1932

Abstract

Density variations in fluid flows can arise due to acoustic or thermal fluctuations, compositional changes during mixing of fluids with different molar masses, or phase inhomogeneities. In particular, thermal and compositional (with miscible fluids) density variations have many similarities, such as in how the flow interacts with a shock wave. Two limiting cases have been of particular interest: () the single-fluid non-Oberbeck–Boussinesq low–Mach number approximation for flows with temperature variations, which describes vertical convection, and () the incompressible limit of mixing between miscible fluids with different molar masses, which describes the Rayleigh–Taylor instability. The equations describing these cases are remarkably similar, with some differences in the molecular transport terms. In all cases, strong inertial effects lead to significant asymmetries of mixing, turbulence, and the shape of mixing layers. In addition, density variations require special attention in turbulence models to avoid viscous contamination of the large scales.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010719-060114
2020-01-05
2024-03-28
Loading full text...

Full text loading...

/deliver/fulltext/fluid/52/1/annurev-fluid-010719-060114.html?itemId=/content/journals/10.1146/annurev-fluid-010719-060114&mimeType=html&fmt=ahah

Literature Cited

  1. Aglitskiy Y, Velikovich AL, Karasik M, Metzler N, Zalesak S et al. 2014. Basic hydrodynamics of Richtmyer-Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions. Philos. Trans. R. Soc. Lond. A 368:1739–68
    [Google Scholar]
  2. Ahlers G, Araujo FF, Funfschilling D, Grossmann S, Lohse D 2007. Non-Oberbeck-Boussinesq effects in gaseous Rayleigh-Bénard convection. Phys. Rev. Lett. 98:054501
    [Google Scholar]
  3. Ahlers G, Brown E, Araujo FF, Funfschilling D, Grossmann S, Lohse D 2006. Non-Oberbeck-Boussinesq effects in gaseous Rayleigh-Bénard convection. J. Fluid Mech. 569:409–45
    [Google Scholar]
  4. Akula B, Ranjan D 2016. Dynamics of buoyancy-driven flows at moderately high Atwood numbers. J. Fluid Mech. 795:313–55
    [Google Scholar]
  5. Almagro A, García-Villalba M, Flores O 2017. A numerical study of a variable-density low-speed turbulent mixing layer. J. Fluid Mech. 830:569–601
    [Google Scholar]
  6. Almgren AS, Bell JB, Rendleman CA, Zingale M 2006a. Low Mach number modeling of type Ia supernovae. I. Hydrodynamics. Astrophys. J. 637:922–36
    [Google Scholar]
  7. Almgren AS, Bell JB, Rendleman CA, Zingale M 2006b. Low Mach number modeling of type Ia supernovae. II. Energy evolution. Astrophys. J. 649:927
    [Google Scholar]
  8. Aluie H 2013. Scale decomposition in compressible turbulence. Physica D 24:54–65
    [Google Scholar]
  9. Amielh M, Djeridane T, Anslemet F, Fulachier F 1996. Velocity near-field of variable density turbulent jets. Int. J. Heat Mass Transfer 39:2149–64
    [Google Scholar]
  10. Andreopoulos Y, Agui JH, Briassulis G 2000. Shock wave–turbulence interactions. Annu. Rev. Fluid Mech. 32:309–45
    [Google Scholar]
  11. Andrews MJ, Youngs DL, Livescu D, Wei T 2014. Computational studies of two-dimensional Rayleigh-Taylor driven mixing for a tilted-rig. ASME J. Fluids Eng. 136:091212
    [Google Scholar]
