Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T08:29:49.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer

Published online by Cambridge University Press:  22 March 2021

Jason D. Bender Open the ORCID record for Jason D. Bender [Opens in a new window] ,
Oleg Schilling Open the ORCID record for Oleg Schilling [Opens in a new window] ,
Kumar S. Raman ,
Robert A. Managan Open the ORCID record for Robert A. Managan [Opens in a new window] ,
Britton J. Olson Open the ORCID record for Britton J. Olson [Opens in a new window] ,
Sean R. Copeland Open the ORCID record for Sean R. Copeland [Opens in a new window] ,
C. Leland Ellison Open the ORCID record for C. Leland Ellison [Opens in a new window] ,
David J. Erskine Open the ORCID record for David J. Erskine [Opens in a new window] ,
Channing M. Huntington  and
Brandon E. Morgan Open the ORCID record for Brandon E. Morgan [Opens in a new window]
...Show all authors
Jason D. Bender*
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Oleg Schilling
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Kumar S. Raman
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Robert A. Managan
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Britton J. Olson
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Sean R. Copeland
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
C. Leland Ellison
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
David J. Erskine
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Channing M. Huntington
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Brandon E. Morgan
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Sabrina R. Nagel
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Shon T. Prisbrey
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Brian S. Pudliner
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Philip A. Sterne
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Christopher E. Wehrenberg
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
Ye Zhou
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA94550, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes a computational investigation of multimode instability growth and multimaterial mixing induced by multiple shock waves in a high-energy-density (HED) environment, where pressures exceed 1 Mbar. The simulations are based on a series of experiments performed at the National Ignition Facility (NIF) and designed as an HED analogue of non-HED shock-tube studies of the Richtmyer–Meshkov instability and turbulent mixing. A three-dimensional computational modelling framework is presented. It treats many complications absent from canonical non-HED shock-tube flows, including distinct ion and free-electron internal energies, non-ideal equations of state, radiation transport and plasma-state mass diffusivities, viscosities and thermal conductivities. The simulations are tuned to the available NIF data, and traditional statistical quantities of turbulence are analysed. Integrated measures of turbulent kinetic energy and enstrophy both increase by over an order of magnitude due to reshock. Large contributions to enstrophy production during reshock are seen from both the baroclinic source and enstrophy–dilatation terms, highlighting the significance of fluid compressibility in the HED regime. Dimensional analysis reveals that Reynolds numbers and diffusive Péclet numbers in the HED flow are similar to those in a canonical non-HED analogue, but conductive Péclet numbers are much smaller in the HED flow due to efficient thermal conduction by free electrons. It is shown that the mechanism of electron thermal conduction significantly softens local spanwise gradients of both temperature and density, which causes a minor but non-negligible decrease in enstrophy production and small-scale mixing relative to a flow without this mechanism.

