Skip to main content
SpringerLink
Log in

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin–Helmholtz instability (KHI) via an efficient discrete Boltzmann model. Technically, two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes. One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures; the other is to evaluate the growth rate of KHI from the slopes of morphological functionals. Physically, it is found that the time histories of width of mixing layer, TNE intensity, and boundary length show high correlation and attain their maxima simultaneously. The viscosity effects are twofold, stabilize the KHI, and enhance both the local and global TNE intensities. Contrary to the monotonically inhibiting effects of viscosity, the heat conduction effects firstly refrain then enhance the evolution afterwards. The physical reasons are analyzed and presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961

    MATH  Google Scholar 

  2. W. D. Smyth and J. N. Moum, Anisotropy of turbulence in stably stratified mixing layers, Phys. Fluids 12, 1327 (2000)

    ADS  MATH  Google Scholar 

  3. Y. Matsumoto and M. Hoshino, Onset of turbulence induced by a Kelvin–Helmholtz vortex, Geophys. Res. Lett. 31, L02807 (2004)

    ADS  Google Scholar 

  4. O. Berné and Y. Matsumoto, The Kelvin–Helmholtz instability in orion: A source of turbulence and chemical mixing, Astrophys. J. Lett. 761, L4 (2012)

    ADS  Google Scholar 

  5. Z. Xia, Y. Shi, and Y. Zhao, Assessment of the shear-improved Smagorinsky model in laminar-turbulent transitional channel flow, J. Turbul. 16, 925 (2015)

    ADS  MathSciNet  Google Scholar 

  6. Z. Xia, Y. Shi, and S. Chen, Direct numerical simulation of turbulent channel flow with spanwise rotation, J. Fluid Mech. 788, 42 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  7. Z. Xia, Y. Shi, Q. Cai, M. Wan, and S. Chen, Multiple states in turbulent plane Couette flow with spanwise rotation, J. Fluid Mech. 837, 477 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  8. R. P. Drake, High-Energy-Density Physics: Fundamentals, Inertial Fusion and Experimental Astrophysics, Springer, New York, 2006

    Google Scholar 

  9. M. T. Montgomery, V. A. Vladimirov, and P. V. Denissenko, An experimental study on hurricane mesovortices, J. Fluid Mech. 471, 1 (2002)

    ADS  MATH  Google Scholar 

  10. K. Wada and J. Koda, Instabilities of spiral shocks (I): Onset of wiggle instability and its mechanism, Mon. Not. R. Astron. Soc. 349, 270 (2004)

    ADS  Google Scholar 

  11. S. N. Borovikov and N. V. Pogorelov, Voyager 1 near the heliopause, Astrophys. J. Lett. 783, L16 (2014)

    ADS  Google Scholar 

  12. K. Avinash, G. P. Zank, B. Dasgupta, and S. Bhadoria, Instability of the heliopause driven by charge exchange interactions, Astrophys. J. Lett. 791, 102 (2014)

    ADS  Google Scholar 

  13. H. Hasegawa, M. Fujimoto, T. D. Phan, H. Rème, A. Balogh, M. W. Dunlop, C. Hashimoto, and R. Tan- Dokoro, Transport of solar wind into Earth’s magnetosphere through rolled-up Kelvin–Helmholtz vortices, Nature 430, 755 (2004)

    ADS  Google Scholar 

  14. C. Foullon, E. Verwichte, V. M. Nakariakov, K. Nykyri, and C. J. Farrugia, Magnetic Kelvin–Helmholtz instability at the Sun, Astrophys. J. Lett. 729, L8 (2011)

    ADS  Google Scholar 

  15. X. T. He and W. Y. Zhang, Inertial fusion research in China, Eur. Phys. J. D 44, 227 (2007)

    ADS  Google Scholar 

  16. L. Wang, W. Ye, X. He, J. Wu, Z. Fan, C. Xue, H. Guo, W. Miao, Y. Yuan, J. Dong, G. Jia, J. Zhang, Y. Li, J. Liu, M. Wang, Y. Ding, and W. Zhang, Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions, Sci. China-Phys. Mech. Astron. 60, 055201 (2017)

    ADS  Google Scholar 

  17. M. Vandenboomgaerde, M. Bonnefille, and P. Gauthier, The Kelvin–Helmholtz instability in National Ignition Facility hohlraums as a source of gold-gas mixing, Phys. Plasmas 23, 052704 (2016)