  12. Ashurst WT, Kerstein AR 2005. One-dimensional turbulence: variable density formulation and application to mixing layers. Phys. Fluids 17:025107
    [Google Scholar]
  13. Aslangil D, Livescu D, Banerjee A 2017. High-Atwood number effects on buoyancy-driven variable density homogeneous turbulence Paper presented at the 16th European Turbulence Conference, Stockholm, Sweden, Aug. 21–24
  14. Attili A, Bisetti F 2012. Statistics and scaling of turbulence in a spatially developing mixing layer at . Phys. Fluids 24:035109
    [Google Scholar]
  15. Balakumar BJ, Orlicz GC, Ristorcelli JR, Balasubramania S, Prestridge KP, Tomkins CD 2012. Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics. J. Fluid Mech. 696:67–93
    [Google Scholar]
  16. Balasubramanian S, Orlicz GC, Prestridge KP, Balakumar BJ 2012. Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock. Phys. Fluids 24:034103
    [Google Scholar]
  17. Baltzer JR, Livescu D 2019. Low-speed turbulent shear-driven mixing layers with large thermal and compositional density variations. Modeling and Simulation of Turbulent Mixing and Reaction: For Power, Energy, and Flight D Livescu, F Battaglia, P Givi Singapore: Springer Nature
    [Google Scholar]
  18. Banerjee A, Andrews MJ Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. Phys. Fluids 18:035107
    [Google Scholar]
  19. Banerjee A, Kraft WN, Andrews MJ 2010. Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers. J. Fluid Mech. 659:127–90
    [Google Scholar]
  20. Batchelor GK, Canuto VM, Chasnov JR 1992. Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235:349–78
    [Google Scholar]
  21. Beale JT, Kato T, Majda A 1984. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys. 94:61–66
    [Google Scholar]
  22. Bird GA 1961. The motion of a shock-wave through a region of non-uniform density. J. Fluid Mech. 11:180–86
    [Google Scholar]
  23. Boffetta G, Mazzino A 2017. Incompressible Rayleigh–Taylor turbulence. Annu. Rev. Fluid Mech. 49:119–43
    [Google Scholar]
  24. Boukharfane R, Bouali Z, Mura A 2018. Evolution of scalar and velocity dynamics in planar shock-turbulence interaction. Shock Waves 28:1117–41
    [Google Scholar]
  25. Brouillette M 2002. The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34:445–68
    [Google Scholar]
  26. Brown G 1974. The entrainment and large structure in turbulent mixing layers. Proceedings of the 5th Australasian Conference on Hydraulics and Fluid Mechanics, Vol. 1, ed. D Lindley, AJ Sutherland, pp. 352–59 Christchurch, N.Z.: Canterbury Univ.
  27. Brown GL, Roshko A 1974. On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64:775–816
    [Google Scholar]
  28. Cabot W, Cook A 2006. Reynolds number effects on Rayleigh–Taylor instability with possible implications for type-Ia supernovae. Nat. Phys. 2:562–68
    [Google Scholar]
  29. Cabot W, Zhou Y 2013. Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh–Taylor instability. Phys. Fluids 25:015107
    [Google Scholar]
  30. Chandrasekhar S 1981. Hydrodynamic and Hydromagnetic Stability New York: Dover
  31. Charonko JJ, Prestridge K 2017. Variable density mixing in turbulent jets with coflow. J. Fluid Mech. 825:887–921
    [Google Scholar]
  32. Chassaing P, Antonia RA, Anselmet F, Joly L, Sarkar S 2002. Variable Density Fluid Turbulence Dordrecht, Neth.: Springer Neth.
