Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T09:53:56.822Z Has data issue: false hasContentIssue false
  • English
  • Français

Richtmyer–Meshkov instability on a dual-mode interface

Published online by Cambridge University Press:  20 October 2020

Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window] ,
Lili Liu ,
Yu Liang Open the ORCID record for Yu Liang [Opens in a new window] ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window]  and
Chih-yung Wen Open the ORCID record for Chih-yung Wen [Opens in a new window]
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Lili Liu
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Juchun Ding*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Chih-yung Wen
Affiliation:
Department of Mechanical Engineering and Interdisciplinary Division of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, PR China
*
†Email address for correspondence: djc@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We report the first shock-tube experiments on dual-mode Richtmyer–Meshkov instability (RMI). An extended soap-film technique is adopted to generate a dual-mode gaseous interface such that its initial wavenumber ($k_0$) and phase of the fundamental waves are well controlled. By extracting interfacial contours from the distinct schlieren images, a Fourier analysis is performed from linear to weakly nonlinear stages and the growth of each basic wave is obtained. A noticeable difference between the growth of each basic mode and the corresponding single-mode RMI is observed, which suggests evident mode coupling effects in the dual-mode RMI. For dual-mode interfaces with in-phase $k_0$ and $k_0/2$ waves, the mode coupling suppresses (promotes) the growth of the $k_0$ ($k_0/2$) mode, while for interfaces with anti-phase $k_0$ and $k_0/2$ modes, the growth of the $k_0$ ($k_0/2$) mode is weakly influenced (evidently inhibited). However, for the combination of $k_0$ and $k_0/3$ waves, the mode coupling has a negligible influence on the growth of each basic wave. The modal theory of Haan (Phys. Fluids B, vol. 3, 1991, pp. 2349–2355), originally for multi-mode Rayleigh–Taylor instability, is reformulated for the dual-mode RMI, and it is found that this model overestimates the present experimental results for ignoring the nonlinear saturation. This model is then modified by accounting for both the mode coupling and nonlinear saturation, which well predicts the experimental results not only for the growth of the basic waves but also for the growth of second harmonics.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A5
Check for updates
Copyright
© The Author(s), 2020. 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

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
Bai, X., Deng, X. L. & Jiang, L. 2018 A comparative study of the single-mode Richtmyer–Meshkov instability. Shock Waves 28, 795–813.CrossRefGoogle Scholar
Balakumar, B. J., Orlicz, G. C., Ristorcelli, J. R., Balasubramanian, S., Prestridge, K. P. & Tomkins, C. D. 2012 Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics. J. Fluid Mech. 696, 67–93.CrossRefGoogle Scholar
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.CrossRefGoogle Scholar
Di Stefano, C. A., Malamud, G., Kuranz, C. C., Klein, S. R., Stoeckl, C. & Drake, R. P. 2015 Richtmyer–Meshkov evolution under steady shock conditions in the high-energy-density regime. Appl. Phys. Lett. 106, 114103.CrossRefGoogle Scholar
Dimonte, G., Frerking, C. E. & Schneider, M. 1995 Richtmyer–Meshkov instability in the turbulent regime. Phys. Rev. Lett. 74 (24), 4855–4858.CrossRefGoogle ScholarPubMed
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.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
Goncharov, V. N. 2002 Analytical model of nonlinear, single-mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett. 88, 134502.CrossRefGoogle ScholarPubMed
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
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
Leinov, E., Malamud, G., Elbaz, Y., Levin, L. A., Ben-Dor, G., Shvarts, D. & Sadot, O. 2009 Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449–475.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
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., 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
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
Martinez, D. A., Smalyuk, V. A., Kane, J. O., Casner, A., Liberatore, S. & Masse, L. P. 2015 Evidence for a bubble-competition regime in indirectly driven ablative Rayleigh–Taylor instability experiments on the NIF. Phys. Rev. Lett. 114, 215004.CrossRefGoogle ScholarPubMed
McFarland, J. A., Reilly, D., Black, W., Greenough, J. A. & Ranjan, D. 2015 Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer–Meshkov instability. Phys. Rev. E 92 (1), 013023.CrossRefGoogle Scholar
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
Miles, A. R., Edwards, M. J., Blue, B., Hansen, J. F., Robey, H. F., Drake, R. P., Kuranz, C. & Leibrandt, D. R. 2004 The effect 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. & Ranjan, D. 2017 Evaluation of turbulent mixing transition in a shock-driven variable-density flow. J. Fluid Mech. 831, 779–825.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
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
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
Reese, D. T., Ames, A. M., Noble, C. D., Oakley, J. G., Rothamer, D. A. & Bonazza, R. 2018 Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability. J. Fluid Mech. 849, 541–575.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
Rollin, B. & Andrews, M. J. 2013 On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing. J. Turbul. 14, 77–106.CrossRefGoogle Scholar
Sadot, O. 2017 Experimental studies of shock wave-related phenomena at the Ben-Gurion university: a review. In 31st International Symposium on Shock Waves (ed. Sasoh, A., Aoki, T. & Katayama, M.), pp. 31–44. Springer.Google 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
Sohn, S. I. 2003 Simple potential-flow model of Rayleigh–Taylor and Richtmyer–Meshkov instabilities for all density ratios. Phys. Rev. E 67, 026301.CrossRefGoogle ScholarPubMed
Sohn, S. I. 2008 Quantitative modeling of bubble competition in Richtmyer–Meshkov instability. Phys. Rev. E 78 (1), 017302.CrossRefGoogle ScholarPubMed
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., Griffond, J., Poujade, O., Attal, N., Varshochi, H., Bigdelou, P., Ramaprabhu, P., Olson, B., Greenough, J., Zhou, Y., 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
Wouchuk, J. G. 2001 Growth rate of the linear Richtmyer–Meshkov instability when a shock is reflected. Phys. Rev. E 63, 056303.CrossRefGoogle ScholarPubMed
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.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
Zhou, Y., Clark, T. T., Clark, D. S., Glendinning, S. G., Skinner, M. A., Huntington, C. M., Hurricane, O. A., Dimits, A. M. & Remington, B. A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26, 080901.CrossRefGoogle Scholar
Zhou, Y., Remington, B. A., Robey, H. F., Cook, A. W., Glendinning, S. G., Dimits, A., Buckingham, A. C., Zimmerman, G. B., Burke, E. W., Peyser, T. A., et al. 2003 Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Plasmas 10, 1883–1896.CrossRefGoogle Scholar