Richtmyer–Meshkov Instability is an instability that develops at the interface between fluids of distinct acoustic impedance when impacted by a shock wave. Its applications include inertial confinement fusion, supernovae explosions, and the evolution of blast waves. We systematically study the effect of the adiabatic index of the fluids on the dynamics of strong-shock-driven flows, particularly the amount of shock energy available for interfacial mixing. Only limited information is currently available about the dynamic properties of matter at these extreme regimes. We employ smooth particle hydrodynamics simulations to ensure accurate shock capturing and interface tracking. A range of adiabatic indexes is considered, approaching limits which, to the best of the author's knowledge, have never been considered before. We analyze the effect of the adiabatic indexes on the interface speed and growth rate immediately after the shock passage. The simulation results are compared wherever possible with rigorous theories, achieving good quantitative and qualitative agreement. We find that the more challenging cases for simulations arise where the adiabatic indexes are further apart, and that the initial growth rate is a non-monotone function of the initial perturbation amplitude, which holds across all adiabatic indexes of the fluids considered. The applications of these findings on experiment design are discussed.
References
1.
Abarzhi
, S. I.
, and Sreenivasan
, K. R.
, “Evgeny Evgrafovich Meshkov
,” Phys. Today
73
(5
), 64
(2020
).2.
Abarzhi
, S.
, “A new type of the evolution of the bubble front in the Richtmyer–Meshkov instability
,” Phys. Lett. A
294
(2
), 95
–100
(2002
).3.
Abarzhi
, S.
, “Review of nonlinear dynamics of the unstable fluid interface: Conservation laws and group theory
,” Phys. Scr.
T132
, 014012
(2008
).4.
Abarzhi
, S.
, Nishihara
, K.
, and Glimm
, J.
, “Rayleigh–Taylor and Richtmyer-Meshkov instabilities for fluids with a finite density ratio
,” Phys. Lett. A
317
(5
), 470
–476
(2003
).5.
Abarzhi
, S. I.
, “Review of theoretical modeling approaches of Rayleigh-Taylor instabilities and turbulent mixing
,” Philos. Trans. R. Soc. A
368
(1916
), 1809
–1828
(2010
).6.
Abarzhi
, S. I.
, Bhowmick
, A. K.
, Naveh
, A.
, Pandian
, A.
, Swisher
, N. C.
, Stellingwerf
, R. F.
, and Arnett
, W. D.
, “Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing
,” Proc. Natl. Acad. Sci. U. S. A.
116
(37
), 18184
–18192
(2019
).7.
A. N.
Aleshin
, E. V.
Lazareva
, S. G.
Zaitsev
, V. B.
Rozanov
, E. G.
Gamalii
, and I. G.
Lebo
, “Linear, nonlinear, and transient stages in the development of the Richtmyer-Meshkov instability
,” Sov. Phys. Dokl.
35
, 159
(1990
).8.
Anisimov
, S. I.
, Drake
, R. P.
, Gauthier
, S.
, Meshkov
, E. E.
, and Abarzhi
, S. I.
, “What is certain and what is not so certain in our knowledge of Rayleigh-Taylor mixing?
,” Philos. Trans. R. Soc. A.
371
(2003
), 20130266
(2013
).9.
Balsara
, D. S.
, “von neumann stability analysis of smoothed particle hydrodynamics–suggestions for optimal algorithms
,” J. Comput. Phys.
121
(2
), 357
–372
(1995
).10.
Benz
, W.
, “Applications of smooth particle hydrodynamics (SPH) to astrophysical problems
,” Comput. Phys. Commun.
48
(1
), 97
–105
(1988
).11.
Benz
, W.
, Smooth Particle Hydrodynamics: A Review
(Springer
Netherlands, Dordrecht
, 1990
), pp. 269
–288
.12.
Bodner
, S. E.
, Colombant
, D. G.
, Gardner
, J. H.
, Lehmberg
, R. H.
, Obenschain
, S. P.
, Phillips
, L.
, Schmitt
, A. J.
, Sethian
, J. D.
, McCrory
, R. L.
, Seka
, W.
, Verdon
, C. P.
, Knauer
, J. P.
, Afeyan
, B. B.
, and Powell
, H. T.
, “Direct-drive laser fusion: Status and prospects
,” Phys. Plasmas
5
(5
), 1901
–1918
(1998
).13.
Dell
, Z.
, Stellingwerf
, R. F.
, and Abarzhi
, S. I.
