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Effects of Atwood and Reynolds numbers on the evolution of buoyancy-driven homogeneous variable-density turbulence

Published online by Cambridge University Press:  18 May 2020

Denis Aslangil*
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA18015, USA Los Alamos National Laboratory, Los Alamos, NM87545, USA
Daniel Livescu
Los Alamos National Laboratory, Los Alamos, NM87545, USA
Arindam Banerjee
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA18015, USA
Email address for correspondence:


The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers up to 0.75 and large Reynolds numbers is studied by using high-resolution direct numerical simulations. To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behaviour of turbulent kinetic energy derivatives. The results show that each regime has a unique type of dependence on both Atwood and Reynolds numbers. It is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. It is also observed that, at higher Atwood numbers, different flow features reach their asymptotic Reynolds-number behaviour at different times. The energy spectrum defined based on the Favre fluctuations momentum has less large-scale contamination from viscous effects for variable-density flows with constant properties, compared to other forms used previously. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from $-7/3$ to $-1$, as a function of the production-to-dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed.

JFM Papers
© The Author(s), 2020. Published by Cambridge University Press

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Adkins, J. F., McIntyre, K. & Schrag, D. P. 2002 The salinity, temperature, and 𝛿18 O of the glacial deep ocean. Science 298 (5599), 17691773.CrossRefGoogle Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.CrossRefGoogle Scholar
Akula, B. & Ranjan, D. 2016 Dynamics of buoyancy-driven flows at moderately high Atwood numbers. J. Fluid Mech. 795, 313355.CrossRefGoogle Scholar
Almagro, A., García-Villalba, M. & Flores, O. 2017 A numerical study of a variable-density low-speed turbulent mixing layer. J. Fluid Mech. 830, 569601.CrossRefGoogle Scholar
Aslangil, D., Banerjee, A. & Lawrie, A. G. W. 2016 Numerical investigation of initial condition effects on Rayleigh–Taylor instability with acceleration reversals. Phys. Rev. E 94, 053114.Google ScholarPubMed
Aslangil, D., Livescu, D. & Banerjee, A. 2019 Flow regimes in buoyancy-driven homogeneous variable-density turbulence. In Progress in Turbulence VIII (ed. Örlü, R., Talamelli, A., Peinke, J. & Oberlack, M.), pp. 235240. Springer International Publishing.CrossRefGoogle Scholar
Aslangil, D., Livescu, D. & Banerjee, A. 2020 Variable-density buoyancy-driven turbulence with asymmetric initial density distribution. Physica D 406, 132444.CrossRefGoogle Scholar
Bailie, C., McFarland, J. A., Greenough, J. A. & Ranjan, D. 2012 Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave. Shock Waves 22 (6), 511519.CrossRefGoogle Scholar
Baltzer, J. R. & Livescu, D. 2020 Variable-density effects in incompressible non-buoyant shear-driven turbulent mixing layers. J. Fluid Mech. (under review).Google Scholar
Banerjee, A. & Andrews, M. J. 2009 3D Simulations to investigate initial condition effects on the growth of Rayleigh–Taylor mixing. Intl J. Heat Mass Transfer 52 (17), 39063917; special Issue Honoring Professor D. Brian Spalding.CrossRefGoogle Scholar
Banerjee, A., Kraft, W. N. & Andrews, M. J. 2010 Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers. J. Fluid Mech. 659, 127190.CrossRefGoogle Scholar
Batchelor, G. K., Canuto, V. M. & Chasnov, J. R. 1992 Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349378.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov Instability. Annu. Rev. Fluid Mech. 34 (1), 445468.CrossRefGoogle Scholar
Cabot, W. & Cook, A. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type ia supernovae. Nat. Phys. 2, 562568.CrossRefGoogle Scholar
Charonko, J. J. & Prestridge, K. 2017 Variable-density mixing in turbulent jets with coflow. J. Fluid Mech. 825, 887921.CrossRefGoogle Scholar
Chung, D. & Pullin, D. I. 2010 Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence. J. Fluid Mech. 643, 279308.CrossRefGoogle Scholar
Clark, T. T. & Spitz, P. B.2005 Two-point correlation equations for variable density turbulence. Tech. Rep. LA-12671-MS. Los Alamos Technical Report.Google Scholar
