Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-01T00:22:47.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Published online by Cambridge University Press:  06 May 2022

Zheng Yan Open the ORCID record for Zheng Yan [Opens in a new window] ,
Yaowei Fu Open the ORCID record for Yaowei Fu [Opens in a new window] ,
Lifeng Wang ,
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window]  and
Xinliang Li
Zheng Yan
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China
Yaowei Fu
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Lifeng Wang
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China Center for Applied Physics and Technology, HEDPS, Peking University, Beijing 100871, PR China
Changping Yu
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Xinliang Li*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of a three-dimensional cylindrical Richtmyer–Meshkov instability with and without chemical reactions are carried out to explore the chemical reaction effects on the statistical characteristics of transition and turbulent mixing. We adopt 9-species and 19-reaction models of non-premixed hydrogen and oxygen separated by a multimode perturbed cylindrical interface. A new definition of mixing width suitable for a chemical reaction is introduced, and we investigate the spatio-temporal evolution of typical flow parameters within the mixing regions. After reshock with a fuller mixing of fuels and oxygen, the chemical reaction becomes sufficiently apparent at affecting the evolution of the flow fields. Because of the generation of a combustion wave within the combustion regions and propagation, the growth of the mixing width with a chemical reaction is accelerated, especially around the outer radius with large temperature gradient profiles. However, the viscous dissipation rate in the early stage of the chemical reaction is greater because of heat release, which results in weakened turbulent mixing within the mixing regions. We confirm that small-scale structures begin to develop after reshock and then decay over time. During the developing process, helicity also begins to develop, in addition to kinetic energy, viscous dissipation rate, enstrophy, etc. In the present numerical simulations with cylindrical geometry, the fluctuating flow fields evolve from quasi-two-dimensional perturbations, and the generations of helicity can capture this transition process. The weakened fluctuations during shock compression can be explained as the inverse energy cascade, and the chemical reaction can promote this inverse energy cascade process.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing Reacting Flows: Turbulent reacting flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A55
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., Bhowmick, A.K., Naveh, A., Pandian, A., Swisher, N.C., Stellingwerf, R.F. & Arnett, W.D. 2019 Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing. Proc. Natl Acad. Sci. USA 116, 18184–18192.CrossRefGoogle ScholarPubMed
Almgren, A.S., Bell, J.B., Rendleman, C.A. & Zingale, M. 2006 Low mach number modeling of type Ia supernovae. I. Hydrodynamics. Astrophys J. 637, 922–936.CrossRefGoogle Scholar
Anderson, J.D. 2010 Fundamentals of Aerodynamics. Tata McGraw-Hill Education.Google Scholar
Attal, N. & Ramaprabhu, P. 2015 Numerical investigation of a single-mode chemically reacting Richtmyer–Meshkov instability. Shock Waves 25, 307–328.CrossRefGoogle Scholar
Attal, N., Ramaprabhu, P., Hossain, J., Karkhanis, V., Uddin, M., Gord, J.R. & Royd, S. 2015 Development and validation of a chemical reaction solver coupled to the flash code for combustion applications. Comput. Fluids 107, 59–76.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
Balakumar, B.J., Orlicz, G.C., Tomkins, C.D. & Prestridge, K.P. 2008 Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock. Phys. Fluids 20, 124103.CrossRefGoogle Scholar
