The Richtmyer-Meshkov instability is experimentally investigated in a vertical shock tube using a new type of broadband initial condition imposed on an interface between a helium-acetone mixture and argon (A = 0.7). The initial condition is created by first setting up a gravitationally stable stagnation plane between the gases and then injecting the same two gases horizontally at the interface to create a shear layer. The perturbations along the shear layer create a statistically repeatable broadband initial condition. The interface is accelerated by a M = 1.6 planar shock wave, and the development of the ensuing turbulent mixing layer is investigated using planar laser induced fluorescence. By the latest experimental time, 2.1 ms after shock acceleration, the layer is shown to be fully turbulent, surpassing both turbulent transition criteria based on the Reynolds number and shear layer scale. Mixing structures are nearly isotropic by the latest time, as seen by the probability density function of gradient angles within the mixing layer. The scalar variance energy spectrum suggests a k−5/3 inertial range by the latest time and an exponential region at higher wavenumbers.
REFERENCES
1.
R. D.
Richtmyer
, “Taylor instability in shock acceleration of compressible fluids
,” Commun. Pure Appl. Math.
13
, 297
–319
(1960
).2.
E. E.
Meshkov
, “Instability of a shock wave accelerated interface between two gases
,” NASA Tech. Transl.
13
, 1
–14
(1970
).3.
J. D.
Lindl
, P.
Amendt
, R. L.
Berger
, S. G.
Glendinning
, S. H.
Glenzer
, S. W.
Haan
, R. L.
Kauffman
, O. L.
Landen
, and L. J.
Suter
, “The physics basis for ignition using indirect-drive targets on the national ignition facility
,” Phys. Plasmas
11
, 339
(2004
).4.
K.
Kifonidis
, T.
Plewa
, L.
Scheck
, H.
Janka
, and E.
Müller
, “Non-spherical core collapse supernovae
,” Astron. Astrophys.
453
, 661
–678
(2006
).5.
F.
Marble
, G.
Hendricks
, and E.
Zukoski
, “Progress toward shock enhancement of supersonic combustion processes
,” in 23rd AIAA, SAE, ASME, and ASEE, Joint Propulsion Conference, San Diego, CA, June 29–July 2 1987
(American Institute of Aeronautics and Astronautics
, New York
, 1987
), pp. 1
–8
.6.
P. E.
Dimotakis
, “Turbulent mixing
,” Ann. Rev. Fluid Mech.
37
, 329
–356
(2005
).7.
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
).8.
R. L.
Holmes
, G.
Dimonte
, B.
Fryxell
, M. L.
Gittings
, J. W.
Grove
, M.
Schneider
, D. H.
Sharp
, A. L.
Velikovich
, R. P.
Weaver
, and Q.
Zhang
, “Richtmyer–Meshkov instability growth: experiment, simulation and theory
,” J. Fluid Mech.
389
, 55
–79
(1999
).9.
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
).10.
A. R.
Miles
, B.
Blue
, M. J.
Edwards
, J. A.
Greenough
, J. F.
Hansen
, H. F.
Robey
, R. P.
Drake
, C.
Kuranz
, and D. R.
Leibrandt
, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems
,” Phys. Plasmas
12
, 056317
(2005
).11.
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
–61
(2006
).12.
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
).13.
A.
Banerjee
, R.
Gore
, and M.
Andrews
, “Development and validation of a turbulent-mix model for variable-density and compressible flows
,” Phys. Rev. E
82
, 046309
(2010
).14.
K.
Meyer
and P.
Blewett
, “Numerical investigation of the stability of a shock-accelerated interface between two fluids
,” Phys. Fluids
15
, 753
–759
(1972
).15.
M.
Vandenboomgaerde
, C.
Mügler
, and S.
Gauthier
, “Impulsive model for the Richtmyer–Meshkov instability
,” Phys. Rev. E
58
, 1874
–1882
(1998
).16.
G.
Dimonte
, C.
Frerking
, and M.
Schneider
, “Richtmyer–Meshkov instability in the turbulent regime
,” Phys. Rev. Lett.
