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Rayleigh–Taylor mixing between density stratified layers

Published online by Cambridge University Press:  01 December 2016

R. J. R. Williams*
Affiliation:
AWE Aldermaston, Reading, Berkshire RG7 4PR, UK
*
Email address for correspondence: [email protected]

Abstract

We have performed numerical calculations of fluid mixing driven by Rayleigh–Taylor instability for density profiles based on the stratified density experiments of Lawrie & Dalziel (J. Fluid Mech., vol. 688, 2011, pp. 507–527) and Davies Wykes & Dalziel (J. Fluid Mech., vol. 756, 2014, pp. 1027–1057). We find that the late-time mixing profiles are similar to their experimental results for similar initial conditions; we consider a range of additional initial conditions to investigate the robustness of the results. A model for the late-time structure of the mixing layer, based on the maximization of configurational entropy, is compared with the results of the numerical calculations, and shows good agreement.

Type
Papers
Copyright
© British Crown Owned Copyright 2016/AWE. Published by Cambridge University Press 2016. 

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References

Andronov, V. A., Bakhrakh, S. M., Mokhov, V. N., Nikiforov, V. V. & Pevnitskii, A. V. 1979 Effect of turbulent mixing in the compression of laser targets. Sov. Phys. JETP 29, 5659.Google Scholar
Bertram, J. 2015 Maximum kinetic energy dissipation and the stability of turbulent Poiseuille flow. J. Fluid Mech. 767, 342363.Google Scholar
Böhm-Vitense, E. 1958 Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Z. für Astrophysik 46, 108.Google Scholar
Boltzmann, L. 1964 Lectures on Gas Theory. University of California Press.CrossRefGoogle Scholar
Carnevale, G. F., Frisch, U. & Salmon, Rick 1981 H theorems in statistical fluid dynamics. J. Phys. A 14 (7), 1701.CrossRefGoogle Scholar
Cloutman, L. D. 1987 A new estimate of the mixing length and convective overshooting in massive stars. Astrophys. J. 313, 699710.CrossRefGoogle Scholar
Coolen, A. C. C., Kühn, R. & Sollich, P. 2005 Theory of Neural Information Processing Systems. Oxford University Press.Google Scholar
Dalziel, S. B., Linden, P. F. & Youngs, D. L. 1999 Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability. J. Fluid Mech. 399, 148.Google Scholar
Davies Wykes, M. S. & Dalziel, S. B. 2014 Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification. J. Fluid Mech. 756, 10271057.Google Scholar
Dewar, R. C. 2005 Maximum entropy production and the fluctuation theorem. J. Phys. A 38, L371L381.CrossRefGoogle Scholar
Gossard, E. E., Jensen, D. R. & Richter, J. H. 1971 An analytical study of tropospheric structure as seen by high-resolution radar. J. Atmos. Sci. 28, 794807.2.0.CO;2>CrossRefGoogle Scholar
Grinstein, F. F., Margolin, L. G. & Rider, W. J. 2007 Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics. Cambridge University Press.Google Scholar
Inogamov, N. A. 1978 Turbulent stage of the Rayleigh–Taylor instability. Sov. Tech. Phys. Lett. 4, 299304.Google Scholar
Jaynes, E. T. 1957a Information theory and statistical mechanics. Phys. Rev. 106, 620630.CrossRefGoogle Scholar
Jaynes, E. T. 1957b Information theory and statistical mechanics. II. Phys. Rev. 108, 171190.Google Scholar
Kaniel, S. & Kovetz, A. 1967 Schwarzschild’s criterion for instability. Phys. Fluids 10, 11861193.CrossRefGoogle Scholar
Lawrie, A. G. W. & Dalziel, S. B. 2011 Rayleigh–Taylor mixing in an otherwise stable stratification. J. Fluid Mech. 688, 507527.Google Scholar
Ledoux, P. 1947 Stellar models with convection and with discontinuity of the mean molecular weight. Astrophys. J. 105, 305.Google Scholar
Lynden-Bell, D. 1967 Statistical mechanics of violent relaxation in stellar systems. Mon. Not. R. Astron. Soc. 136, 101.Google Scholar
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow. J. Fluid Mech. 1, 521539.Google Scholar
Margolin, L. G. & Rider, W. J. 2002 A rationale for implicit turbulence modelling. Intl J. Numer. Meth. Fluids 39 (9), 821841.Google Scholar
Montgomery, D. 1985 Maximal entropy in fluid and plasma turbulence. In Maximum Entropy and Bayesian Methods (ed. Ray Smith, C. & Grandy, W. T.), pp. 455468. Reidel.Google Scholar
Onsager, L. 1931a Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405426.Google Scholar
Onsager, L. 1931b Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 22652279.Google Scholar
Prigogine, I. 1962 Introduction to Non-Equilibrium Thermodynamics. Wiley-Interscience.Google Scholar
Rayleigh, Lord 1882 Investigation into the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. s1–14 (1), 170177.Google Scholar
Reible, D. D. 1998 Fundamentals of Environmental Engineering. CRC Press.Google Scholar
Robert, R. & Sommeria, J. 1991 Statistical equilibrium states for two-dimensional flows. J. Fluid Mech. 229, 291310.Google Scholar
Schwarzschild, K. 1906 On the equilibrium of the Sun’s atmosphere. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Math.-phys. Klasse 195, 4153.Google Scholar
Schwarzschild, M. 1958 Structure and Evolution of the Stars. Princeton University Press.Google Scholar
Shannon, C. E. 1948 A mathematical theory of communication. Part I. Bell Sys. Tech. J. 27, 379423.Google Scholar
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192196.Google Scholar
Thornber, B., Drikakis, D., Williams, R. J. R. & Youngs, D. L. 2008 On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes. J. Comput. Phys. 227, 48534872.Google Scholar
Thornber, B., Mosedale, A. & Drikakis, D. 2007 On the implicit large eddy simulations of homogeneous decaying turbulence. J. Comput. Phys. 226, 19021929.Google Scholar
Tremaine, S., Hénon, M. & Lynden-Bell, D. 1986 H-functions and mixing in violent relaxation. Mon. Not. R. Astron. Soc. 219, 285297.Google Scholar
Youngs, D. L. 1991 Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3, 13121320.Google Scholar
Youngs, D. L. 2009 Application of monotone integrated large eddy simulation to Rayleigh–Taylor mixing. Phil. Trans. R. Soc. Lond. A 367, 29712983.Google Scholar