Bambauer, M., Chakraborty, N., Klein, M. & Hasslberger, J. 2021 Vortex dynamics and fractal structures in reactive and nonreactive Richtmyer–Meshkov instability. Phys. Fluids 33, 044114.CrossRefGoogle Scholar
Bambauer, M., Hasslberger, J. & Klein, M. 2020 Direct numerical simulation of the Richtmyer–Meshkov instability in reactive and nonreactive flows. Combust. Sci. Technol. 192, 2010–2027.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1947 Decay of vorticity in isotropic turbulence. Proc. R. Soc. A 191, 534–550.Google Scholar
Bell, G.I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Tech. Rep. LA-1321. Los Alamos National Laboratory.Google Scholar
Bender, J.D., et al. 2021 Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer. J. Fluid Mech. 915, A84.CrossRefGoogle Scholar
Bengoechea, S., Stein, L., Reiss, J. & Sesterhenn, J. 2014 Numerical investigation of reactive and non-reactive Richtmyer–Meshkov instabilities. In Active Flow and Combustion Control 2014 (ed. K. Rudibert), pp. 343–361. Springer.CrossRefGoogle Scholar
Billet, G. 2005 Improvement of convective concentration fluxes in a one step reactive flow solver. J. Comput. Phys. 204, 319–352.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Budzinski, J.M., Benjamin, R.F. & Jacobs, J.W. 1994 Influence of initial conditions on the flow patterns of a shock-accelerated thin fluid layer. Phys. Fluids 6, 3510–3512.CrossRefGoogle Scholar
Chertkov, M., Lebedev, V. & Vladimirova, N. 2009 Reactive Rayleigh–Taylor turbulence. J. Fluid Mech. 633, 1–16.CrossRefGoogle Scholar
Chisnell, R.F. 1998 An analytic description of converging shock waves. J. Fluid Mech. 354, 357–375.CrossRefGoogle Scholar
Cook, A.W. & Zhou, Y. 2002 Energy transfer in Rayleigh–Taylor instability. Phys. Rev. E 66, 026312.CrossRefGoogle ScholarPubMed
Debue, P., Valori, V., Cuvier, C., Daviaud, F., Foucaut, J.M., Laval, J.P., Wiertel, C., Padilla, V. & Dubrulle, B. 2021 Three-dimensional analysis of precursors to non-viscous dissipation in an experimental turbulent flow. J. Fluid Mech. 914, A9.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
Dimotakis, P.E. 2000 The mixing transition in turbulent flow. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Dimotakis, P.E. & Samtaney, R. 2006 Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18, 031705.CrossRefGoogle Scholar
Ding, J., Li, J., Sun, R., Zhai, Z. & Luo, X. 2019 Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface. J. Fluid Mech. 878, 277–291.CrossRefGoogle Scholar
Dyke, M.V. & Guttmann, A.J. 1982 The converging shock wave from a spherical or cylindrical piston. J. Fluid Mech. 120, 451–462.CrossRefGoogle Scholar
Eyink, G.L. & Drivas, T.D. 2018 Cascades and dissipative anomalies in compressible fluid turbulence. Phys. Rev. X 8, 011022.Google Scholar
Fu, Y., Yu, C. & Li, X. 2020 Energy transport characteristics of converging Richtmyer–Meshkov instability. AIP Adv. 10, 105302.CrossRefGoogle Scholar
Fu, Y., Yu, C., Yan, Z. & Li, X. 2019 a DNS analysis of the effects of combustion on turbulence in a supersonic H2/air jet flow. Aerosp. Sci. Technol. 93, 105362.CrossRefGoogle Scholar
Fu, Y., Yu, C., Yan, Z. & Li, X. 2019 b The effects of combustion on turbulent statistics in a supersonic turbulent jet. Adv. Appl. Math. Mech. 11, 664–674.CrossRefGoogle Scholar
Gatski, T.B. & Bonnet, J.P. 2013 Compressibility, Turbulence and High Speed Flow. Academic Press.Google Scholar
Gauthier, S. 2017 Compressible Rayleigh–Taylor turbulent mixing layer between newtonian miscible fluids. J. Fluid Mech. 830, 211–256.CrossRefGoogle Scholar
Gordon, S. & McBride, B.J. 1971 Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks and Chapman-Jouguet detonations. Tech. Rep. SF-273. NASA.Google Scholar
Graves, R.E. & Argrow, B.M. 1999 Bulk viscosity: past to present. J. Thermophys. Heat Transfer 13, 337–342.CrossRefGoogle Scholar
Groom, M. & Thornber, B. 2019 Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability. Comput. Fluids 194, 104309.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