74
, 4855
–4858
(1995
).17.
G. I.
Barenblatt
, “Selfsimilar turbulence propagation from an instantaneous plane source
,” in Nonlinear Dynamics and Turbulence
, edited by G. I.
Barenblatt
, G.
Iooss
, and D. D.
Joseph
(Pitmann
, 1983
), pp. 48
–60
.18.
D. L.
Youngs
, “Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
,” Laser Part. Beams
12
, 725
–750
(1994
).19.
J. K.
Prasad
, A.
Rasheed
, S.
Kumar
, and B.
Sturtevant
, “The late-time development of the Richtmyer–Meshkov instability
,” Phys. Fluids
12
, 2108
–2115
(2000
).20.
M.
Huang
and A.
Leonard
, “Power-law decay of homogeneous turbulence at low Reynolds numbers
,” Phys. Fluids
6
, 3765
–3775
(1994
).21.
G.
Dimonte
and M.
Schneider
, “Turbulent Richtmyer–Meshkov instability experiments with strong radiatively driven shocks
,” Phys. Plasmas
4
, 4347
–4357
(1997
).22.
G.
Dimonte
and M.
Schneider
, “Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories
,” Phys. Fluids
12
, 304
(2000
).23.
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
–139
(2010
).24.
K. O.
Mikaelian
, “Extended model for Richtmyer-Meshkov mix
,” Phys. D: Nonlinear Phenom.
240
, 935
–942
(2011
).25.
P.
Rightley
, P.
Vorobieff
, R.
Martin
, and R.
Benjamin
, “Experimental observations of the mixing transition in a shock-accelerated gas curtain
,” Phys. Fluids
11
, 186
–200
(1999
).26.
K.
Prestridge
, P. M.
Rightley
, P.
Vorobieff
, R. F.
Benjamin
, and N. A.
Kurnit
, “Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain
,” Exp. Fluids
29
, 339
–346
(2000
).27.
B.
Balakumar
, G.
Orlicz
, C.
Tomkins
, and K.
Prestridge
, “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
(2008
).28.
K. A.
Buch
and W. J.
Dahm
, “Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 2. Sc≈1
,” J. Fluid Mech.
364
, 1
–29
(1998
).29.
L. K.
Su
and N. T.
Clemens
, “The structure of fine-scale scalar mixing in gas-phase planar turbulent jets
,” J. Fluid Mech.
488
, 1
–29
(2003
).30.
G.
Wang
, A.
Karpetis
, and R.
Barlow
, “Dissipation length scales in turbulent nonpremixed jet flames
,” Combust. Flame
148
, 62
–75
(2007
).31.
G.
Wang
and R. S.
Barlow
, “Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames
,” Exp. Fluids
44
, 633
–645
(2008
).32.
B. R.
Petersen
, D. M.
Heim
, and J. B.
Ghandhi
, “High-Resolution scalar and velocity measurements in an internal combustion engine
,” J. Eng. Gas Turbines Power
132
, 092804
(2010
).33.
B.
Petersen
and J.
Ghandhi
, “High-resolution turbulent scalar field measurements in an optically accessible internal combustion engine
,” Exp. Fluids
51
, 1695
–1708
(2011
).34.
A. W.
Cook
and P. E.
Dimotakis
, “Transition stages of Rayleigh–Taylor instability between miscible fluids
,” J. Fluid Mech.
443
, 69
–99
(2001
).35.
K. A.
Buch
and W. J.
Dahm
, “Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc≫1
,” J. Fluid Mech.
317
, 21
–71
(1996
).36.
C.
Tomkins
, S.
Kumar
, G.
Orlicz
, and K.
Prestridge
, “An experimental investigation of mixing mechanisms in shock-accelerated flow
,” J. Fluid Mech.
611
, 131
–150
(2008
).37.
H.
Pitsch
, “Large-eddy simulation of turbulent combustion
,” Annu. Rev. Fluid Mech.
38
, 453
–482
(2006
).38.
A.
Obukhov
, “Structure of the temperature field in turbulent flow
,” Izv. Akad. Nauk. SSSR, Geogr. Geofiz.