  33. Chenoweth DR, Paolucci S 1986. Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169:173–210
    [Google Scholar]
  34. Chisnell R 1955. The normal motion of a shock wave through a non-uniform one-dimensional medium. Proc. R. Soc. Lond. A 232:350–70
    [Google Scholar]
  35. Chung D, Pullin DI 2010. Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence. J. Fluid Mech. 643:279–308
    [Google Scholar]
  36. Cook AW, Cabot WH, Miller PL 2004. The mixing transition in Rayleigh–Taylor instability. J. Fluid Mech. 511:333–62
    [Google Scholar]
  37. Cook AW, Dimotakis PE 2001. Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443:69–99
    [Google Scholar]
  38. Day MS, Bell JB 2000. Numerical simulation of laminar reacting flow with complex chemistry. Combust. Theor. Model. 4:535–56
    [Google Scholar]
  39. de Lira CHR, Velikovich AL, Wouchuk JG 2011. Analytical linear theory for the interaction of a planar shock wave with a two-or three-dimensional random isotropic density field. Phys. Rev. E 83:056320
    [Google Scholar]
  40. Dimonte G, Schneider M 2000. Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12:304–21
    [Google Scholar]
  41. Dimonte G, Youngs DL, Wunsch S, Garasi C, Robinson A et al. 2004. A comparative study of the turbulent Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: the Alpha-Group collaboration. Phys. Fluids 16:1668–92
    [Google Scholar]
  42. Dimotakis PE 1984. Two-dimensional shear layer entrainment. AIAA J. 24:1791–96
    [Google Scholar]
  43. Dimotakis PE 2000. The mixing transition in turbulent flows. J. Fluid Mech. 409:69–98
    [Google Scholar]
  44. Dimotakis PE 2005. Turbulent mixing. Annu. Rev. Fluid Mech. 37:329–56
    [Google Scholar]
  45. Donzis DA, Gibbon JD, Kerr RM, Gupta A, Pandit R, Vincenzi D 2013. Vorticity moments in four numerical simulations of the 3D Navier–Stokes equations. J. Fluid Mech. 732:316–31
    [Google Scholar]
  46. Eyink GL 2005. Locality of turbulent cascades. Physica D 207:91–116
    [Google Scholar]
  47. Freund JB, Lele SK, Moin P 2000. Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech 421:229–67
    [Google Scholar]
  48. Fusegi T, Hyun JM, Kuwahara K, Farouk B 1990. A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure. Int. J. Heat Mass Transfer 34:1543–57
    [Google Scholar]
  49. Garnier E, Adams N, Sagaut P 2009. Large Eddy Simulation for Compressible Flows Dordrecht, Neth.: Springer Sci. Bus. Media
  50. Gat I, Matheou G, Chung D, Dimotakis PE 2017. Incompressible variable-density turbulence in an external acceleration field. J. Fluid Mech. 827:506–35
    [Google Scholar]
  51. Gauthier S 2017. Compressible Rayleigh–Taylor turbulent mixing layer between Newtonian miscible fluids. J. Fluid Mech. 830:211–56
    [Google Scholar]
  52. Gerashchenko S, Prestridge K 2015. Density and velocity statistics in variable density turbulent mixing. J. Turbul. 16:1011–35
    [Google Scholar]
  53. Gibbon JD 2015. High–low frequency slaving and regularity issues in the 3D Navier–Stokes equations. IMA J. Appl. Math. 812:308–20
    [Google Scholar]
  54. Gibbon JD, Donzis DA, Kerr RM, Gupta A, Pandit R, Vincenzi D 2014. Regimes of nonlinear depletion and regularity in the 3D Navier–Stokes equations. Nonlinearity 27:2605
    [Google Scholar]
  55. Gilet C, Almgren AS, Bell JB, Nonaka A, Woosley SE, Zingale M 2013. Low Mach number modeling of core convection in massive stars. Astrophys. J. 773:137
    [Google Scholar]
  56. Givi P 1989. Model-free simulations of turbulent reacting flows. Progr. Energy Combust. Sci. 15:1–107
    [Google Scholar]
  57. Gray DD, Giorgini A 1976. The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transf. 19:545–51
    [Google Scholar]
