion. Phys. Fluids B 3, 2349–2355.CrossRefGoogle Scholar
Hecht, J., Alon, U. & Shvarts, D. 1994 Potential flow models of Rayleigh–Taylor and Richtmyer-Meshkov bubble fronts. Phys. Fluids 6, 4019–4030.CrossRefGoogle Scholar
Jacobs, J.W. & Krivets, V.V. 2005 Experiments on the late-time development of single-mode Richtmyer-Meshkov instability. Phys. Fluids 17, 034105.CrossRefGoogle Scholar
Jacobs, J.W. & Sheeley, J.M. 1996 Experimental study of incompressible Richtmyer-Meshkov instability. Phys. Fluids 8, 405–415.CrossRefGoogle Scholar
Kuranz, C.C., et al. 2018 How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants. Nat. Commun. 9, 1564.CrossRefGoogle ScholarPubMed
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.CrossRefGoogle Scholar
Liang, Y. 2022 Fundamental Studies of Shock-Driven Hydrodynamic Instabilities. Springer Nature Singapore.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Ding, J., Si, T. & Luo, X. 2021 a Richtmyer-Meshkov instability on two-dimensional multi-mode interfaces. J. Fluid Mech. 928, A37.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Si, T. & Luo, X. 2021 b Universal perturbation growth of Richtmyer-Meshkov instability for minimum-surface featured interface induced by weak shock waves. Phys. Fluids 33 (3), 032110.CrossRefGoogle Scholar
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer-Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729–751.CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.CrossRefGoogle Scholar
Liu, L., Liang, Y., Ding, J., Liu, N. & Luo, X. 2018 An elaborate experiment on the single-mode Richtmyer-Meshkov instability. J. Fluid Mech. 853, R2.CrossRefGoogle Scholar
Livescu, D. 2020 Turbulence with large thermal and compositional density variations. Annu. Rev. Fluid Mech. 52, 309–341.CrossRefGoogle Scholar
Lombardini, M. & Pullin, D.I. 2009 Startup process in the Richtmyer-Meshkov instability. Phys. Fluids 21 (4), 044104.CrossRefGoogle Scholar
Luo, X., Liang, Y., Si, T. & Zhai, Z. 2019 Effects of non-periodic portions of interface on Richtmyer-Meshkov instability. J. Fluid Mech. 861, 309–327.CrossRefGoogle Scholar
Luo, X., Liu, L., Liang, Y., Ding, J. & Wen, C.Y. 2020 Richtmyer-Meshkov instability on a dual-mode interface. J. Fluid Mech. 905, A5.CrossRefGoogle Scholar
Mansoor, M.M., Dalton, S.M., Martinez, A.A., Desjardins, T., Charonko, J.J. & Prestridge, K.P. 2020 The effect of initial conditions on mixing transition of the Richtmyer-Meshkov instability. J. Fluid Mech. 904, A3.CrossRefGoogle Scholar
Mariani, C., Vandenboomgaerde, M., Jourdan, G., Souffland, D. & Houas, L. 2008 Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces. Phys. Rev. Lett. 100, 254503.CrossRefGoogle ScholarPubMed
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Mikaelian, K.O. 1989 Turbulent mixing generated by Rayleigh–Taylor and Richtmyer-Meshkov instabilities. Physica D 36, 343–357.CrossRefGoogle Scholar
Miles, A.R., Edwards, M.J., Blue, B., Hansen, J.F., Robey, H.F., Drake, R.P., Kuranz, C. & Leibrandt, D.R. 2004 The effects of a short-wavelength mode on the evolution of a long-wavelength perturbatoin driven by a strong blast wave. Phys. Plasmas 11, 5507–5519.CrossRefGoogle Scholar
Mohaghar, M., Carter, J., Pathikonda, G. & Ranjan, D. 2019 The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions. J. Fluid Mech. 871, 595–635.CrossRefGoogle Scholar
Niederhaus, C.E. & Jacobs, J.W. 2003 Experimental study of the Richtmyer-Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243–277.CrossRefGoogle Scholar
Nishihara, K., Wouchuk, J.G., Matsuoka, C., Ishizaki, R. & Zhakhovsky, V.V. 2010 Richtmyer-Meshkov instability: theory of linear and nonlinear evolution. Phil. Trans. R. Soc. A 368, 1769–1807.CrossRefGoogle ScholarPubMed
Ofer, D., Alon, U., Shvarts, D., McCrory, R.L. & Verdon, C.P. 1996 Modal model for the nonlinear multimode Rayleigh–Taylor instability. Phys. Plasmas 3 (8), 3073–3090.CrossRefGoogle Scholar
Oron, D., Arazi, L., Kartoon, D., Rikanati, A., Alon, U. & Shvarts, D. 2001 Dimensionality dependence of the Rayleigh–Taylor and Richtmyer-Meshkov instability late-time scaling laws. Phys. Plasmas 8, 2883–2889.CrossRefGoogle Scholar
Pandian, A., Stellingwerf, R.F. & Abarzhi, S.I. 2017 Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows. Phys. Rev. Fluids 2 (7), 073903.CrossRefGoogle Scholar
Ramaprabhu, P., Dimonte, G. & Andrews, M.J. 2005 A numerical study of the influence of initial perturbations on the turbulent Rayleigh–Taylor instability. J. Fluid Mech. 536, 285–319.CrossRefGoogle Scholar
