Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-28T07:29:51.930Z Has data issue: false hasContentIssue false
  • English
  • Français

Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces

Published online by Cambridge University Press:  15 October 2021

Yu Liang Open the ORCID record for Yu Liang [Opens in a new window] ,
Lili Liu ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window] ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  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
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn
†Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF$_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A37
Check for updates
Copyright
© The Author(s), 2021. 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
Chandrasekhar, S. 2013 Hydrodynamic and Hydromagnetic Stability. Courier Corporation.Google Scholar
Cohen, R.D. 1991 Shattering of a liquid drop due to impact. Proc. R. Soc. Lond. A 435, 483–503.Google Scholar
Collins, B.D. & Jacobs, J.W. 2002 PLIF flow visualization and measurements of the Richtmyer-Meshkov instability of an air/SF$_6$ interface. J. Fluid Mech. 464, 113–136.CrossRefGoogle Scholar
Dell, Z., Stellingwerf, R.F. & Abarzhi, S.I. 2015 Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks. Phys. Plasmas 22 (9), 092711.CrossRefGoogle Scholar
Dell, Z.R., Pandian, A., Bhowmick, A.K., Swisher, N.C., Stanic, M., Stellingwerf, R.F. & Abarzhi, S.I. 2017 Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability. Phys. Plasmas 24 (9), 090702.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., Frerking, C.E., Schneider, M. & Remington, B. 1996 Richtmyer-Meshkov instability with strong radiatively driven shocks. Phys. Plasmas 3 (2), 614–630.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
Ding, J.C., Si, T., Chen, M.J., Zhai, Z.G., Lu, X.Y. & Luo, X.S. 2017 On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech. 828, 289–317.CrossRefGoogle Scholar
Drazin, P.G. & Reid, W.H. 2004 Hydrodynamic Stability. Cambridge University Press.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
Goncharov, V.N. 1999 Theory of the ablative Richtmyer-Meshkov instability. Phys. Rev. Lett. 82 (10), 2091.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., Ding, J., Si, T. & Luo, X. 2020 Effects of transverse shock waves on early evolution of multi-mode chevron interface. Phys. Fluids 32 (10), 106101.CrossRefGoogle Scholar
Haan, S.W. 1989 Onset of nonlinear saturation for Rayleigh–Taylor growth in the presence of a full spectrum of modes. Phys. Rev. A 39 (11), 5812.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
Hosseini, S.H.R. & Takayama, K. 2005 Experimental study of Richtmyer-Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17, 084101.CrossRefGoogle Scholar
Hurricane, O.A., Burke, E., Maples, S. & Viswanathan, M. 2000 Saturation of Richtmyer's impulsive model. Phys. Fluids 12 (8), 2148–2151.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
Lei, F., Ding, J., Si, T., Zhai, Z. & Luo, X. 2017 Experimental study on a sinusoidal air/SF$_6$ interface accelerated by a cylindrically converging shock. J. Fluid Mech. 826, 819–829.CrossRefGoogle Scholar
Liang, Y., Liu, L., Zhai, Z., Si, T. & Luo, X. 2021 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, H. & Xiao, Z. 2016 Scale-to-scale energy transfer in mixing flow induced by the Richtmyer-Meshkov instability. Phys. Rev. E 93 (5), 053112.CrossRefGoogle ScholarPubMed
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
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
Luo, X., Wang, X. & Si, T. 2013 The Richtmyer-Meshkov instability of a three-dimensional air/SF$_6$ interface with a minimum-surface feature. J. Fluid Mech. 722, R2.CrossRefGoogle Scholar
Luo, X., Wang, M., Si, T. & Zhai, Z. 2015 On the interaction of a planar shock with an SF$_6$ polygon. J. Fluid Mech. 773 (2), 366–394.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
Meyer, K.A. & Blewett, P.J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753–759.CrossRefGoogle Scholar
Mikaelian, K.O. 1998 Analytic approach to nonlinear Rayleigh–Taylor and Richtmyer-Meshkov instabilities. Phys. Rev. Lett. 80, 508–511.CrossRefGoogle Scholar
Mikaelian, K.O. 2003 Explicit expressions for the evolution of single-mode Rayleigh–Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E 67, 026319.CrossRefGoogle ScholarPubMed
Mikaelian, K.O. 2005 Richtmyer-Meshkov instability of arbitrary shapes. Phys. Fluids 17, 034101.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., Musci, B., Reilly, D., McFarland, J.A. & Ranjan, D. 2017 Evaluation of turbulent mixing transition in a shock-driven variable-density flow. J. Fluid Mech. 831, 779–825.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
Mügler, C. & Gauthier, S. 1998 Numerical simulations of single-mode Richtmyer-Meshkov experiments. Phys. Rev. E 58 (4), 4548.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
Ranjan, D., Anderson, M., Oakley, J. & Bonazza, R. 2005 Experimental investigation of a strongly shocked gas bubble. Phys. Rev. Lett. 94, 184507.CrossRefGoogle ScholarPubMed
Rayleigh, L. 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Remington, B.A., Weber, S.V., Marinak, M.M., Haan, S.W., Kilkenny, J.D., Wallace, R.J. & Dimonte, G 1995 Single-mode and multimode Rayleigh–Taylor experiments on nova. Phys. Plasmas 2 (1), 241–255.CrossRefGoogle 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
Rikanati, A., Oron, D., Sadot, O. & Shvarts, D. 2003 High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability. Phys. Rev. E 67, 026307.CrossRefGoogle ScholarPubMed
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
Sewell, E.G., Ferguson, K.J., Krivets, V.V. & Jacobs, J.W. 2021 Time-resolved particle image velocimetry measurements of the turbulent Richtmyer–Meshkov instability. J. Fluid Mech. 917, A41.CrossRefGoogle Scholar
Si, T., Long, T., Zhai, Z. & Luo, X. 2015 Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder. J. Fluid Mech. 784, 225–251.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
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., 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
Velikovich, A.L. & Dimonte, G. 1996 Nonlinear perturbation theory of the incompressible Richtmyer-Meshkov instability. Phys. Rev. Lett. 76 (17), 3112.CrossRefGoogle ScholarPubMed
Zhai, Z., Dong, P., Si, T. & Luo, X. 2016 The Richtmyer-Meshkov instability of a V shaped air/helium interface subjected to a weak shock. Phys. Fluids 28 (8), 082104.CrossRefGoogle Scholar
Zhai, Z., Wang, M., Si, T. & Luo, X. 2014 On the interaction of a planar shock with a light SF$_6$ polygonal interface. J. Fluid Mech. 757 (2), 800–816.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. Engrs C 232, 2830–2849.Google 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. 2007 Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations. Phys. Plasmas 14 (8), 082701.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., Robey, H.F. & Buckingham, A.C. 2003 Onset of turbulence in accelerated high-Reynolds-number flow. Phys. Rev. E 67 (5), 056305.CrossRefGoogle ScholarPubMed