Groom, M. & Thornber, B. 2021 Reynolds number dependence of turbulence induced by the Richtmyer–Meshkov instability using direct numerical simulations. J. Fluid Mech. 908, A31.CrossRefGoogle Scholar
Guderley, K.G. 1942 Starke kugelige und zylindrische verdichtungsstosse in der nahe des kugelmittelpunktes bzw. der zylinderachse. Luftfahrtforschung 19, 302–312.Google Scholar
Hill, D.J., Pantano, C. & Pullin, D.I. 2006 Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557, 29–61.CrossRefGoogle Scholar
Houas, L. & Chemouni, I. 1996 Experimental investigation of Richtmyer–Meshkov instability in shock tube. Phys. Fluids 8, 614–627.CrossRefGoogle Scholar
Huang, M.J. & Leonard, A. 1994 Power-law decay of homogeneous turbulence at low Reynolds numbers. Phys. Fluids 6, 3765–3775.CrossRefGoogle Scholar
Jiang, H., Dong, G., Chen, X. & Li, B. 2016 a A parameterization of the Richtmyer–Meshkov instability on a premixed flame interface induced by the successive passages of shock waves. Combust. Flame 169, 229–241.CrossRefGoogle Scholar
Jiang, H., Dong, G. & Wu, J.T. 2016 b Numerical simulations of the process of multiple shock–flame interactions. Acta Mech. Sin. 32, 659–669.CrossRefGoogle Scholar
Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164, 192–215.CrossRefGoogle Scholar
Kee, R.J., Rupley, F.M. & Miller, J.A. 1989 Chemkin-II: a Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. Tech. Rep. SAND89-8009. Sandia National Laboratories.CrossRefGoogle Scholar
Khokhlov, A.M., Oran, E.S., Chtchelkanova, A.Y. & Wheelerc, J.C. 1999 Interaction of a shock with a sinusoidally perturbed flame. Combust. Flame 117, 99–116.CrossRefGoogle Scholar
Kilchyk, V., Nalim, R. & Merkle, C. 2011 Laminar premixed flame fuel consumption rate modulation by shocks and expansion waves. Combust. Flame 158, 1140–1148.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 reshock conditions. J. Fluid Mech. 626, 449–112.CrossRefGoogle Scholar
Lesieur, M. 1997 Turbulence in Fluids. Kluwer Academic.CrossRefGoogle Scholar
Li, X., Fu, Y., Yu, C. & Li, L. 2021 Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities. J. Fluid Mech. 928, A10.CrossRefGoogle Scholar
Li, X., Leng, Y. & He, Z. 2013 Optimized sixth-order monotonicity-preserving scheme by nonlinear spectral analysis. Intl J. Numer. Meth. Fluids 73, 560–577.CrossRefGoogle Scholar
Li, J., Zhao, Z., Kazakov, A. & Dryer, F.L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36, 566–575.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, W., Yu, C., Ye, W., Wang, L. & He, X. 2014 Nonlinear theory of classical cylindrical Richtmyer–Meshkov instability for arbitrary Atwood numbers. Phys. Plasmas 21, 062119.Google Scholar
Lombardini, M., Hill, D.J., Pullin, D.I. & Meiron, D.I. 2011 Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech. 670, 439–480.CrossRefGoogle Scholar
Lombardini, M. & Pullin, D.I. 2009 Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability. Phys. Fluids 21, 114103.CrossRefGoogle Scholar
Lombardini, M., Pullin, D. & Meiron, D. 2012 Transition to turbulence in shock-driven mixing: a Mach number study. J. Fluid Mech. 690, 203–226.CrossRefGoogle Scholar
Lombardini, M., Pullin, D. & Meiron, D. 2014 a Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.CrossRefGoogle Scholar
Lombardini, M., Pullin, D. & Meiron, D. 2014 b Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. J. Fluid Mech. 748, 113–142.CrossRefGoogle Scholar
Luo, X., Ding, J., Wang, M., Zhai, Z. & Si, T. 2015 A semi-annular shock tube for studying cylindrically converging Richtmyer–Meshkov instability. Phys. Fluids 27, 091702.CrossRefGoogle Scholar
Luo, X., Si, T., Yang, J. & Zhai, Z. 2014 A cylindrical converging shock tube for shock-interface studies. Rev. Sci. Instrum. 85, 015107.CrossRefGoogle ScholarPubMed
Massa, L. & Jha, P. 2012 Linear analysis of the Richtmyer–Meshkov instability in shock-flame interactions. Phys. Fluids 24, 056101.CrossRefGoogle Scholar
