A computational study of the Richtmyer–Meshkov instability (RMI) is presented for an inclined interface perturbation in support of experiments being performed at the Texas A&M shock tube facility. The study is comprised of 2D, viscous, diffusive, compressible simulations performed using the arbitrary Lagrange Eulerian code, ARES, developed at Lawrence Livermore National Laboratory. These simulations were performed to late times after reshock with two initial interface perturbations, in the linear and nonlinear regimes each, prescribed by the interface inclination angle. The interaction of the interface with the reshock wave produced a complex 2D set of compressible wave interactions including expansion waves, which also interacted with the interface. Distinct differences in the interface growth rates prior to reshock were found in previous work. The current work provides in-depth analysis of the vorticity and enstrophy fields to elucidate the physics of reshock for the inclined interface RMI. After reshock, the two cases exhibit some similarities in integral measurements despite their disparate initial conditions but also show different vorticity decay trends, power law decay for the nonlinear and linear decay for the linear perturbation case.

References

References
1.
Richtmyer
,
R. D.
,
1960
, “
Taylor Instability in Shock Acceleration of Compressible Fluids
,”
Commun. Pure Appl. Math.
,
13
(
2
), pp.
297
319
.10.1002/cpa.3160130207
2.
Meshkov
,
E.
,
1969
, “
Instability of the Interface of Two Gases Accelerated by a Shock Wave
,”
Fluid Dyn.
,
4
(
5
), pp.
101
104
.10.1007/BF01015969
3.
Taylor
,
G.
,
1950
, “
The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes. I
,”
Proc. R. Soc. London, Ser. A: Math. Phys. Sci.
,
201
(
1065
), pp.
192
196
.10.1098/rspa.1950.0052
4.
Marble
,
F. E.
,
Zukoski
,
E. E.
,
Jacobs
,
J.
,
Hendricks
,
G.
, and
Waitz
,
I.
,
1990
, “
Shock Enhancement and Control of Hypersonic Mixing and Combustion
,” AIAA Paper No 90-1981.
5.
Kane
,
J.
,
Drake
,
R.
, and
Remington
,
B.
,
1999
, “
An Evaluation of the Richtmyer-Meshkov Instability in Supernova Remnant Formation
,”
Astrophys. J.
,
511
(
1
), pp.
335
340
.10.1086/306685
6.
Anderson
,
M.
,
Puranik
,
B.
,
Oakley
,
J.
,
Brooks
,
P.
, and
Bonazza
,
R.
,
2000
, “
Shock Tube Investigation of Hydrodynamic Issues Related to Inertial Confinement Fusion
,”
Shock Waves
,
10
(
5
), pp.
377
387
.10.1007/s001930000067
7.
Brouillette
,
M.
,
2002
, “
The Richtmyer-Meshkov Instability
,”
Ann. Rev. Fluid Mech.
,
34
(
1
), pp.
445
468
.10.1146/annurev.fluid.34.090101.162238
8.
Ranjan
,
D.
,
Oakley
,
J.
, and
Bonazza
,
R.
,
2011
, “
Shock-Bubble Interactions
,”
Ann. Rev. Fluid Mech.
,
43
, pp.
117
140
.10.1146/annurev-fluid-122109-160744
9.
Chapman
,
P.
, and
Jacobs
,
J.
,
2006
, “
Experiments on the Three-Dimensional Incompressible Richtmyer-Meshkov Instability
,”
Phys. Fluids
,
18
, p.
074101
.10.1063/1.2214647
10.
Robey
,
H. F.
,
Kane
,
J.
,
Remington
,
B.
,
Drake
,
R.
,
Hurricane
,
O.
,
Louis
,
H.
,
Wallace
,
R.
,
Knauer
,
J.
,
Keiter
,
P.
,
Arnett
,
D.
, and
Ryutov
,
D. D.
,
2001
, “
An Experimental Testbed for the Study of Hydrodynamic Issues in Supernovae
,”
Phys. Plasmas
,
8
(
5
), pp.
2446
2453
.10.1063/1.1352594
11.