Clemens, N. T. & Mungal, M. G. 1995 Large-scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284, 171216.CrossRefGoogle Scholar
Colgate, S. A. & White, R. H. 1966 The hydrodynamic behavior of supernovae explosions. Astrophys. J. 143, 626681.CrossRefGoogle Scholar
Cook, A. W. & Dimotakis, P. E. 2001 Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 6999.CrossRefGoogle Scholar
Cook, A. W. & Zhou, Y. 2002 Energy transfer in Rayleigh–Taylor instability. Phys. Rev. E 66, 026312.Google ScholarPubMed
Daniel, D., Livescu, D. & Ryu, J. 2018 Reaction analogy based forcing for incompressible scalar turbulence. Phys. Rev. Fluids 3, 094602.CrossRefGoogle Scholar
Dimonte, G. & Schneider, M. 1996 Turbulent Rayleigh–Taylor instability experiments with variable acceleration. Phys. Rev. E 54, 37403743.Google ScholarPubMed
Dimonte, G., Youngs, D. L., Dimits, A., Weber, S., Marinak, M., Wunsch, S., Garasi, C., Robinson, A., Andrews, M. J., Ramaprabhu, P. 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 (5), 16681693.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.CrossRefGoogle Scholar
Gat, I., Matheou, G., Chung, D. & Dimotakis, P. E. 2017 Incompressible variable-density turbulence in an external acceleration field. J. Fluid Mech. 827, 506535.CrossRefGoogle Scholar
Getling, A. V. 1998 Rayleigh–Beńard Convection. World Scientific.CrossRefGoogle Scholar
Givi, P. 1989 Model-free simulations of turbulent reactive flows. Prog. Energy Combust. Sci. 15 (1), 1107.CrossRefGoogle Scholar
Gull, S. F. 1975 The x-ray, optical and radio properties of young supernova remnants. Mon. Not. R. Astron. Soc. 171 (2), 263278.CrossRefGoogle Scholar
Haworth, D. C. 2010 Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36 (2), 168259.CrossRefGoogle Scholar
Kida, S. & Orszag, S. A. 1990 Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5, 85125.CrossRefGoogle Scholar
Klimenko, A. Y. & Pope, S. B. 2003 The modeling of turbulent reactive flows based on multiple mapping conditioning. Phys. Fluids 15 (7), 19071925.CrossRefGoogle Scholar
Kolla, H., Rogerson, J. W., Chakraborty, N. & Swaminathan, N. 2009 Scalar dissipation rate modeling and its validation. Combust. Sci. Technol. 181 (3), 518535.CrossRefGoogle Scholar
Lai, C. C. K., Charonko, J. J. & Prestridge, K. P. 2018 A Karman–Howarth–Monin equation for variable-density turbulence. J. Fluid Mech. 843, 382418.CrossRefGoogle Scholar
Lesieur, M. & Rogallo, R. 1989 Large-eddy simulation of passive scalar diffusion in isotropic turbulence. Phys. Fluids A 1 (4), 718722.CrossRefGoogle Scholar
Linden, P. F., Redondo, J. M. & Youngs, D. L. 1994 Molecular mixing in Rayleigh–Taylor instability. J. Fluid Mech. 265, 97124.CrossRefGoogle Scholar
Lindl, J. 1995 Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas 2 (11), 39334024.CrossRefGoogle Scholar
Lindl, J. D. 1998 Inertial Confinement Fusion: The Quest for Ignition and Energy Gain Using Indirect Drive. AIP Press.Google Scholar
Livescu, D. 2013 Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability. Phil. Trans. R. Soc. Lond. A 371, 20120185.Google ScholarPubMed
Livescu, D. 2020 Turbulence with large thermal and compositional density variations. Annu. Rev. Fluid Mech. 52, 309341.CrossRefGoogle Scholar
Livescu, D., Canada, C., Kanov, K., Burns, R., IDIES staff & Pulido, J.2014 Homogeneous buoyancy driven turbulence dataset. Available at Scholar
Livescu, D., Jaberi, F. A. & Madnia, C. K. 2000 Passive-scalar wake behind a line source in grid turbulence. J. Fluid Mech. 416, 117149.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2007 Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591, 4371.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2008 Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech. 605, 145180.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2009 Mixing asymmetry in variable density turbulence. In Advances in Turbulence XII (ed. Eckhardt, B.), vol. 132, pp. 545548. Springer.CrossRefGoogle Scholar
Livescu, D., Ristorcelli, J. R., Gore, R. A., Dean, S. H., Cabot, W. H. & Cook, A. W. 2009 High-Reynolds number Rayleigh–Taylor turbulence. J. Turbul. 10, N13.Google Scholar
Livescu, D., Ristorcelli, J. R., Petersen, M. R. & Gore, R. A. 2010 New phenomena in variable-density Rayleigh–Taylor turbulence. Phys. Scr. 2010 (T142), 014015.Google Scholar