    ADS  Google Scholar 

  18. M. Hishida, T. Fujiwara, and P. Wolanski, Fundamentals of rotating detonations, Shock Waves 19, 1 (2009)

    ADS  MATH  Google Scholar 

  19. V. Bychkov, D. Valiev, V. Akkerman, and C. K. Law, Gas compression moderates flame acceleration in deflagrationto-detonation transition, Combust. Sci. Technol. 184, 1066 (2012)

    Google Scholar 

  20. A. Petrarolo, M. Kobald, and S. Schlechtriem, Understanding Kelvin–Helmholtz instability in paraffin-based hybrid rocket fuels, Exp. Fluids 59, 62 (2018)

    Google Scholar 

  21. H. Takeuchi, N. Suzuki, K. Kasamatsu, H. Saito, and M. Tsubota, Quantum Kelvin–Helmholtz instability in phase-separated two-component Bose–Einstein condensates, Phys. Rev. B 81, 094517 (2010)

    ADS  Google Scholar 

  22. D. Kobyakov, A. Bezett, E. Lundh, M. Marklund, and V. Bychkov, Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh–Taylor and Kelvin–Helmholtz instabilities, Phys. Rev. A 89, 013631 (2014)

    ADS  Google Scholar 

  23. R. V. Coelho, M. Mendoza, M. M. Doria, and H. J. Herrmann, Kelvin–Helmholtz instability of the Dirac fluid of charge carriers on graphene, Phys. Rev. B 96, 184307 (2017)

    ADS  Google Scholar 

  24. M. Livio, Astrophysical jets: A phenomenological examination of acceleration and collimation, Phys. Rep. 311, 225 (1999)

    ADS  Google Scholar 

  25. L. F. Wang, W. H. Ye, and Y. J. Li, Combined effect of the density and velocity gradients in the combination of Kelvin–Helmholtz and Rayleigh–Taylor instabilities, Phys. Plasmas 17, 042103 (2010)

    ADS  Google Scholar 

  26. W. H. Ye, L. F. Wang, C. Xue, Z. F. Fan, and X. T. He, Competitions between Rayleigh–Taylor instability and Kelvin–Helmholtz instability with continuous density and velocity profiles, Phys. Plasmas 18, 022704 (2011)

    ADS  Google Scholar 

  27. A. P. Lobanov and J. A. Zensus, A cosmic double helix in the archetypical quasar 3C273, Science 294, 128 (2001)

    ADS  Google Scholar 

  28. B. A. Remington, R. P. Drake, and D. D. Ryutov, Experimental astrophysics with high power lasers and Z pinches, Rev. Mod. Phys. 78, 775 (2006)

    ADS  Google Scholar 

  29. X. Luo, F. Zhang, J. Ding, T. Si, J. Yang, Z. Zhai, and C. Wen, Long-term effect of Rayleigh–Taylor stabilization on converging Richtmyer–Meshkov instability, J. Fluid Mech. 849, 231 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  30. J. J. Tao, X. T. He, and W. H. Ye, and F. H. Busse, Nonlinear Rayleigh–Taylor instability of rotating inviscid fluids, Phys. Rev. E 87, 013001 (2013)

    ADS  Google Scholar 

  31. C. Y. Xie, J. J. Tao, and Z. L. Sun, and J. Li, Retarding viscous Rayleigh–Taylor mixing by an optimized additional mode, Phys. Rev. E 95, 023109 (2017)

    ADS  Google Scholar 

  32. W. Liu, C. Yu, H. Jiang, and X. Li, Bell-Plessett effect on harmonic evolution of spherical Rayleigh–Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers, Phys. Plasmas 24, 022102 (2017)

    ADS  Google Scholar 

  33. Y. Zhou, Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing (I), Phys. Rep. 720–722, 1 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  34. Y. Zhou, Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing (II), Phys. Rep. 723–725, 1 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  35. L. F. Wang, W. H. Ye, Z. F. Fan, Y. J. Li, X. T. He and M. Y. Yu, Weakly nonlinear analysis on the Kelvin–Helmholtz instability, EPL 86, 15002 (2009)

    ADS  Google Scholar 

  36. U. V. Amerstorfer, N. V. Erkaev, U. Taubenschuss, and H. K. Biernat, Influence of a density increase on the evolution of the Kelvin–Helmholtz instability and vortices, Phys. Plasmas 17, 072901 (2010)