McFarland, J., Reilly, D., Creel, S., McDonald, C., Finn, T. & Ranjan, D. 2014 Experimental investigation of the inclined interface Richtmyer–Meshkov instability before and after reshock. Exp. Fluids 55, 1–14.CrossRefGoogle Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 43, 101–104.Google Scholar
Mikaelian, K.O. 1989 Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Physica D 36, 343–357.CrossRefGoogle Scholar
Mikaelian, K.O. 2005 Rayleigh–Taylor and Richtmyer–Meshkov instabilities and mixing in stratified cylindrical shells. Phys. Fluids 17, 094105.CrossRefGoogle Scholar
Mikaelian, K.O. & Olson, B.J. 2020 On modeling Richtmyer–Meshkov turbulent mixing widths. Physica D 402, 132243.CrossRefGoogle Scholar
Moffatt, H.K. 2021 Extreme events in turbulent flow. J. Fluid Mech. 914, F1.CrossRefGoogle Scholar
Moffatt, H.K. & Tsinober, A. 1992 Helicity in laminar and turbulence flow. Annu. Rev. Fluid Mech. 24, 281–312.CrossRefGoogle Scholar
Motl, B., Oakley, J., Ranjan, D., Weber, C. & Anderson, M. 2009 Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges. Phys. Fluids 21, 126102.CrossRefGoogle Scholar
Orlicz, G.C., Balakumar, B.J., Tomkins, C.D. & Prestridge, K.P. 2009 A Mach number study of the Richtmyer–Meshkov instability in a varicose, heavy-gas curtain. Phys. Fluids 21, 064102.CrossRefGoogle Scholar
Orszag, S.A. 1977 Statistical theory of turbulence. In Fluid Dynamics 1973, Les Houches Summer School of Theoretical Physics (ed. R. Balian & J.L. Peube), pp. 237–374. Gordon and Breach.Google Scholar
Plesset, M.S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.CrossRefGoogle Scholar
Pope, S.B. 2010 Turbulent Flows. Combridge University Press.Google Scholar
Pouquet, A., Lesieur, M., André, J.C. & Basdevant, C. 1975 Evolution of high Reynolds number two-dimensional turbulence. J. Fluid Mech. 72, 305–319.Google Scholar
Ramaprabhu, P., Dimonte, G., Woodward, P., Fryer, C., Rockefeller, G., Muthuraman, K., Lin, P.H. & Jayaraj, J. 2012 The late-time dynamics of the single-mode Rayleigh–Taylor instability. Phys. Fluids 24, 074107.CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Robey, H.F., Zhou, Y., Buckingham, A.C., Keiter, P., Remington, B.A. & Drake, R.P. 2003 The time scale for the transition to turbulence in a high Reynolds number, accelerated flow. Phys. Plasmas 10, 614–622.CrossRefGoogle Scholar
Saffman, P.G. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
Sahoo, G., Bonaccorso, F. & Biferale, L. 2015 Role of helicity for large- and small-scale turbulent fluctuations. Phys. Rev. E 92, 051002.CrossRefGoogle ScholarPubMed
Samtaney, R., Pullin, D.I. & Kosovié, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13, 1415–1430.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
Teng, J., Wang, J., Li, H. & Chen, S. 2020 Spectra and scaling in chemically reacting compressible isotropic turbulence. Phys. Rev. Fluids 5, 084601.CrossRefGoogle Scholar
Teng, J., Wang, J., Li, H. & Chen, S. 2021 Interscale kinetic energy transfer in chemically reacting compressible isotropic turbulence. J. Fluid Mech. 912, A36.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, 105107.CrossRefGoogle Scholar
Thornber, B., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2010 The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability. J. Fluid Mech. 654, 99–139.CrossRefGoogle Scholar
Tomkins, C.D., Balakumar, B.J., Orlicz, G., Prestridge, K.P. & Ristorcelli, J.R. 2013 Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence. J. Fluid Mech. 735, 288–306.CrossRefGoogle Scholar
Tomkins, C.D., Kumar, S., Orlicz, G.C. & Prestridge, K.P. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131–150.CrossRefGoogle Scholar
Tran, C.V. & Dritschel, D.G. 2006 Vanishing enstrophy dissipation in two-dimensional Navier–Stokes turbulence in the inviscid limit. J. Fluid Mech. 559, 107–116.CrossRefGoogle Scholar
Tritschler, V.K., Zubel, M., Hickel, S. & Adams, N.A. 2014 Evolution of length scales and statistics of Richtmyer–Meshkov instability from direct numerical simulations. Phys. Rev. E 90, 063001.CrossRefGoogle ScholarPubMed