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140.CrossRefGoogle Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. London Math. Soc. 14, 170–177.Google Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Rikanati, A., Alon, U. & Shvarts, D. 1998 Vortex model for the nonlinear evolution of the multimode Richtmyer-Meshkov instability at low Atwood numbers. Phys. Rev. E 58, 7410–7418.CrossRefGoogle Scholar
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L.A., Erez, G., Ben-Dor, G. & Shvarts, D. 1998 Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability. Phys. Rev. Lett. 80, 1654–1657.CrossRefGoogle Scholar
Sharp, D.H. 1984 An overview of Rayleigh–Taylor instability. Physica D 12 (1), 3–18.CrossRefGoogle Scholar
Srebro, Y., Elbaz, Y., Sadot, O., Arazi, L. & Shvarts, D. 2003 A general buoyancy-drag model for the evolution of the Rayleigh–Taylor and Richtmyer-Meshkov instabilities. Laser Part. Beams 21, 347–353.CrossRefGoogle Scholar
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201 (1065), 192–196.Google Scholar
Thornber, B. 2016 Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability. Phys. Fluids 28 (4), 045106.CrossRefGoogle Scholar
Thornber, B., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2010 The influence of initial condition on turbulent mixing due to Richtmyer-Meshkov instability. J. Fluid Mech. 654, 99–139.CrossRefGoogle Scholar
Thornber, B., et al. 2017 Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: the $\theta$-group collaboration. Phys. Fluids 29 (10), 105107.CrossRefGoogle Scholar
Vandenboomgaerde, M., Gauthier, S. & Mügler, C. 2002 Nonlinear regime of a multimode Richtmyer-Meshkov instability: a simplified perturbation theory. Phys. Fluids 14 (3), 1111–1122.CrossRefGoogle Scholar
Vandenboomgaerde, M., Souffland, D., Mariani, C., Biamino, L., Jourdan, G. & Houas, L. 2014 An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability. Phys. Fluids 26, 024109.CrossRefGoogle Scholar
Velikovich, A.L. & Dimonte, G. 1996 Nonlinear perturbation theory of the incompressible Richtmyer-Meshkov instability. Phys. Rev. Lett. 76 (17), 3112.CrossRefGoogle ScholarPubMed
Velikovich, A., Herrmann, M. & Abarzhi, S. 2014 Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer-Meshkov instability. J. Fluid Mech. 751, 432–479.CrossRefGoogle Scholar
Wadas, M.J. & Johnsen, E. 2020 Interactions of two bubbles along a gaseous interface undergoing the Richtmyer-Meshkov instability in two dimensions. Physica D 409, 132489.CrossRefGoogle Scholar
Yang, J., Kubota, T. & Zukoski, E.E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.CrossRefGoogle Scholar
Youngs, D.L. 1991 Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12 (1–3), 32–44.CrossRefGoogle Scholar
Youngs, D.L. 2013 The density ratio dependence of self-similar Rayleigh–Taylor mixing. Phil. Trans. R. Soc. A 371, 20120173.CrossRefGoogle ScholarPubMed
Youngs, D.L. & Thornber, B. 2020 Buoyancy-drag modelling of bubble and spike distances for single-shock Richtmyer-Meshkov mixing. Physica D 410, 132517.CrossRefGoogle Scholar
Zhai, Z., Zou, L., Wu, Q. & Luo, X. 2018 Review of experimental Richtmyer-Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engng, Part C 232, 2830–2849.CrossRefGoogle Scholar
Zhang, Q., Deng, S. & Guo, W. 2018 Quantitative theory for the growth rate and amplitude of the compressible Richtmyer-Meshkov instability at all density ratios. Phys. Rev. Lett. 121 (17), 174502.CrossRefGoogle ScholarPubMed
Zhang, Q. & Guo, W. 2016 Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer-Meshkov instabilities with all density ratios. J. Fluid Mech. 786, 47–61.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.I. 1997 Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106–1124.CrossRefGoogle Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1–160.Google Scholar
Zhou, Y., Clark, T.T., Clark, D.S., Glendinning, S.S., Skinner, A.A., Huntington, C., Hurricane, O.A., Dimits, A.M. & Remington, B.A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26 (8), 080901.CrossRefGoogle Scholar
Zhou, Y., et al. 2021 Rayleigh–Taylor and Richtmyer-Meshkov instabilities: a journey through scales. Physica D 423, 132838.CrossRefGoogle Scholar
Zhou, Z.R., Zhang, Y.S. & Tian, B.L. 2018 Dynamic evolution of Rayleigh–Taylor bubbles from sinusoidal, w-shaped, and random perturbations. Phys. Rev. E 97 (3), 033108.CrossRefGoogle ScholarPubMed