    ADS  Google Scholar 

  37. M. Zellinger, U. V. Möstl, N. V. Erkaev, and H. K. Biernat, 2.5D magnetohydrodynamic simulation of the Kelvin–Helmholtz instability around Venus-Comparison of the influence of gravity and density increase, Phys. Plasmas 19, 022104 (2012)

    ADS  Google Scholar 

  38. H. G. Lee and J. Kim, Two-dimensional Kelvin–Helmholtz instabilities of multi-component fluids, Eur. J. Mech. B. Fluids 49, 77 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  39. A. Fakhari and T. Lee, Multiple-relaxation-time lattice Boltzmann method for immiscible fluids at high Reynolds numbers, Phys. Rev. E 87, 023304 (2013)

    ADS  Google Scholar 

  40. T. A. Howson, I. De Moortel, and P. Antolin, The effects of resistivity and viscosity on the Kelvin–Helmholtz instability in oscillating coronal loops, Astron. Astrophys. 602, A74 (2017)

    ADS  Google Scholar 

  41. K. S. Kim and M. Kim, Simulation of the Kelvin–Helmholtz instability using a multi-liquid moving particle semi-implicit method, Ocean Eng. 130, 531 (2017)

    Google Scholar 

  42. R. Zhang, X. He, G. Doolen, and S. Chen, Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities, Adv. Water Res. 24, 461 (2001)

    Google Scholar 

  43. N. D. Hamlin and W. I. Newman, Role of the Kelvin–Helmholtz instability in the evolution of magnetized relativistic sheared plasma flows, Phys. Rev. E 87, 043101 (2013)

    ADS  Google Scholar 

  44. Y. Liu, Z. H. Chen, H. H. Zhang, and Z. Y. Lin, Physical effects of magnetic fields on the Kelvin–Helmholtz instability in a free shear layer, Phys. Fluids 30, 044102 (2018)

    ADS  Google Scholar 

  45. W. C. Wan, G. Malamud, A. Shimony, C. A. Di Stefano, M. R. Trantham, S. R. Klein, D. Shvarts, C. C. Kuranz, and R. P. Drake, Observation of single-mode, Kelvin–Helmholtz instability in a supersonic flow, Phys. Rev. Lett. 115, 145001 (2015)

    Google Scholar 

  46. M. Karimi and S. S. Girimaji, Suppression mechanism of Kelvin–Helmholtz instability in compressible fluid flows, Phys. Rev. E 93, 041102(R) (2016)

    ADS  Google Scholar 

  47. Y. Gan, A. Xu, G. Zhang, and Y. Li, Lattice Boltzmann study on Kelvin–Helmholtz instability: Roles of velocity and density gradients, Phys. Rev. E 83, 056704 (2011)

    ADS  Google Scholar 

  48. L. F. Wang, C. Xue, W. H. Ye, and Y. J. Li, Destabilizing effect of density gradient on the Kelvin–Helmholtz instability, Phys. Plasmas 16, 112104 (2009)

    ADS  Google Scholar 

  49. L. F. Wang, W. H. Ye, and Y. J. Li, Numerical investigation on the ablative Kelvin–Helmholtz instability, EPL 87, 54005 (2009)

    ADS  Google Scholar 

  50. L. F. Wang, W. H. Ye, W. Don, Z. M. Sheng, Y. J. Li, and X. T. He, Formation of large-scale structures in ablative Kelvin–Helmholtz instability, Phys. Plasmas 17, 122308 (2010)

    ADS  Google Scholar 

  51. R. Asthana and G. S. Agrawal, Viscous potential flow analysis of electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer, Int. J. Eng. Sci. 48, 1925 (2010)

    MathSciNet  MATH  Google Scholar 

  52. M. K. Awasthi, R. Asthana, and G. S. Agrawal, Viscous corrections for the viscous potential flow analysis of magnetohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer, Eur. Phys. J. A 48, 174 (2012)

    ADS  Google Scholar 

  53. M. K. Awasthi, R. Asthana, and G. S. Agrawal, Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfe, Int. J. Heat Mass Transfer 78, 251 (2014)

    Google Scholar 

  54. G. Liu, Y. Wang, G. Zang, and H. Zhao, Viscous Kelvin–Helmholtz instability analysis of liquid-vapor two-phase stratified flow for condensation in horizontal tubes, Int. J. Heat Mass Transfer 84, 592 (2015)

    Google Scholar 

  55. Y. Gan, A. Xu, G. Zhang, and S. Succi, Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic non-equilibrium effects, Soft Matter 11, 5336 (2015)

