We present results of well-resolved direct numerical simulations (DNS) of the turbulent flow evolving from Richtmyer-Meshkov instability (RMI) in a shock-tube with square cross section. The RMI occurs at the interface between a mixture of O2 and N2 (light gas) and SF6 and acetone (heavy gas). The interface between the light and heavy gas is accelerated by a Ma = 1.5 planar shock wave. RMI is triggered by a well-defined multimodal initial disturbance at the interface. The DNS exhibit grid-resolution independent statistical quantities and support the existence of a Kolmogorov-like inertial range with a k−5/3 scaling unlike previous simulations found in the literature. The results are in excellent agreement with the experimental data of Weber et al. [“Turbulent mixing measurements in the Richtmyer-Meshkov instability,” Phys. Fluids 24, 074105 (2012)] https://doi.org/10.1063/1.4733447.
REFERENCES
1.
R. D.
Richtmyer
, “Taylor instability in shock acceleration of compressible fluids
,” Commun. Pure Appl. Math.
13
, 297
(1960
).2.
E. E.
Meshkov
, “Instability of the interface of two gases accelerated by a shock wave
,” Fluid Dyn.
4
, 151
(1969
).3.
N. J.
Zabusky
, “Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments
,” Annu. Rev. Fluid Mech.
31
, 495
(1999
).4.
M.
Brouillette
, “The Richtmyer-Meshkov instability
,” Annu. Rev. Fluid Mech.
34
, 445
(2002
).5.
G. I.
Taylor
, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes
,” Proc. R. Soc. London, Ser. A
201
, 192
(1950
).6.
M.
Chertkov
, “Phenomenology of Rayleigh-Taylor turbulence
,” Phys. Rev. Lett.
91
, 115001
(2003
).7.
W. H.
Cabot
and A.
Cook
, “Reynolds number effects on Rayleigh–Taylor instability with possible implications for type-Ia supernovae
,” Nat. Phys.
2
, 562
(2006
).8.
N.
Vladimirova
and M.
Chertkov
, “Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence
,” Phys. Fluids
21
, 015102
(2009
).9.
G.
Boffetta
, A.
Mazzino
, S.
Musacchio
, and L.
Vozella
, “Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence
,” Phys. Rev. E
79
, 065301
(2009
).10.
Y.
Zhou
, “A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
,” Phys. Fluids
13
, 538
(2001
).11.
A. N.
Kolmogorov
, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
,” Dokl. Akad. Nauk SSSR
30
, 301
(1941
).12.
R. H.
Kraichnan
, “Inertial range spectrum of hydromagnetic turbulence
,” Phys. Fluids
8
, 1385
(1965
).13.
B.
Thornber
, D.
Drikakis
, D. L.
Youngs
, and R. J. R.
Williams
, “Growth of a Richtmyer-Meshkov turbulent layer after reshock
,” Phys. Fluids
23
, 095107
(2011
).14.
B.
Thornber
, D.
Drikakis
, D. L.
Youngs
, and R. J. R.
Williams
, “The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability
,” J. Fluid Mech.
654
, 99
(2010
).15.
D. J.
Hill
, C.
Pantano
, and D. I.
Pullin
, “Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock
,” J. Fluid Mech.
557
, 29
(2006
).16.
M.
Lombardini
, D. I.
Pullin
, and D. I.
Meiron
, “Transition to turbulence in shock-driven mixing: A Mach number study
,” J. Fluid Mech.
690
, 203
(2012
).17.
R. H.
Cohen
, W. P.
Dannevik
, A. M.
Dimits
, D. E.
Eliason
, A. A.
Mirin
, Y.
Zhou
, D. H.
Porter
, and P. R.
Woodward
, “Three-dimensional simulation of a Richtmyer–Meshkov instability with a two-scale initial perturbation
,” Phys. Fluids
14
, 3692
(2002
).18.
F. F.
Grinstein
, A. A.
Gowardhan
, and A. J.
Wachtor
, “Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
,” Phys. Fluids
23
, 034106
(2011
).19.
C.
Weber
, N.
Haehn
, J.
Oakley
, D.
Rothamer
, and R.
Bonazza
, “Turbulent mixing measurements in the Richtmyer-Meshkov instability
,” Phys. Fluids
24
, 074105
(2012
).20.
A. W.
Cook
, “Enthalpy diffusion in multicomponent flows
,” Phys. Fluids
21
, 055109
(2009
).21.
E. F.
Toro
, Riemann Solvers and Numerical Methods for Fluid Dynamics
(Springer-Verlag
, Berlin
, 1999
).22.
X. Y.
Hu
, Q.
Wang
, and N. A.
Adams
, “An adaptive central-upwind weighted essentially non-oscillatory scheme
,” J. Comput. Phys.
229
, 8952
(2010
).23.
X. Y.
Hu
and N. A.
Adams
, “Scale separation for implicit large eddy simulation
,” J. Comput. Phys.
230
, 7240
(2011
).24.
X. Y.
Hu
, N. A.
Adams
, and C.-W.
Shu
, “Positivity-preserving method for high-order conservative schemes solving compressible Euler equations
,” J. Comput. Phys.
242
, 169
(2013
).25.
V. K.
Tritschler
, X. Y.
Hu
, S.
Hickel
, and N. A.
Adams
, “Numerical simulation of a Richtmyer-Meshkov instability with an adaptive central-upwind 6th-order WENO scheme
,” Phys. Scr.
(to be published).26.
P.
Moin
and K.
Mahesh
, “Direct numerical simulation: A tool in turbulence research
,” Annu. Rev. Fluid Mech.
30
, 539
(1998
).27.
S. B.
Pope
, Turbulent Flows
(Cambridge University Press
, Cambridge
, 2000
).28.
G. K.
Batchelor
, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity
,” J. Fluid Mech.
5
, 113
(1958
).29.
P. E.
Dimotakis
, “Turbulent mixing
,” Annu. Rev. Fluid Mech.
37
, 329
(2005
).30.
M.
Latini
, O.
Schilling
, and W. S.
Don
, “High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions
,” Phys. Fluids
19
, 024104
(2007
).31.
M.
Latini
, O.
Schilling
, and W. S.
Don
, “Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability
,” J. Comput. Phys.
221
, 805
(2007
).32.
O.
Schilling
, M.
Latini
, and W. S.
Don
, “Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability
,” Phys. Rev. E
76
, 1
(2007
).33.
S.
Balasubramanian
, G. C.
Orlicz
, K. P.
Prestridge
, and B. J.
Balakumar
, “Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock
,” Phys. Fluids
24
, 034103
(2012
).34.
G. K.
Batchelor
and I.
Proudman
, “The large-scale structure of homogeneous turbulence
,” Philos. Trans. R. Soc. London, Ser. A
248
, 369
(1956
).35.
P. G.
Saffman
, “The large-scale structure of homogeneous turbulence
,” J. Fluid Mech.
27
, 581
(1967
).36.
P. G.
Saffman
, “Note on decay of homogeneous turbulence
,” Phys. Fluids
10
, 1349
(1967
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