, “Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks
,” Phys. Plasmas
22
(9
), 092711
(2015
).14.
Dell
, Z. R.
, Pandian
, A.
, Bhowmick
, A. K.
, Swisher
, N. C.
, Stanic
, M.
, Stellingwerf
, R. F.
, and Abarzhi
, S. I.
, “Maximum initial growth rate of strong-shock-driven Richtmyer-Meshkov instability
,” Phys. Plasmas
24
(9
), 090702
(2017
).15.
Demskoĭ
, D. K.
, Marikhin
, V. G.
, and Meshkov
, A. G.
, “Lax representations for triplets of two-dimensional scalar fields of chiral type
,” Teoret. Mat. Fiz
148
(2
), 189
–205
(2006
).16.
Dimonte
, G.
, Frerking
, C. E.
, Schneider
, M.
, and Remington
, B.
, “Richtmyer–Meshkov instability with strong radiatively driven shocks
,” Phys. Plasmas
3
(2
), 614
–630
(1996
).17.
Dimonte
, G.
, and Remington
, B.
, “Richtmyer-Meshkov experiments on the nova laser at high compression
,” Phys. Rev. Lett.
70
, 1806
(1993
).18.
Dimonte
, G.
, Youngs
, D. L.
, Dimits
, A.
, Weber
, S.
, Marinak
, M.
, Wunsch
, S.
, Garasi
, C.
, Robinson
, A.
, Andrews
, M. J.
, Ramaprabhu
, P.
, Calder
, A. C.
, Fryxell
, B.
, Biello
, J.
, Dursi
, L.
, MacNeice
, P.
, Olson
, K.
, Ricker
, P.
, Rosner
, R.
, Timmes
, F.
, Tufo
, H.
, Young
, Y.-N.
, and Zingale
, M.
, “A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration
,” Phys. Fluids
16
(5
), 1668
–1693
(2004
).19.
Drake
, R. P.
, “Perspectives on high-energy-density physics
,” Phys. Plasmas
16
(5
), 055501
(2009
).20.
Glendinning
, S. G.
, Bolstad
, J.
, Braun
, D. G.
, Edwards
, M. J.
, Hsing
, W. W.
, Lasinski
, B. F.
, Louis
, H.
, Miles
, A.
, Moreno
, J.
, Peyser
, T. A
, Remington
, B. A.
, Robey
, H. F.
, Turano
, E. J.
, Verdon
, C. P.
, and Zhou
, Y.
, “Effect of shock proximity on Richtmyer–Meshkov growth
,” Phys. Plasmas
10
(5
), 1931
–1936
(2003
).21.
Guan
, B.
, Wang
, D.
, Wang
, G.
, Fan
, E.
, and Wen
, C.-Y.
, “Numerical study of the Richtmyer–Meshkov instability of a three-dimensional minimum-surface featured SF6/air interface
,” Phys. Fluids
32
(2
), 024108
(2020
).22.
Herrmann
, M.
, Moin
, P.
, and Abarzhi
, S. I.
, “Nonlinear evolution of the Richtmyer-Meshkov instability
,” J. Fluid Mech.
612
, 311
–338
(2008
).23.
Holmes
, R. L.
, Dimonte
, G.
, Fryxell
, B.
, Gittings
, M. L.
, Grove
, J. W.
, Schneider
, M.
, Sharp
, D. H.
, Velikovich
, A. L.
, Weaver
, R. P.
, and Zhang
, Q.
, “Richtmyer–Meshkov instability growth: Experiment, simulation and theory
,” J. Fluid Mech.
389
, 55
–79
(1999
).24.
Huang
, S.
, Xu
, J.
, Luo
, Y.
, Sun
, P.
, Luo
, X.
, and Ding
, J.
, “Smoothed particle hydrodynamics simulation of converging Richtmyer–Meshkov instability
,” Phys. Fluids
32
(8
), 086102
(2020
).25.
Jacobs
, J. W.
, and Krivets
, V. V.
, “Experiments on the late-time development of single-mode Richtmyer-Meshkov instability
,” Phys. Fluids
17
(3
), 034105
(2005
).26.
Li
, H.
, He
, Z.
, Zhang
, Y.
, and Tian
, B.
, “On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with Reshock
,” Phys. Fluids
31
(5
), 054102
(2019
).27.
Li
, Y.
, Samtaney
, R.
, and Wheatley
, V.
, “The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics
,” Matter Radiat. Extremes
3
(4
), 207
–218
(2018
).28.
Lindl
, J. D.