    ADS  Google Scholar 

  56. Y. Gan, A. Xu, G. Zhang, Y. Zhang, and S. Succi, Discrete Boltzmann trans-scale modeling of high-speed compressible flows, Phys. Rev. E 97, 053312 (2018)

    ADS  MathSciNet  Google Scholar 

  57. S. Li and Q. Li, Thermal non-equilibrium effect of smallscale structures in compressible turbulence, Mod. Phys. Lett. B 32, 1840013 (2018)

    ADS  Google Scholar 

  58. A. Xu, G. Zhang, Y. Gan, F. Chen and X. Yu, Lattice Boltzmann modeling and simulation of compressible flows, Front. Phys. 7, 582 (2012)

    ADS  Google Scholar 

  59. A. Xu, G. Zhang, Y. Ying, and C. Wang, Complex fields in heterogeneous materials under shock: Modeling, simulation and analysis, Sci. China-Phys. Mech. Astron. 59, 650501 (2016)

    Google Scholar 

  60. Y. Gan, A. Xu, G. Zhang, and Y. Yang, Lattice BGK kinetic model for high-speed compressible flows: Hydrodynamic and nonequilibrium behaviors, EPL 103, 24003 (2013)

    ADS  Google Scholar 

  61. B. Yan, A. Xu, G. Zhang, Y. Ying, and H. Li, Lattice Boltzmann model for combustion and detonation, Front. Phys. 8, 94 (2013)

    ADS  Google Scholar 

  62. C. Lin, A. Xu, G. Zhang, Y. Li, and S. Succi, Polarcoordinate lattice Boltzmann modeling of compressible flows, Phys. Rev. E 89, 013307 (2014)

    ADS  Google Scholar 

  63. A. Xu, C. Lin, G. Zhang, and Y. Li, Multiple-relaxationtime lattice Boltzmann kinetic model for combustion, Phys. Rev. E 91, 043306 (2015)

    ADS  Google Scholar 

  64. F. Chen, A. Xu, and G. Zhang, Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor instability, Front. Phys. 11, 114703 (2016)

    ADS  Google Scholar 

  65. H. Lai, A. Xu, G. Zhang, Y. Gan, Y. Ying, and S. Succi, Nonequilibrium thermohydrodynamic effects on the Rayleigh–Taylor instability in compressible flows, Phys. Rev. E 94, 023106 (2016)

    ADS  Google Scholar 

  66. C. Lin, A. Xu, G. Zhang, and Y. Li, Double-distributionfunction discrete Boltzmann model for combustion, Combust. Flame 164, 137 (2016)

    Google Scholar 

  67. Y. Zhang, A. Xu, G. Zhang, C. Zhu, and C. Lin, Kinetic modeling of detonation and effects of negative temperature coefficient, Combust. Flame 173, 483 (2016)

    Google Scholar 

  68. C. Lin, A. Xu, G. Zhang, K. H. Luo, and Y. Li, Discrete Boltzmann modeling of Rayleigh–Taylor instability in two-component compressible flows, Phys. Rev. E 96, 053305 (2017)

    ADS  Google Scholar 

  69. C. Lin, K. H. Luo, L. Fei, and S. Succi, A multicomponent discrete Boltzmann model for nonequilibrium reactive flows, Sci. Rep. 7, 14580 (2017)

    ADS  Google Scholar 

  70. C. Lin and K. H. Luo, MRT discrete Boltzmann method for compressible exothermic reactive flows, Comput. Fluids 166, 176 (2018)

    MathSciNet  MATH  Google Scholar 

  71. Y. Gan, A. Xu, G. Zhang, and H. Lai, Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 232, 477 (2018)

    Google Scholar 

  72. Y. Zhang, A. Xu, G. Zhang, Z. Chen, and P. Wang, Discrete ellipsoidal statistical BGK model and Burnett equations, Front. Phys. 13, 135101 (2018)

    ADS  Google Scholar 

  73. A. Xu, G. Zhang, Y. Zhang, P. Wang, and Y. Ying, Discrete Boltzmann model for implosion- and explosion-related compressible flow with spherical symmetry, Front. Phys. 13, 135102 (2018)

    ADS  Google Scholar 

  74. C. Lin and K. H. Luo, Mesoscopic simulation of nonequilibrium detonation with discrete Boltzmann method, Combust. Flame 198, 356 (2018)