  58. Griffond J 2005. Linear interaction analysis applied to a mixture of two perfect gases. Phys. Fluids 17:086101
    [Google Scholar]
  59. Griffond J, Soulard O 2012. Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves. Phys. Fluids 24:115108
    [Google Scholar]
  60. Griffond J, Soulard O, Souffland D 2010. A turbulent mixing Reynolds stress model fitted to match linear interaction analysis prediction. Phys. Scr. 2010:014059
    [Google Scholar]
  61. Hesselink L, Sturtevant B 1988. Propagation of weak shocks through a random medium. J. Fluid Mech. 196:513–53
    [Google Scholar]
  62. Hill DJ, Pantano C, Pullin DI 2006. Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557:29–61
    [Google Scholar]
  63. Hughes GO, Griffiths RW 2008. Horizontal convection. Annu. Rev. Fluid Mech. 40:185–208
    [Google Scholar]
  64. Jamme S, Cazalbou JB, Torres F, Chassaing P 2002. Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence. Flow Turbul. Combust. 68:227–68
    [Google Scholar]
  65. Joseph DD 1990. Fluid dynamics of two miscible liquids with diffusion and gradient stresses. Eur. J. Mech. B 6:565–96
    [Google Scholar]
  66. Khokhlov AM, Oran ES, Thomas GO 1999. Numerical simulation of deflagration-to-detonation transition: the role of shock–flame interactions in turbulent flames. Combust. Flame 117:323–39
    [Google Scholar]
  67. Koochesfahani MM, Dimotakis PE 1986. Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170:83–112
    [Google Scholar]
  68. Kovasznay LSG 1953. Turbulence in supersonic flow. J. Aeronaut. Sci. 20:657–74
    [Google Scholar]
  69. Larsson J, Bermejo-Moreno I, Lele SK 2013. Reynolds- and Mach-number effects in canonical shock–turbulence interaction. J. Fluid Mech. 717:293–321
    [Google Scholar]
  70. Larsson J, Lele SK 2009. Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21:126101
    [Google Scholar]
  71. Lee S, Lele SK, Moin P 1993. Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251:533–62
    [Google Scholar]
  72. Livescu D 2013. Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability. Philos. Trans. R. Soc. A 371:20120185
    [Google Scholar]
  73. Livescu D, Canada C, Kanov K, Burns R, IDIES Staff, Pulido J 2014. Homogeneous buoyancy driven turbulence data set Data Set README, Johns Hopkins Turbul. Databases, Johns Hopkins Univ., Baltimore, MD http://turbulence.pha.jhu.edu/docs/README-HBDT.pdf
  74. Livescu D, Ristorcelli JR 2007. Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591:43–71
    [Google Scholar]
  75. Livescu D, Ristorcelli JR 2008. Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech. 605:145–80
    [Google Scholar]
  76. Livescu D, Ristorcelli JR 2009. Mixing asymmetry in variable-density turbulence. Advances in Turbulence XII: Proceedings of the 12th EUROMECH European Turbulence Conference, September 7–10, 2009, Marburg, Germany, ed. B Eckhardt, pp. 545–48 Berlin: Springer
  77. Livescu D, Ristorcelli JR, Gore RA, Dean SH, Cabot WH, Cook AW 2009. High–Reynolds number Rayleigh–Taylor turbulence. J. Turbul. 10:N13
    [Google Scholar]
  78. Livescu D, Ristorcelli JR, Petersen MR, Gore RA 2010. New phenomena in variable–density Rayleigh–Taylor turbulence. Phys. Scr. 2010:014015
    [Google Scholar]
  79. Livescu D, Ryu J 2016. Vorticity dynamics after the shock–turbulence interaction. Shock Waves 26:241–51
    [Google Scholar]
  80. Livescu D, Wei T, Petersen MR 2011. Direct numerical simulations of Rayleigh-Taylor instability. J. Phys. Conf. Ser. 318:082007
    [Google Scholar]
  81. Lohse D, Xia KQ 2010. Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 42:335–64
    [Google Scholar]
  82. Lombardini M, Hill DJ, Pullin DI, Meiron DI 2011. Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech. 670:439–80
    [Google Scholar]