JFM classification

Mixing: Mixing MHD and Electrohydrodynamics: Plasmas Compressible Flows: Compressible Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A84
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, J.D. 2003 Modern Compressible Flow: With Historical Perspective, 3rd edn. McGraw-Hill.Google Scholar
Andreopoulos, Y., Agui, J.H. & Briassulis, G. 2000 Shock wave–turbulence interactions. Annu. Rev. Fluid Mech. 32, 309–345.CrossRefGoogle Scholar
Andronov, V.A., Bakhrakh, S.M., Meshkov, E.E., Mokhov, V.N., Nikiforov, V.V., Pevnitskiĭ, A.V. & Tolshmyakov, A.I. 1976 Turbulent mixing at contact surface accelerated by shock waves. Sov. Phys. JETP 44, 424–427.Google Scholar
Atzeni, S. & Meyer-ter-Vehn, J. 2004 The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter. Oxford University Press.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
Bar-Shalom, A., Oreg, J., Goldstein, W.H., Shvarts, D. & Zigler, A. 1989 Super-transition-arrays: a model for the spectral analysis of hot, dense plasma. Phys. Rev. A 40, 3183–3193.CrossRefGoogle Scholar
Bell, A.R. 1985 Non-Spitzer heat flow in a steadily ablating laser-produced plasma. Phys. Fluids 28, 2007–2014.CrossRefGoogle Scholar
Bergeson, S.D., Baalrud, S.D., Ellison, C.L., Grant, E., Graziani, F.R., Killian, T.C., Murillo, M.S., Roberts, J.L. & Stanton, L.G. 2019 Exploring the crossover between high-energy-density plasma and ultracold neutral plasma physics. Phys. Plasmas 26, 100501.CrossRefGoogle Scholar
Bowers, R.L. & Wilson, J.R. 1991 Numerical Modeling in Applied Physics and Astrophysics. Jones and Bartlett Publishers.Google Scholar
Braginskii, S.I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics, (ed. M.A. Leontovich), vol. 1, pp. 205–311. Consultants Bureau.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Brunner, T.A. 2002 Forms of approximate radiation transport. Tech. Rep. SAND2002-1778. Sandia National Laboratories. Available at: https://www.osti.gov.CrossRefGoogle Scholar
Brysk, H. 1974 Electron–ion equilibration in a partially degenerate plasma. Plasma Phys. 16, 927–932.CrossRefGoogle Scholar
Burgers, J.M. 1969 Flow Equations for Composite Gases. Academic Press.Google Scholar
Castor, J.I. 2004 Radiation Hydrodynamics. Cambridge University Press.CrossRefGoogle Scholar
Celliers, P.M., Bradley, D.K., Collins, G.W., Hicks, D.G., Boehly, T.R. & Armstrong, W.J. 2004 Line-imaging velocimeter for shock diagnostics at the OMEGA laser facility. Rev. Sci. Instrum. 75, 4916–4929.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover Publications.Google Scholar
Chapman, S. & Cowling, T.G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.Google Scholar
Chassaing, P., Antonia, R.A., Anselmet, F., Joly, L. & Sarkar, S. 2010 Variable Density Fluid Turbulence. Kluwer Academic Publishers.Google Scholar
Childs, H., et al. 2013 VisIt: an end-user tool for visualizing and analyzing very large data. In High Performance Visualization: Enabling Extreme-Scale Scientific Insight (ed. E.W. Bethel, H. Childs & C. Hansen), pp. 357–372. Taylor & Francis.Google Scholar
Clark, D.S., et al. 2013 Detailed implosion modeling of deuterium-tritium layered experiments on the National Ignition Facility. Phys. Plasmas 20, 056318.CrossRefGoogle Scholar
Clark, D.S., et al. 2019 Three-dimensional modeling and hydrodynamic scaling of National Ignition Facility implosions. Phys. Plasmas 26, 050601.CrossRefGoogle Scholar
Collins, B.D. & Jacobs, J.W. 2002 PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF$_6$ interface. J. Fluid Mech. 464, 113–136.CrossRefGoogle Scholar