    Google Scholar 

  75. F. Chen, A. Xu and G. Zhang, Collaboration and competition between Richtmyer–Meshkov instability and Rayleigh–Taylor instability, Phys. Fluids 30, 102105 (2018)

    ADS  Google Scholar 

  76. P. Henri, S. S. Cerri, F. Califano, F. Pegoraro, C. Rossi, M. Faganello, O. Šebek, P. M. Tráavnícek, P. Hellinger, J. T. Frederiksen, A. Nordlund, S. Markidis, R. Keppens, and G. Lapenta, Nonlinear evolution of the magnetized Kelvin–Helmholtz instability: From fluid to kinetic modeling, Phys. Plasmas 20, 102118 (2013)

    ADS  Google Scholar 

  77. T. Umeda, N. Yamauchi, Y. Wada, and S. Ueno, Evaluating gyro-viscosity in the Kelvin–Helmholtz instability by kinetic simulations, Phys. Plasmas 23, 054506 (2016)

    ADS  Google Scholar 

  78. A. Rosenfeld and A. C. Kak, Digital Picture Processing, Academic Press, New York, 1976

    MATH  Google Scholar 

  79. V. Sofonea and K. R. Mecke, Morphological characterization of spinodal decomposition kinetics, Eur. Phys. J. B 8, 99 (1999)

    ADS  Google Scholar 

  80. Y. Gan, A. Xu, G. Zhang, Y. Li, and H. Li, Phase separation in thermal systems: A lattice Boltzmann study and morphological characterization, Phys. Rev. E 84, 046715 (2011)

    ADS  Google Scholar 

  81. Y. Gan, A. Xu, G. Zhang, P. Zhang and Y. Li, Lattice Boltzmann study of thermal phase separation: Effects of heat conduction, viscosity and Prandtl number, EPL 97, 44002 (2012)

    Google Scholar 

  82. A. Xu, G. Zhang, X. Pan, P. Zhang and J. Zhu, Morphological characterization of shocked porous material, J. Phys. D 42, 075409 (2009)

    ADS  Google Scholar 

  83. R. Machado, On the generalized Hermite-based lattice Boltzmann construction, lattice sets, weights, moments, distribution functions and high-order models, Front. Phys. 9, 490 (2014)

    ADS  Google Scholar 

  84. T. Kataoka and M. Tsutahara, Lattice Boltzmann model for the compressible Navier–Stokes equations with flexible specific-heat ratio, Phys. Rev. E 69, 035701(R) (2004)

    ADS  Google Scholar 

  85. Y. Zhang, R. Qin, and D. R. Emerson, Lattice Boltzmann simulation of rarefied gas flows in microchannels, Phys. Rev. E 71, 047702 (2005)

    ADS  Google Scholar 

  86. Y. H. Zhang, R. S. Qin, Y. H. Sun, R. W. Barber, and D. R. Emerson, Gas flow in microchannels — A lattice Boltzmann method approach, J. Stat. Phys. 121, 257 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  87. B. I. Green and P. Vedula, A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows, J. Stat. Mech: Theory Exp. P07016 (2013)

    Google Scholar 

  88. L. H. Holway, New statistical models for kinetic theory: Methods of construction, Phys. Fluids 9, 1658 (1966)

    ADS  Google Scholar 

  89. E. M. Shakhov, Generalization of the Krook kinetic relaxation equation, Fluid Dyn. 3, 95 (1968)

    ADS  Google Scholar 

  90. G. Liu, A method for constructing a model form for the Boltzmann equation, Phys. Fluids A 2, 277 (1990)

    ADS  MATH  Google Scholar 

  91. X. Shan, Simulation of Rayleigh–Bénard convection using a lattice Boltzmann method, Phys. Rev. E 55, 2770 (1997)

    ADS  Google Scholar 

  92. F. Chen, A. Xu, G. Zhang, Y. Li, and S. Succi, Multiplerelaxation-time lattice Boltzmann approach to compressible flows with flexible specific-heat ratio and Prandtl number, EPL 90, 54003 (2010)

    ADS  Google Scholar 

  93. F. Chen, A. Xu, G. Zhang, and Y. Wang, Twodimensional MRT LB model for compressible and incompressible flows, Front. Phys. 9, 246 (2014)

    ADS  Google Scholar 

  94. R. Machado, On the moment system and a flexible Prandtl number, Mod. Phys. Lett. B 28, 1450048 (2014)

    ADS  MathSciNet  Google Scholar 

  95. F. M. White, Viscous Fluid Flow, McGraw-Hill, New York, 1974

    MATH  Google Scholar 

  96. G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 27, 1 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  97. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys. 54, 115 (1984)