  83. Lombardini M, Pullin DI, Meiron DI 2012. Transition to turbulence in shock-driven mixing: a Mach number study. J. Fluid Mech. 690:203–26
    [Google Scholar]
  84. Lombardini M, Pullin DI, Meiron DI 2014a. Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748:85–112
    [Google Scholar]
  85. Lombardini M, Pullin DI, Meiron DI 2014b. Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. J. Fluid Mech. 748:113–42
    [Google Scholar]
  86. Mahesh K, Lee S, Lele SK, Moin P 1995. The interaction of an isotropic field of acoustic waves with a shock wave. J. Fluid Mech. 300:383–407
    [Google Scholar]
  87. Mahesh K, Lele SK, Moin P 1997. The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334:353–79
    [Google Scholar]
  88. Majda A, Sethian J 1985. The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Tech. 42:185–205
    [Google Scholar]
  89. McMurtry PA, Jou WH, Riley JJ, Metcalfe RW 1986. Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24:962–70
    [Google Scholar]
  90. Miller RS, Harstad KG, Bellan J 2001. Direct numerical simulation of supercritical fluid mixing layers applied to heptane-nitrogen. J. Fluid Mech. 436:1–39
    [Google Scholar]
  91. 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
    [Google Scholar]
  92. Moore FK 1954. Unsteady oblique interaction of a shock wave with a plane disturbance Tech. Rep. 1165, Natl. Advis. Comm. Aeronaut., Lewis Flight Propuls. Lab., Cleveland, OH
  93. Motheau E, Abraham J 2016. A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy. J. Comput. Phys. 313:430–54
    [Google Scholar]
  94. Nicoud F 2000. Conservative high-order finite-difference schemes for low-Mach number flows. J. Comp. Phys. 158:71–97
    [Google Scholar]
  95. Nonaka A, Almgren AS, Bell JB, Lijewski MJ, Malone CM, Zingale M 2010. MAESTRO: An adaptive low Mach number hydrodynamics algorithm for stellar flows. Astrophys. J. Suppl. 188:358
    [Google Scholar]
  96. O'Brien J, Urzay J, Ihme M, Moin P, Saghafian A 2014. Subgrid-scale backscatter in reacting and inert supersonic hydrogen air turbulent mixing layers. J. Fluid Mech. 743:554–84
    [Google Scholar]
  97. Olson BJ, Larsson J, Lele SK, Cook AW 2011. Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability. Phys. Fluids 23:114107
    [Google Scholar]
  98. Orlicz GC, Balasubramanian S, Vorobieff P, Prestridge KP 2015. Mixing transition in a shocked variable-density flow. Phys. Fluids 27:114102
    [Google Scholar]
  99. Pantano C, Sarkar S 2002. A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451:329–71
    [Google Scholar]
  100. Paolucci S, Chenoweth DR 1989. Transition to chaos in a differentially heated vertical cavity. J. Fluid Mech. 201:379–410
    [Google Scholar]
  101. Patel A, Boersma BJ, Pecnik R 2016. The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809:793–820
    [Google Scholar]
  102. Pember RP, Howell LH, Bell JB, Collela P, Cruthfield WY et al. 1998. An adaptive projection method for unsteady, low Mach number combustion. Combust. Sci. Tech. 140:123–68
    [Google Scholar]
  103. Poggi F, Thorembey MH, Rodriguez G 1998. Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability. Phys. Fluids 10:2698–700
    [Google Scholar]
  104. Prestridge KP 2018. Experimental adventures in variable-density mixing. Phys. Rev. Fluids 3:110501
    [Google Scholar]
  105. Quadros R, Sinha K, Larsson J 2016. Turbulent energy flux generated by shock/homogeneous-turbulence interaction. J. Fluid Mech. 796:113–57
    [Google Scholar]
  106. Rajagopal KR, Ruzicka M, Srinivasa AR 1996. On the Oberbeck–Boussinesq approximation. Math. Model. Meth. Appl. 6:1157–67
    [Google Scholar]
  107. Ramaprabhu P, Dimonte G, Andrews MJ 2005. A numerical study of the influence of initial perturbations on the turbulent Rayleigh–Taylor instability. J. Fluid Mech. 536:285–319