Cook, A.W. 2009 Enthalpy diffusion in multicomponent flows. Phys. Fluids 21, 055109.CrossRefGoogle Scholar
Cook, A.W. & Dimotakis, P.E. 2001 Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 66–99.CrossRefGoogle Scholar
Cowie, L.L. & McKee, C.F. 1977 The evaporation of spherical clouds in a hot gas. I. Classical and saturated mass loss rates. Astrophys. J. 211, 135–146.CrossRefGoogle Scholar
Darlington, R.M., McAbee, T.L. & Rodrigue, G. 2001 A study of ALE simulations of Rayleigh–Taylor instability. Comput. Phys. Commun. 135, 58–73.CrossRefGoogle Scholar
Davidson, P.A. 2015 Turbulence: An Introduction for Scientists and Engineers, 2nd edn. Oxford University Press.CrossRefGoogle Scholar
Desjardins, T.R., et al. 2019 A platform for thin-layer Richtmyer–Meshkov at OMEGA and the NIF. High Energy Dens. Phys. 33, 100705.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. & Remington, B. 1996 Richtmyer–Meshkov instability with strong radiatively driven shocks. Phys. Plasmas 3, 614–630.CrossRefGoogle Scholar
Dimonte, G. & Remington, B. 1993 Richtmyer–Meshkov experiments on the Nova laser at high compression. Phys. Rev. Lett. 70, 1806–1809.CrossRefGoogle ScholarPubMed
Dimotakis, P.E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Drake, R.P. 2018 High-Energy-Density Physics: Foundations of Inertial Fusion and Experimental Astrophysics, 2nd edn. Springer.CrossRefGoogle Scholar
Eckart, C. 1948 An analysis of the stirring and mixing processes in incompressible fluids. J. Mar. Res. 7, 265–275.Google Scholar
Ellison, C.L., et al. 2018 Development and modeling of a polar-direct-drive exploding pusher platform at the National Ignition Facility. Phys. Plasmas 25, 072710.CrossRefGoogle Scholar
Feynman, R.P., Metropolis, N. & Teller, E. 1949 Equations of state of elements based on the generalized Fermi–Thomas theory. Phys. Rev. 75, 1561–1573.CrossRefGoogle Scholar
Gatski, T.B. & Bonnet, J.-P. 2013 Compressibility, Turbulence, and High Speed Flow, 2nd edn. Academic Press, Elsevier.Google Scholar
Glendinning, S.G., et al. 2003 Effect of shock proximity on Richtmyer–Meshkov growth. Phys. Plasmas 10, 1931–1936.CrossRefGoogle Scholar
Grinstein, F.F., Gowardhan, A.A. & Wachtor, A.J. 2011 Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments. Phys. Fluids 23, 034106.CrossRefGoogle Scholar
Grinstein, F.F., Margolin, L.G. & Rider, W.J. 2007 Implicit Large-Eddy Simulation: Computing Turbulent Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Hahn, M., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2011 Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow. Phys. Fluids 23, 046101.CrossRefGoogle Scholar
Haines, B.M., et al. 2016 Detailed high-resolution three-dimensional simulations of OMEGA separated reactants inertial confinement fusion experiments. Phys. Plasmas 23, 072709.CrossRefGoogle Scholar
Haines, B.M., Grinstein, F.F., Welser-Sherrill, L. & Fincke, J.R. 2013 Simulations of material mixing in laser-driven reshock experiments. Phys. Plasmas 20, 022309.CrossRefGoogle Scholar
Haines, B.M., et al. 2020 Observation of persistent species temperature separation in inertial confinement fusion mixtures. Nat. Commun. 11, 1–9.CrossRefGoogle ScholarPubMed
Hansen, S.B., Isaacs, W.A., Sterne, P.A., Wilson, B.G., Sonnad, V. & Young, D.A. 2006 Electrical conductivity calculations from the Purgatorio code. Tech. Rep. UCRL-PROC-218150. Lawrence Livermore National Laboratory. Available at: https://www.osti.gov.Google Scholar