Vandenboomgaerde, M. & Aymard, C. 2011 Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs. Phys. Fluids 23, 016101.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
Vetter, M. & Sturtevant, B. 1995 Experiments on the Richtmyer–Meshkov instability of an air/SF6 interface. Shock Waves 4, 247–252.CrossRefGoogle Scholar
Wang, L., et al. 2017 b Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions. Sci. China: Phys. Mech. Astron. 60, 055201.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017 a Spectra and statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2, 013403.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C., Wang, L. & Chen, S. 2019 Cascades of temperature and entropy fluctuations in compressible turbulence. J. Fluid Mech. 867, 195–215.CrossRefGoogle Scholar
Wang, L., Wu, J., Guo, H., Ye, W., Liu, J., Zhang, W. & He, X. 2015 Weakly nonlinear Bell–Plesset effects for a uniformly converging cylinder. Phys. Plasmas 22, 082702.Google Scholar
Wang, L., Wu, J., Ye, W., Zhang, W. & He, X. 2013 b Weakly nonlinear incompressible Rayleigh–Taylor instability growth at cylindrically convergent interfaces. Phys. Plasmas 20, 042708.Google Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. & Chen, S. 2013 a Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.CrossRefGoogle ScholarPubMed
Wu, J., Liu, H. & Xiao, Z. 2021 Refined modelling of the single-mode cylindrical Richtmyer–Meshkov instability. J. Fluid Mech. 908, A9.CrossRefGoogle Scholar
Yan, Z., Li, X., Wang, J. & Yu, C. 2019 Effect of pressure on joint cascade of kinetic energy and helicity in compressible helical turbulence. Phys. Rev. E 99, 033114.CrossRefGoogle ScholarPubMed
Yan, Z., Li, X.L., Yu, C.P. & Wang, J.C. 2020 a Cross-chirality transfer of kinetic energy and helicity in compressible helical turbulence. Phys. Rev. Fluids 5, 084604.CrossRefGoogle Scholar
Yan, Z., Li, X.L., Yu, C.P., Wang, J.C. & Chen, S.Y. 2020 b Dual channels of helicity cascade in turbulent flows. J. Fluid Mech. 894, R2.CrossRefGoogle Scholar
Yeung, P.K., Zhai, X.M. & Sreenivasan, K.R. 2015 Extreme events in computational turbulence. Proc. Natl Acad. Sci. USA 112, 12633–12638.CrossRefGoogle ScholarPubMed
Youngs, D.L. 2013 The density ratio dependence of self-similar Rayleigh–Taylor mixing. Phil. Trans. R. Soc. A 371, 20120173.CrossRefGoogle ScholarPubMed
Zhai, Z., Liu, C., Qin, F., Yang, J. & Luo, X. 2010 Generation of cylindrical converging shock waves based on shock dynamics theory. Phys. Fluids 22, 041701.CrossRefGoogle Scholar
Zhai, Z., Si, T., Luo, X., Yang, J., Liu, C., Tan, D. & Zou, L. 2012 Parametric study of cylindrical converging shock waves generated based on shock dynamics theory. Phys. Fluids 24, 026101.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, Y., Ruan, Y., Xie, H. & Tian, B. 2020 Mixed mass of classical Rayleigh–Taylor mixing at arbitrary density ratios. Phys. Fluids 22, 011702.CrossRefGoogle Scholar
Zhao, Z., Liu, N.S. & Lu, X.Y. 2020 Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor turbulence. J. Fluid Mech. 904, A37.CrossRefGoogle Scholar
Zhou, Y. 2001 A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids 13, 538–543.CrossRefGoogle Scholar
Zhou, Y. 2007 Unification and extension of the concepts of similarity criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations. Phys. Plasmas 14, 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., Cabot, W.H. & Thornber, B. 2016 Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows. Phys. Plasmas 23, 052712.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., Groom, M. & Thornber, B. 2020 Dependence of enstrophy transport and mixed mass on dimensionality and initial conditions in the Richtmyer–Meshkov instability induced flows. Trans. ASME J. Fluids Engng 142, 121104.CrossRefGoogle Scholar
Zhou, Y., et al. 2003 Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Plasmas 10, 1883–1896.CrossRefGoogle Scholar
Zhou, Y., et al. 2021 Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales. Physica D 423, 132838.CrossRefGoogle Scholar