    [Google Scholar]
  108. Ramaprabhu P, Dimonte G, Young Y, Calder AC, Fryxell B 2006. Limits of the potential flow approach to the single-mode Rayleigh-Taylor problem. Phys. Rev. E 74:066308
    [Google Scholar]
  109. Ranjan D, Oakley J, Bonazza R 2011. Shock-bubble interactions. Annu. Rev. Fluid Mech. 43:117–40
    [Google Scholar]
  110. Rao P, Caulfield CP, Gibbon JD 2017. Nonlinear effects in buoyancy-driven variable-density turbulence. J. Fluid Mech. 810:362–77
    [Google Scholar]
  111. Reese DT, Ames AM, Noble CD, Oakley JG, Rothamer DA, Bonazza R 2018. Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability. J. Fluid Mech. 849:541–75
    [Google Scholar]
  112. Rehm RG, Baum HR 1978. The equations of motion of thermally driven buoyant flows. J. Res. Natl. Bur. Stand. 83:297–308
    [Google Scholar]
  113. Remington BA, Park HS, Casey DT, Cavallo RM, Clark DS 2019. Rayleigh–Taylor instabilities in high-energy density settings on the National Ignition Facility. PNAS 11618233–38
  114. Ribner HS 1954. Convection of a pattern of vorticity through a shock wave Tech. Rep. 1164, Natl. Advis. Comm. Aeronaut., Lewis Flight Propuls. Lab., Cleveland, OH
  115. Ristorcelli J, Clark T 2004. Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations. J. Fluid Mech. 507:213–53
    [Google Scholar]
  116. Roberts MS, Jacobs JW 2016. The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability. J. Fluid Mech. 787:50–83
    [Google Scholar]
  117. Ryu J, Livescu D 2014. Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756:R1
    [Google Scholar]
  118. Safta C, Ray J, Najm HN 2010. A high-order low-Mach number AMR construction for chemically reacting flows. J. Comput. Phys. 229:9299–322
    [Google Scholar]
  119. Sagaut P, Cambon C 2018. Homogeneous Turbulence Dynamics Cham, Switz.: Springer. 2nd ed.
  120. Sandoval D 1995. The dynamics of variable-density turbulence Ph.D. Thesis, Univ. Wash., Seattle, WA
  121. Schwarzkopf JD, Livescu D, Baltzer JR, Gore RA, Ristorcelli JR 2016. A two length-scale turbulence model for single-phase multi-fluid mixing. Flow Turbul. Combust. 96:1–43
    [Google Scholar]
  122. Sethuraman YPM, Sinha K, Larsson J 2018. Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength. Theor. Comput. Fluid Dyn. 32:629–54
    [Google Scholar]
  123. Sharp D 1984. An overview of Rayleigh-Taylor instability. Physica D 12:3–18
    [Google Scholar]
  124. Soukhomlinov VS, Kolosov VY, Sheverev VA, Ötügen MV 2002. Formation and propagation of a shock wave in a gas with temperature gradients. J. Fluid Mech. 473:245–64
    [Google Scholar]
  125. Swisher NC, Kuranz CC, Arnett D, Hurricane O, Remington BA et al. 2015. Rayleigh-Taylor mixing in supernova experiments. Phys. Plasmas 22:102707
    [Google Scholar]
  126. Thornber B, Drikakis D, Youngs DL, Williams RJR 2010. The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability. J. Fluid Mech. 654:99–139
    [Google Scholar]
  127. Thornber B, Drikakis D, Youngs DL, Williams RJR 2011. Growth of a Richtmyer–Meshkov turbulent layer after reshock. Phys. Fluids 23:095107
    [Google Scholar]
  128. Thornber B, Griffond J, Poujade O, Attal A, Varshochi H et al. 2017. Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: the θ-group collaboration. Phys. Fluids 29:105107
    [Google Scholar]
  129. Thornber B, Zhou Y 2015. Numerical simulations of the two-dimensional multimode Richtmyer–Meshkov instability. Phys. Plasmas 22:032309
    [Google Scholar]
  130. Tian Y, Jaberi FA, Li Z, Livescu D 2017. Numerical study of variable density turbulence interaction with a normal shock wave. J. Fluid Mech. 829:551–88
    [Google Scholar]
  131. Tian Y, Jaberi FA, Livescu D 2019a. Density effects on the post-shock turbulence structure and dynamics. J. Fluid Mech 880935–68