Haxhimali, T., Rudd, R.E., Cabot, W.H. & Graziani, F.R. 2015 Shear viscosity for dense plasmas by equilibrium molecular dynamics in asymmetric Yukawa ionic mixtures. Phys. Rev. E 92, 053110.CrossRefGoogle ScholarPubMed
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
Hirsch, C. 2007 Numerical Computation of Internal and External Flows, 2nd edn. Elsevier.Google Scholar
Hirschfelder, J.O., Curtiss, C.F. & Bird, R.B. 1954 The Molecular Theory of Gases and Liquids. John Wiley & Sons.Google Scholar
Holmes, R.L., Dimonte, G., Fryxell, B., Gittings, M.L., Grove, J.W., Schneider, M., Sharp, D.H., Velikovich, A.L., Weaver, R.P. & Zhang, Q. 1999 Richtmyer–Meshkov instability growth: experiment, simulation and theory. J. Fluid Mech. 389, 55–79.CrossRefGoogle Scholar
Houas, L. & Chemouni, I. 1996 Experimental investigation of Richtmyer–Meshkov instability in shock tube. Phys. Fluids 8, 614–627.CrossRefGoogle Scholar
Hunter, J.D. 2007 Matplotlib: a 2D graphics environment. Comput. Sci. Engng 9, 90–95.CrossRefGoogle Scholar
Huntington, C.M., Raman, K.S., Nagel, S.R., MacLaren, S.A., Baumann, T., Bender, J.D., Prisbrey, S.T., Simmons, L., Wang, P. & Zhou, Y. 2020 Split radiographic tracer technique to measure the full width of a high energy density mixing layer. High Energy Dens. Phys. 35, 100733.CrossRefGoogle Scholar
Iglesias, C.A. & Rogers, F.J. 1996 Updated OPAL opacities. Astrophys. J. 464, 943–953.CrossRefGoogle Scholar
Iglesias, C.A., Rogers, F.J. & Wilson, B.G. 1992 Spin-orbit interaction effects on the Rosseland mean opacity. Astrophys. J. 387, 717–728.CrossRefGoogle Scholar
Incropera, F.P., DeWitt, D.P., Bergman, T.L. & Lavine, A.S. 2007 Fundamentals of Heat and Mass Transfer, 6th edn. John Wiley & Sons.Google Scholar
Ishida, T., Davidson, P.A. & Kaneda, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475.CrossRefGoogle Scholar
Jacobs, J.W., Krivets, V.V., Tsiklashvili, V. & Likhachev, O.A. 2013 Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation. Shock Waves 23, 407–413.CrossRefGoogle Scholar
Ji, J.-Y. & Held, E.D. 2013 Closure and transport theory for high-collisionality electron–ion plasmas. Phys. Plasmas 20, 042114.CrossRefGoogle Scholar
Jones, E., et al. 2001 SciPy: open source scientific tools for Python. Available at: https://www.scipy.org.Google Scholar
Larsson, J., Bermejo-Moreno, I. & Lele, S.K. 2013 Reynolds- and Mach-number effects in canonical shock–turbulence interaction. J. Fluid Mech. 717, 293–321.CrossRefGoogle Scholar
Larsson, J. & Lele, S.K. 2009 Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21, 126101.CrossRefGoogle Scholar
Latini, M. & Schilling, O. 2020 A comparison of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability growth. Physica D 401, 132201.CrossRefGoogle Scholar
Latini, M., Schilling, O. & Don, W.S. 2007 Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability. J. Comput. Phys. 221, 805–836.CrossRefGoogle Scholar
Lee, Y.T. & More, R.M. 1984 An electron conductivity model for dense plasmas. Phys. Fluids 27, 1273–1286.CrossRefGoogle Scholar
van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32, 101–136.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
Levermore, C.D. & Pomraning, G.C. 1981 A flux-limited diffusion theory. Astrophys. J. 248, 321–334.CrossRefGoogle Scholar
Li, H., He, Z., Zhang, Y. & Tian, B. 2019 On the role of rarefaction/compression waves in Richtmyer–Meshkov instability with reshock. Phys. Fluids 31, 054102.Google Scholar
Livescu, D. & Ryu, J. 2016 Vorticity dynamics after the shock–turbulence interaction. Shock Waves 26, 241–251.CrossRefGoogle 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 simulation. J. Fluid Mech. 670, 439–480.CrossRefGoogle Scholar