    ADS  MathSciNet  MATH  Google Scholar 

  98. G. S. Jiang and C. W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126, 202 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  99. H. X. Zhang, Non-oscillatory and non-free-parameter dissipation difference scheme, Acta Aerodyna. Sinica 6, 143 (1988)

    Google Scholar 

  100. U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, Implicitexplicit Runge–Kutta methods for time-dependent partial differential equations, Appl. Numer. Math. 25, 151 (1997)

    MathSciNet  MATH  Google Scholar 

  101. Q. Li, Y. L. He, Y. Wang, and W. Q. Tao, Coupled double-distribution-function lattice Boltzmann method for the compressible Navie–Stokes equations, Phys. Rev. E 76, 056705 (2007)

    ADS  MathSciNet  Google Scholar 

  102. L. M. Yang, C. Shu, and Y. Wang, Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows, Phys. Rev. E 93, 033311 (2016)

    ADS  MathSciNet  Google Scholar 

  103. F. Gao, Y. Zhang, Z. He, and B. Tian, Formula for growth rate of mixing width applied to Richtmyer–Meshkov instability, Phys. Fluids 28, 114101 (2016)

    ADS  Google Scholar 

  104. Y. Zhang, Z. He, F. Gao, X. Li, and B. Tian, Evolution of mixing width induced by general Rayleigh–Taylor instability, Phys. Rev. E 93, 063102 (2016)

    ADS  Google Scholar 

  105. F. Gao, Y. Zhang, Z. He, L. Li, and B. Tian, Characteristics of turbulent mixing at late stage of the Richtmyer–Meshkov instability, AIP Adv. 7, 075020 (2017)

    ADS  Google Scholar 

  106. F. Lei, J. Ding, T. Si, Z. Zhai and X. Luo, Experimental study on a sinusoidal air/SF6 interface accelerated by a cylindrically converging shock, J. Fluid Mech. 826, 819 (2017)

    ADS  Google Scholar 

  107. J. Ding, T. Si, J. Yang, X. Lu, Z. Zhai, and X. Luo, Measurement of a Richtmyer–Meshkov instability at an air-SF6 interface in a semiannular shock tube, Phys. Rev. Lett. 119, 014501 (2017)

    ADS  Google Scholar 

  108. B. Guan, Z. Zhai, T. Si, X. Lu, and X. Luo, Manipulation of three-dimensional Richtmyer–Meshkov instability by initial interfacial principal curvatures, Phys. Fluids 29, 032106 (2017)

    ADS  Google Scholar 

  109. S. Huang, W. Wang, and X. Luo, Molecular-dynamics simulation of Richtmyer–Meshkov instability on a Li-H2 interface at extreme compressing conditions, Phys. Plasmas 25, 062705 (2018)

    ADS  Google Scholar 

Download references

Acknowledgements

Y. G., C. L., H. L. and Z. L. acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 11875001, 51806116, and 11602162), Natural Science Foundation of Hebei Province (Grants Nos. A2017409014 and 2018J01654), Natural Science Foundations of Hebei Educational Commission (Grant No. ZD2017001). A. X. and G. Z. acknowledge the support from the National Natural Science Foundation of China (Grant No. 11772064), CAEP Foundation (Grant No. CX2019033), Science Challenge Project (Grant No. JCKY2016212A501), the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology, Grant No. KFJJ19- 01M).

Author information

Authors and Affiliations

  1. North China Institute of Aerospace Engineering, Langfang, 065000, China

    Yan-Biao Gan

  2. College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou, 350007, China

    Yan-Biao Gan & Hui-Lin Lai

  3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing, 100088, China

    Ai-Guo Xu & Guang-Cai Zhang

  4. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Ai-Guo Xu

  5. Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing, 100871, China

    Ai-Guo Xu

  6. Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    Chuan-Dong Lin

  7. Department of Physics, School of Science, Tianjin Chengjian University, Tianjin, 300384, China

    Zhi-Peng Liu

Authors
  1. Yan-Biao Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ai-Guo Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guang-Cai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chuan-Dong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hui-Lin Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhi-Peng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ai-Guo Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gan, YB., Xu, AG., Zhang, GC. et al. Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows. Front. Phys. 14, 43602 (2019). https://doi.org/10.1007/s11467-019-0885-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-019-0885-4

Keywords

Search

Navigation