Livescu, D. & Wei, T. 2012 Direct numerical simulations of Rayleigh–Taylor instability with gravity reversal. In Proceedings of the Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Islannd, HI, July 9–13, 2012, p. 2304.Google Scholar
Livescu, D., Wei, T. & Petersen, M. R. 2011 Direct numerical simulations of Rayleigh–Taylor instability. J. Phys.: Conf. Ser. 318 (8), 082007.Google Scholar
Lumley, J. L. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10 (4), 855858.CrossRefGoogle Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4 (5), 101104.Google Scholar
Molchanov, O. A. 2004 On the origin of low- and middler-latitude ionospheric turbulence. Phys. Chem. Earth A/B/C 29 (4), 559567; seismo Electromagnetics and Related Phenomena.CrossRefGoogle Scholar
Nakai, S. & Mima, K. 2004 Laser driven inertial fusion energy: present and prospective. Rep. Prog. Phys. 67 (3), 321.CrossRefGoogle Scholar
Nakai, S. & Takabe, H. 1996 Principles of inertial confinement fusion – physics of implosion and the concept of inertial fusion energy. Rep. Prog. Phys. 59 (9), 1071.CrossRefGoogle Scholar
Nishihara, K., Wouchuk, J. G., Matsuoka, C., Ishizaki, R. & Zhakhovsky, V. V. 2010 Richtmyer–Meshkov instability: theory of linear and nonlinear evolution. Phil. Trans. R. Soc. Lond. A 368 (1916), 17691807.CrossRefGoogle ScholarPubMed
Nouri, A. G., Givi, P. & Livescu, D. 2019 Modeling and simulation of turbulent nuclear flames in type ia supernovae. Prog. Aerosp. Sci. 108, 156179.CrossRefGoogle Scholar
Overholt, M. R. & Pope, S. B. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8 (11), 31283148.CrossRefGoogle Scholar
Pal, N., Kurien, S., Clark, T. T., Aslangil, D. & Livescu, D. 2018 Two-point spectral model for variable-density homogeneous turbulence. Phys. Rev. Fluids 3, 124608.CrossRefGoogle Scholar
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11 (2), 119192.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ramaprabhu, P., Karkhanis, V. & Lawrie, A. G. W. 2013 The Rayleigh–Taylor Instability driven by an accel-decel-accel profile. Phys. Fluids 25 (11), 115104.CrossRefGoogle Scholar
Rao, P., Caulfield, C. P. & Gibbon, J. D. 2017 Nonlinear effects in buoyancy-driven variable-density turbulence. J. Fluid Mech. 810, 362377.CrossRefGoogle Scholar
Rayleigh, Lord 1884 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. s1‐14 (1), 170177.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13 (2), 297319.CrossRefGoogle Scholar
Ristorcelli, J. R. & Clark, T. T. 2004 Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations. J. Fluid Mech. 507, 213253.CrossRefGoogle Scholar
Sandoval, D. L.1995 The dynamics of variable density turbulence. PhD thesis, University of Washington.CrossRefGoogle Scholar
Sandoval, D. L., Clark, T. T. & Riley, J. J. 1997 Buoyancy-generated variable-density turbulence. In IUTAM Symposium on Variable Density Low-Speed Turbulent Flows: Proceedings of the IUTAM Symposium held in Marseille, France, 8–10 July 1996 (ed. Fulachier, L., Lumley, J. L. & Anselmet, F.), pp. 173180. Springer Netherlands.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 Mathematica Scientia 30 (2), 595620; Mathematics dedicated to professor James Glimm on the occasion of his 75th birthday.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.Google ScholarPubMed
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A. & Ristorcelli, J. R. 2016 A two-length scale turbulence model for single-phase multi-fluid mixing. Flow Turbul. Combust. 96, 143.CrossRefGoogle Scholar
Sellers, C. L. & Chandra, S. 1997 Compressibility effects in modelling turbulent high speed mixing layers. Engng Comput. 14 (1), 513.CrossRefGoogle Scholar
Soulard, O. & Griffond, J. 2012 Inertial-range anisotropy in Rayleigh–Taylor turbulence. Phys. Fluids 24, 025101.CrossRefGoogle Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201 (1065), 192196.Google Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36 (1), 281314.CrossRefGoogle Scholar
Youngs, D. L. 1991 Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3 (5), 13121320.CrossRefGoogle Scholar
Zhao, D. & Aluie, H. 2018 Inviscid criterion for decomposing scales. Phys. Rev. Fluids 3, 054603.CrossRefGoogle Scholar
Zhou, Y. 2017a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1136.Google Scholar
Zhou, Y. 2017b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1160.Google Scholar