Lombardini, M., Pullin, D.I. & Meiron, D.I. 2012 Transition to turbulence in shock-driven mixing: a Mach number study. J. Fluid Mech. 690, 203–226.CrossRefGoogle Scholar
Malamud, G., Di Stefano, C.A., Elbaz, Y., Huntington, C.M., Kuranz, C.C., Keiter, P.A. & Drake, R.P. 2013 A design of a two-dimensional, multimode RM experiment on OMEGA-EP. High Energy Dens. Phys. 9, 122–131.CrossRefGoogle Scholar
Malamud, G., Leinov, E., Sadot, O., Elbaz, Y., Ben-Dor, G. & Shvarts, D. 2014 Reshocked Richtmyer–Meshkov instability: numerical study and modeling of random multi-mode experiments. Phys. Fluids 26, 084107.CrossRefGoogle Scholar
Managan, R.A. 2015 Plasma physics approximations in Ares. Tech. Rep. LLNL-PROC-666110. Lawrence Livermore National Laboratory. Available at: https://www.osti.gov.Google Scholar
McQuarrie, D.A. 2000 Statistical Mechanics. University Science Books.Google Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Mikaelian, K.O. 1989 Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Physica D 36, 343–357.CrossRefGoogle Scholar
More, R.M. 1991 Atomic physics in inertial confinement fusion. Tech. Rep. UCRL-84991 Rev. 1. Lawrence Livermore Laboratory. Available at: https://www.osti.gov.Google Scholar
More, R.M., Warren, K.H., Young, D.A. & Zimmerman, G.B. 1988 A new quotidian equation of state (QEOS) for hot dense matter. Phys. Fluids 31, 3059–3078.CrossRefGoogle Scholar
Morgan, B.E. & Greenough, J.A. 2016 Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder. Shock Waves 26, 355–383.CrossRefGoogle Scholar
Morgan, B.E., Olson, B.J., Black, W.J. & McFarland, J.A. 2018 Large-eddy simulation and Reynolds-averaged Navier–Stokes modeling of a reacting Rayleigh–Taylor mixing layer in a spherical geometry. Phys. Rev. E 98, 033111.CrossRefGoogle Scholar
Moses, E.I., Boyd, R.N., Remington, B.A., Keane, C.J. & Al-Ayat, R. 2009 The National Ignition Facility: ushering in a new age for high energy density science. Phys. Plasmas 16, 041006.CrossRefGoogle Scholar
Murillo, M.S. 2008 Viscosity estimates of liquid metals and warm dense matter using the Yukawa reference system. High Energy Dens. Phys. 4, 49–57.CrossRefGoogle Scholar
Nagel, S.R., et al. 2017 A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the National Ignition Facility. Phys. Plasmas 24, 072704.CrossRefGoogle Scholar
von Neumann, J. & Richtmyer, R.D. 1950 A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232–237.CrossRefGoogle Scholar
Oliphant, T.E. 2006 A guide to NumPy. Trelgol.Google Scholar
Olson, B.J. & Greenough, J. 2014 Large eddy simulation requirements for the Richtmyer–Meshkov instability. Phys. Fluids 26, 044103.CrossRefGoogle Scholar
Olson, G.L., Auer, L.H. & Hall, M.L. 2000 Diffusion, $P_1$, and other approximate forms of radiation transport. J. Quant. Spectrosc. Radiat. Transfer 64, 619–634.CrossRefGoogle Scholar
Peyser, T.A., Miller, P.L., Stry, P.E., Budil, K.S., Burke, E.W., Wojtowicz, D.A., Griswold, D.L., Hammel, B.A. & Phillion, D.W. 1995 Measurement of radiation-driven shock-induced mixing from nonlinear initial perturbations. Phys. Rev. Lett. 75, 2332–2335.CrossRefGoogle ScholarPubMed
Poggi, F., Thorembey, M.-H. & Rogriguez, G. 1998 Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability. Phys. Fluids 10, 2698–2700.CrossRefGoogle Scholar
Pomraning, G.C. 1982 Flux limiters and Eddington factors. J. Quant. Spectrosc. Radiat. Transfer 27, 517–530.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. 1992 Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd edn. Cambridge University Press.Google Scholar