  132. Tian Y, Jaberi FA, Livescu D 2019b. Shock propagation in media with non-uniform density. 31st International Symposium on Shock Waves I, ed. A Sasoh, T Aoki, M Katayama, pp. 1167–75 Cham, Switz.: Springer
  133. Tomkins C, Kumar S, Orlicz GC, Prestridge KP 2008. An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611:131–50
    [Google Scholar]
  134. Tritschler VK, Olson BJ, Lele SK, Hickel S, Hu XY, Adams NA 2014a. On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface. J. Fluid Mech. 755:429–62
    [Google Scholar]
  135. Tritschler VK, Zubel M, Hickel S, Adams NA 2014b. Evolution of length scales and statistics of Richtmyer-Meshkov instability from direct numerical simulations. Phys. Rev. E 90:063001
    [Google Scholar]
  136. Villermaux E 2019. Mixing versus stirring. Annu. Rev. Fluid Mech. 51:245–73
    [Google Scholar]
  137. Vreman AW, Sandham ND, Luo KH 1996. Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320:235–58
    [Google Scholar]
  138. Wang Q, Xia SN, Yan R, Sun DJ, Wan ZH 2019. Non-Oberbeck-Boussinesq effects due to large temperature differences in a differentially heated square cavity filled with air. Int. J. Heat Mass Transfer 128:479–91
    [Google Scholar]
  139. Weber CR, Cook AW, Bonazza R 2013. Growth rate of a shocked mixing layer with known initial perturbations. J. Fluid Mech. 725:372–401
    [Google Scholar]
  140. Weber CR, Haehn NS, Oakley JG, Rothamer DA, Bonazza R 2014. An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability. J. Fluid Mech. 748:457–87
    [Google Scholar]
  141. Wei T, Livescu D 2012. Late-time quadratic growth in single-mode Rayleigh-Taylor instability. Phys. Rev. E 86:046405
    [Google Scholar]
  142. Whitham G 1958. On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4:337–60
    [Google Scholar]
  143. Williams F 1985. Combustion Theory Cambridge, MA: Perseus
  144. Wong ML, Livescu D, Lele SK 2019. High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with re-shock. Phys. Rev. Fluids 4:104609
  145. Youngs D 1984. Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12:32–44
    [Google Scholar]
  146. Youngs D 1994. Numerical simulation of mixing by Rayleigh–Taylor and Richtmeyer–Meshkov instabilities. Laser Part. Beams 12:725–50
    [Google Scholar]
  147. Youngs DL 2013. The density ratio dependence of self-similar Rayleigh–Taylor mixing. Philos. Trans. R. Soc. A 371:20120173
    [Google Scholar]
  148. Youngs DL 2017. Rayleigh–Taylor mixing: direct numerical simulation and implicit large eddy simulation. Phys. Scr. 92:074006
    [Google Scholar]
  149. Zabusky NJ 1999. Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments. Annu. Rev. Fluid Mech. 31:495–536
    [Google Scholar]
  150. Zhao D, Aluie H 2018. Inviscid criterion for decomposing scales. Phys. Rev. Fluids 3:054603
    [Google Scholar]
  151. Zhou Y 2017a. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–22:1–136
    [Google Scholar]
  152. Zhou Y 2017b. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–25:1–160
    [Google Scholar]
  153. Zhou Y, Cabot WH, Thornber B 2016. Asymptotic behavior of the mixed-mass in Rayleigh–Taylor and Richtmyer–Meshkov induced flows. Phys. Plasmas 23:052712
    [Google Scholar]
  154. Zingale M, Almgren AS, Bell JB, Nonaka A, Woosley SE 2009. Low Mach number modeling of type Ia supernovae. IV. White dwarf convection. Astrophys. J. 704:196–210
    [Google Scholar]
  155. Zingale M, Malone CM, Nonaka A, Almgren AS, Bell JB 2015. Comparisons of two- and three-dimensional convection in type I X-ray bursts. Astrophys. J. 807:60
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-010719-060114
Loading
/content/journals/10.1146/annurev-fluid-010719-060114
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error