, Amendt
, P.
, Berger
, R. L.
, Glendinning
, S. G.
, Glenzer
, S. H.
, Haan
, S. W.
, Kauffman
, R. L.
, Landen
, O. L.
, and Suter
, L. J.
, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility
,” Phys. Plasmas
11
(2
), 339
–491
(2004
).29.
McFarland
, J. A.
, Greenough
, J. A.
, and Ranjan
, D.
, “Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface
,” Phys. Rev. E
84
, 026303
(2011
).30.
Meshkov
, E. E.
, “Instability of the interface of two gases accelerated by a shock wave
,” Fluid Dyn.
4
(5
), 101
–104
(1972
).31.
Monaghan
, J.
, “An introduction to SPH
,” Comput. Phys. Commun.
48
(1
), 89
–96
(1988
).32.
Monaghan
, J.
, and Gingold
, R.
, “Shock simulation by the particle method SPH
,” J. Comput. Phys.
52
(2
), 374
–389
(1983
).33.
Monaghan
, J. J.
, “Smoothed particle hydrodynamics
,” Rep. Prog. Phys.
68
(8
), 1703
–1759
(2005
).34.
Motl
, B.
, Oakley
, J.
, Ranjan
, D.
, Weber
, C.
, Anderson
, M.
, and Bonazza
, R.
, “Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges
,” Phys. Fluids
21
(12
), 126102
(2009
).35.
Nishihara
, K.
, Wouchuk
, J. G.
, Matsuoka
, C.
, Ishizaki
, R.
, and Zhakhovsky
, V. V.
, “Richtmyer-Meshkov instability: Theory of linear and nonlinear evolution
,” Philos. Trans. R. Soc. A
368
(1916
), 1769
–1807
(2010
).36.
Orlicz
, G. C.
, Balakumar
, B. J.
, Tomkins
, C. D.
, and Prestridge
, K. P.
, “A Mach number study of the Richtmyer–Meshkov instability in a varicose, heavy-gas curtain
,” Phys. Fluids
21
(6
), 064102
(2009
).37.
Pandian
, A.
, Stellingwerf
, R. F.
, and Abarzhi
, S. I.
, “Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows
,” Phys. Rev. Fluids
2
, 073903
(2017
).38.
Richtmyer
, R. D.
, “Taylor instability in shock acceleration of compressible fluids
,” Commun. Pure Appl. Math.
13
(2
), 297
–319
(1960
).39.
Stanic
, M.
, McFarland
, J.
, Stellingwerf
, R. F.
, Cassibry
, J. T.
, Ranjan
, D.
, Bonazza
, R.
, Greenough
, J. A.
, and Abarzhi
, S. I.
, “Non-uniform volumetric structures in Richtmyer-Meshkov flows
,” Phys. Fluids
25
(10
), 106107
(2013
).40.
Stanic
, M.
, Stellingwerf
, R. F.
, Cassibry
, J. T.
, and Abarzhi
, S. I.
, “Scale coupling in Richtmyer-Meshkov flows induced by strong shocks
,” Phys. Plasmas
19
(8
), 082706
(2012
).41.
42.
Stellingwerf
, R.
, Robinson
, J.
, Richardson
, S.
, Evans
, S.
, Stallworth
, R.
, and Hovater
, M.
, in Foam Tile Impact Modeling STS-107 Investigation
(2004
), p. 5
.43.
Stellingwerf
, R. F.
, Smooth Particle Hydrodynamics
(Springer Verlag
, 1990
), Chap. 25, pp. 239
–247
.44.
Sun
, P.
, Ding
, J.
, Huang
, S.
, Luo
, X.
, and Cheng
, W.
, “Microscopic Richtmyer–Meshkov instability under strong shock
,” Phys. Fluids
32
(2
), 024109
(2020
).45.
Thornber
, B.
, Griffond
, J.
, Bigdelou
, P.
, Boureima
, I.
, Ramaprabhu
, P.
, Schilling
, O.
, and Williams
, R. J. R.
, “Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability
,” Phys. Fluids
31
(9
), 096105
(2019
).46.
Velikovich
, A. L.
, Herrmann
, M.
, and Abarzhi
, S. I.
, “Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer-Meshkov instability
,” J. Fluid Mech.
751
, 432
–479
(2014
).47.
Wouchuk
, J. G.
, “Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected
,” Phys. Rev. E
63
, 056303
(2001
).48.
Zel'dovich
, I. B.
, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena
(Academic Press
, New York
, 1967
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