Ramshaw, J.D. 2004 Approximate thermodynamic state relations in partially ionized gas mixtures. Phys. Plasmas 11, 3572–3578.CrossRefGoogle Scholar
Ramshaw, J.D. & Cook, A.W. 2014 Approximate equations of state in two-temperature plasma mixtures. Phys. Plasmas 21, 022706.CrossRefGoogle Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Richtmyer, R.D. & Morton, K.W. 1967 Difference Methods for Initial-Value Problems, 2nd edn. John Wiley & Sons.Google 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
Rogers, F.J. & Iglesias, C.A. 1992 Radiative atomic Rosseland mean opacity tables. Astrophys. J. Suppl. 79, 507–568.CrossRefGoogle Scholar
Ryu, J. & Livescu, D. 2014 Turbulence structure behind the shock in canonical shock–vortical turbulence interaction. J. Fluid Mech. 756, R1.CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows: An Introduction, 3rd edn. Springer.Google Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Schilling, O. & Latini, M. 2010 High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data. Acta Math. Sci. 30B, 595–620.CrossRefGoogle Scholar
Schilling, O., Latini, M. & Don, W.S. 2007 Physics of reshock and mixing in single-mode Richtmyer–Meshkov instability. Phys. Rev. E 76, 026319.CrossRefGoogle ScholarPubMed
Schroeder, D.V. 2000 An Introduction to Thermal Physics. Addison Wesley Longman.Google Scholar
Sharp, D.H. 1984 An overview of the Rayleigh–Taylor instability. Physica D 12, 3–18.CrossRefGoogle Scholar
Sharp, R.W. Jr. & Barton, R.T. 1981 HEMP advection model. Tech. Rep. UCID-17809 Rev. 1. Lawrence Livermore Laboratory. Available at: https://www.osti.gov.Google Scholar
Stanton, L.G. & Murillo, M.S. 2016 Ionic transport in high-energy-density matter. Phys. Rev. E 93, 043203.CrossRefGoogle ScholarPubMed
Sterne, P.A., Hansen, S.B., Wilson, B.G. & Isaacs, W.A. 2007 Equation of state, occupation probabilities and conductivities in the average atom Purgatorio code. High Energy Dens. Phys. 3, 278–282.CrossRefGoogle Scholar
Taylor, G.I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. A 201, 192–196.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Thornber, B. 2007 Implicit large eddy simulation for unsteady multi-component compressible turbulent flows. PhD thesis, Cranfield University, Cranfield, UK.Google 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
Thornber, B., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2011 Growth of a Richtmyer–Meshkov turbulent layer after reshock. Phys. Fluids 23, 095107.CrossRefGoogle Scholar
Thornber, B., Griffond, J., Bigdelou, P., Boureima, I., Ramaprabhu, P., Schilling, O. & Williams, R.J.R. 2019 Turbulent transport and mixing in the multimode narrowband Richtmyer–Meshkov instability. Phys. Fluids 31, 096105.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
Toro, E.F. 2009 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd edn. Springer.CrossRefGoogle Scholar
Tritschler, V.K., Olson, B.J., Lele, S.K., Hickel, S., Hu, X.Y. & Adams, N.A. 2014 On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface. J. Fluid Mech. 755, 429–462.CrossRefGoogle Scholar
Vetter, M. & Sturtevant, B. 1995 Experiments on the Richtmyer–Meshkov instability of an air/SF$_6$ interface. Shock Waves 4, 247–252.CrossRefGoogle Scholar
Viciconte, G., Gréa, B.-J., Godeferd, F.S., Arnault, P. & Clérouin, J. 2019 Sudden diffusion of turbulent mixing layers in weakly coupled plasmas under compression. Phys. Rev. E 100, 063205.CrossRefGoogle ScholarPubMed