13
, 58
–69
(1968
).39.
S.
Corrsin
, “On the spectrum of isotropic temperature fluctuations in isotropic turbulence
,” J. Appl. Phys.
22
, 469
–73
(1951
).40.
A.
Kolmogorov
, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
,” Dokl. Akad. Nauk SSSR
30
, 299
–301
(1941
).41.
Z.
Warhaft
, “Passive scalars in turbulent flows
,” Ann. Rev. Fluid Mech.
32
, 203
–240
(2000
).42.
M.
Anderson
, B.
Puranik
, J.
Oakley
, P.
Brooks
, and R.
Bonazza
, “Shock tube investigation of hydrodynamic issues related to inertial confinement fusion
,” Shock Waves
10
, 377
–387
(2000
).43.
M. A.
Jones
and J. W.
Jacobs
, “A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface
,” Phys. Fluids
9
, 3078
–3085
(1997
).44.
W. E.
Kaskan
and A. B. F.
Duncan
, “Mean lifetime of the fluorescence of acetone and biacetyl vapors
,” J. Chem. Phys.
18
, 427
(1950
).45.
R. B.
Cundall
and A. S.
Davies
, “The mechanism of the gas phase photolysis of acetone
,” Proc. R. Soc. London, Ser. A
290
, 563
–582
(1966
).46.
M. A.
Blitz
, D. E.
Heard
, and M. J.
Pilling
, “Study of acetone photodissociation over the wavelength range 248–330 nm: Evidence of a mechanism involving both the singlet and triplet excited states
,” J. Phys. Chem. A
110
, 6742
–6756
(2006
).47.
B. D.
Collins
and J. W.
Jacobs
, “PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface
,” J. Fluid Mech.
464
, 113
–136
(2002
).48.
M. C.
Thurber
, F.
Grisch
, B. J.
Kirby
, M.
Votsmeier
, and R. K.
Hanson
, “Measurements and modeling of acetone laser-induced fluorescence with implications for temperature-imaging diagnostics
,” Appl. Opt.
37
, 4963
–4978
(1998
).49.
B.
Motl
, J.
Oakley
, D.
Ranjan
, C.
Weber
, M.
Anderson
, and R.
Bonazza
, “Experimental validation of a Richtmyer-Meshkov scaling law over large density ratio and shock strength ranges
,” Phys. Fluids
21
, 126102
(2009
).50.
M.
Vetter
and B.
Sturtevant
, “Experiments on the Richtmyer–Meshkov instability of an air/SF6 interface
,” Shock Waves
4
, 247
–252
(1995
).51.
E.
Leinov
, G.
Malamud
, Y.
Elbaz
, L. A.
Levin
, G.
Ben-Dor
, D.
Shvarts
, and O.
Sadot
, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions
,” J. Fluid Mech.
626
, 449
–475
(2009
).52.
K.
Mikaelian
, “Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
,” Phys. D: Nonlinear Phenom.
36
, 343
–357
(1989
).53.
K. I.
Read
, “Experimental investigation of turbulent mixing by Rayleigh–Taylor instability
,” Phys. D: Nonlinear Phenom.
12
, 45
–58
(1984
).54.
D. L.
Youngs
, “Numerical simulation of turbulent mixing by Rayleigh–Taylor instability
,” Phys. D: Nonlinear Phenom.
12
, 32
–44
(1984
).55.
A. W.
Cook
, W.
Cabot
, and P. L.
Miller
, “The mixing transition in Rayleigh–Taylor instability
,” J. Fluid Mech.
511
, 333
–362
(2004
).56.
P. E.
Dimotakis
, “The mixing transition in turbulent flows
,” J. Fluid Mech.
409
, 69
–98
(2000
).57.
Y.
Zhou
, H.
Robey
, and A.
Buckingham
, “Onset of turbulence in accelerated high-Reynolds-number flow
,” Phys. Rev. E
67
, 056305
(2003
).58.
H.
Tennekes
and J.
Lumley
, A First Course in Turbulence
(MIT
, 1972
).59.
D. L.
Cotrell
and A. W.