Wang, P., Raman, K.S., MacLaren, S.A., Huntington, C.M., Nagel, S.R., Flippo, K.A. & Prisbrey, S.T. 2018 Three-dimensional design simulations of a high-energy-density reshock experiment at the National Ignition Facility. Trans. ASME: J. Fluids Engng 140, 041207.Google Scholar
Weber, C.R., Clark, D.S., Cook, A.W., Busby, L.E. & Robey, H.F. 2014 a Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation. Phys. Rev. E 89, 053106.CrossRefGoogle ScholarPubMed
Weber, C.R., Haehn, N.S., Oakley, J.G., Rothamer, D.A. & Bonazza, R. 2014 b An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability. J. Fluid Mech. 748, 457–487.CrossRefGoogle Scholar
Welser-Sherrill, L., Fincke, J., Doss, F., Loomis, E., Flippo, K., Offermann, D., Keiter, P., Haines, B. & Grinstein, F. 2013 Two laser-driven mix experiments to study reshock and shear. High Energy Dens. Phys. 9, 496–499.CrossRefGoogle Scholar
White, F.M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Wilson, B., Sonnad, V., Sterne, P. & Isaacs, W. 2006 PURGATORIO—a new implementation of the INFERNO algorithm. J. Quant. Spectrosc. Radiat. Transfer 99, 658–679.CrossRefGoogle Scholar
Wissink, A.M., Hornung, R.D., Kohn, S.R., Smith, S.S. & Elliott, N. 2001 Large scale parallel structured AMR calculations using the SAMRAI framework. In Proceedings of the 2001 ACM/IEEE Conference on Supercomputing (SC2001). Association for Computing Machinery.CrossRefGoogle Scholar
Wong, M.L., Livescu, D. & Lele, S.K. 2019 High-resolution Navier–Stokes simulations of Richtmyer–Meshkov instability with reshock. Phys. Rev. Fluids 4, 104609.CrossRefGoogle Scholar
Young, D.A. & Corey, E.M. 1995 A new global equation of state model for hot, dense matter. J. Appl. Phys. 78, 3748–3755.CrossRefGoogle Scholar
Youngs, D.L. 1991 Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3, 1312–1320.CrossRefGoogle Scholar
Youngs, D.L. 1994 Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Part. Beams 12, 725–750.CrossRefGoogle Scholar
Zel'dovich, Y.B. & Raizer, Y.P. 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Publications.Google Scholar
Zhou, Y. 2007 Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations. Phys. Plasmas 14, 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. 2019 Time-dependent study of anisotropy in Rayleigh–Taylor instability induced turbulent flows with a variety of density ratios. Phys. Fluids 31, 084106.CrossRefGoogle 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.Google Scholar

Bender et al. supplementary movie 1

See pdf file for movie caption

Download Bender et al. supplementary movie 1(Video)
Video 28.4 MB

Bender et al. supplementary movie 2

See pdf file for movie captions

Download Bender et al. supplementary movie 2(Video)
Video 24.4 MB

Bender et al. supplementary movie 3

See pdf file for movie caption

Download Bender et al. supplementary movie 3(Video)
Video 10.1 MB

Bender et al. supplementary movie 4

See pdf file for movie caption

Download Bender et al. supplementary movie 4(Video)
Video 18.4 MB

Bender et al. supplementary movie 5

See pdf file for movie caption

Download Bender et al. supplementary movie 5(Video)
Video 20.2 MB
Supplementary material: PDF

Bender et al. supplementary material

Captions for movies 1-5

Download Bender et al. supplementary material(PDF)
PDF 145.8 KB
Supplementary material: PDF

Bender et al. supplementary material

Supplementary Appendices

Download Bender et al. supplementary material(PDF)
PDF 428.6 KB
Supplementary material: PDF

Bender et al. supplementary material

Notice to publisher

Download Bender et al. supplementary material(PDF)
PDF 95.4 KB