Cook
, “Scaling the incompressible Richtmyer–Meshkov instability
,” Phys. Fluids
19
, 078105
(2007
).60.
S.
Kumar
, G.
Orlicz
, C.
Tomkins
, C.
Goodenough
, K.
Prestridge
, P.
Vorobieff
, and R.
Benjamin
, “Stretching of material lines in shock-accelerated gaseous flows
,” Phys. Fluids
17
, 082107
(2005
).61.
P.
Miller
and P.
Dimotakis
, “Stochastic geometric properties of scalar interfaces in turbulent jets
,” Phys. Fluids A
3
, 168
–177
(1991
).62.
S. B.
Dalziel
, P. F.
Linden
, and D. L.
Youngs
, “Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability
,” J. Fluid Mech.
399
, 1
–48
(1999
).63.
P. N.
Wilson
and M. J.
Andrews
, “Spectral measurements of Rayleigh-Taylor mixing at small Atwood number
,” Phys. Fluids
14
, 938
(2002
).64.
P.
Ramaprabhu
and M. J.
Andrews
, “Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers
,” J. Fluid Mech.
502
, 233
–271
(2004
).65.
N. J.
Mueschke
, M. J.
Andrews
, and O.
Schilling
, “Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh-Taylor mixing layer
,” J. Fluid Mech.
567
, 27
(2006
).66.
A.
Banerjee
, W. N.
Kraft
, and M. J.
Andrews
, “Detailed measurements of a statistically steady Rayleigh-Taylor mixing layer from small to high Atwood numbers
,” J. Fluid Mech.
659
, 127
–190
(2010
).67.
P.
Vorobieff
, P. M.
Rightley
, and R. F.
Benjamin
, “Power-Law spectra of incipient Gas-Curtain turbulence
,” Phys. Rev. Lett.
81
, 2240
–2243
(1998
).68.
P.
Vorobieff
, N. G.
Mohamed
, C.
Tomkins
, C.
Goodenough
, M.
Marr-Lyon
, and R. F.
Benjamin
, “Scaling evolution in shock-induced transition to turbulence
,” Phys. Rev. E
68
, 065301
(2003
).69.
Y.
Zhou
, “A scaling analysis of turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities
,” Phys. Fluids
13
, 538
(2001
).70.
O.
Schilling
and M.
Latini
, “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.
30
, 595
–620
(2010
).71.
S. A.
Kaiser
and J. H.
Frank
, “Imaging of dissipative structures in the near field of a turbulent non-premixed jet flame
,” Proc. Combust. Inst.
31
, 1515
–1523
(2007
).72.
S.
Pope
, Turbulent Flows
(Cambridge University Press
, Cambridge
, 2000
).73.
G.
Batchelor
, The Theory of Homogeneous Turbulence
(Cambridge University Press
, Cambridge
, 1982
).74.
R. A.
Antonia
, H.
Abe
, and H.
Kawamura
, “Analogy between velocity and scalar fields in a turbulent channel flow
,” J. Fluid Mech.
628
, 241
(2009
).75.
G. H.
Wang
, N. T.
Clemens
, R. S.
Barlow
, and P. L.
Varghese
, “A system model for assessing scalar dissipation measurement accuracy in turbulent flows
,” Meas. Sci. Technol.
18
, 1287
(2007
).76.
P.
Papanicolaou
and E.
List
, “Statistical and spectral properties of tracer concentration in round buoyant jets
,” Int. J. Heat Mass Transf.
30
, 2059
–2071
(1987
).77.
Z.
Dai
, L.
Tseng
, and G. M.
Faeth
, “Structure of round, fully developed, buoyant turbulent plumes
,” J. Heat Transf.
116
, 409
(1994
).78.
C. E.
Fisher
and K. S.
Ball
, “Plume dynamics in natural convection in a horizontal cylindrical annulus
,” J. Heat Transf.
121
, 598
(1999
).79.
J. B.
Ghandhi
, “Spatial resolution and noise considerations in determining scalar dissipation rate from passive scalar image data
,” Exp. Fluids
40
, 577
–588
(2006
).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.