Harding
,
E.
,
Hansen
,
J.
,
Hurricane
,
O.
,
Drake
,
R.
,
Robey
,
H.
,
Kuranz
,
C.
,
Remington
,
B.
,
Bono
,
M.
,
Grosskopf
,
M.
, and
Gillespie
,
R.
,
2009
, “
Observation of a Kelvin-Helmholtz Instability in a High-Energy-Density Plasma on the Omega Laser
,”
Phys. Rev. Lett.
,
103
(
4
), p.
045005
.10.1103/PhysRevLett.103.045005
12.
Drake
,
R.
,
Doss
,
F.
,
McClarren
,
R.
,
Adams
,
M.
,
Amato
,
N.
,
Bingham
,
D.
,
Chou
,
C.
,
DiStefano
,
C.
,
Fidkowski
,
K.
,
Fryxell
,
B.
,
Gombosi
,
T. I.
,
Grosskopf
,
M. J.
,
Holloway
,
J. P.
,
Van Der Holst
,
B.
,
Huntington
,
C. M.
,
Karni
,
S.
,
Krauland
,
C. M.
,
Kuranz
,
C. C.
,
Larsen
,
E.
,
Van Leer
,
B.
,
Mallick
,
B.
,
Marion
,
D.
,
Martin
,
W.
,
Morel
,
J. E.
,
Myra
,
E. S.
,
Nair
,
V.
,
Powell
,
K. G.
,
Rauchwerger
,
L.
,
Roe
,
P.
,
Rutter
,
E.
,
Sokolov
,
I. V.
,
Stout
,
Q.
,
Torralva
,
B. R.
,
Toth
,
G.
,
Thornton
,
K.
, and
Visco
,
A. J.
,
2011
, “
Radiative Effects in Radiative Shocks in Shock Tubes
,”
High Energy Dens. Phys.
,
7
(
3
), pp.
130
140
.10.1016/j.hedp.2011.03.005
13.
Bailie
,
C.
,
McFarland
,
J.
,
Greenough
,
J.
, and
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
), pp.
511
519
.10.1007/s00193-012-0382-y
14.
Vetter
,
M.
, and
Sturtevant
,
B.
,
1995
, “
Experiments on the Richtmyer-Meshkov Instability of an Air/SF6 Interface
,”
Shock Waves
,
4
(
5
), pp.
247
252
.10.1007/BF01416035
15.
Erez
,
L.
,
Sadot
,
O.
,
Oron
,
D.
,
Erez
,
G.
,
Levin
,
L.
,
Shvarts
,
D.
, and
Ben-Dor
,
G.
,
2000
, “
Study of the Membrane Effect on Turbulent Mixing Measurements in Shock Tubes
,”
Shock Waves
,
10
(
4
), pp.
241
251
.10.1007/s001930000053
16.
Abakumov
,
A.
,
Fadeev
,
V. Y.
,
Kholkin
,
S.
,
Meshkov
,
E.
,
Nikiforov
,
V.
,
Nizovtzev
,
P.
,
Sadilov
,
N.
,
Sobolev
,
S.
,
Tilkunov
,
V.
,
Tochilin
,
V.
,
Tolshmyakov
,
A. I.
, and
Zhidov
,
N. V.
,
1996
, “
Studies of Film Effects on the Turbulent Mixing Zone Evolution in Shock Tube Experiments
,”
Proceedings of the 5th International Workshop on Compressible Turbulent Mixing
,
R.
Young
,
J.
Glimm
, and
B.
Boston
, eds.,
World Scientific
,
Singapore
, pp.
118
123
.
17.
Houas
,
L.
, and
Chemouni
,
I.
,
1996
, “
Experimental Investigation of Richtmyer–Meshkov Instability in Shock Tube
,”
Phys. Fluids
,
8
, pp.
614
627
.10.1063/1.868845
18.
Kucherenko
,
Y. A.
,
Pavlenko
,
A.
,
Shestachenko
,
O.
,
Balabin
,
S.
,
Pylaev
,
A.
, and
Tyaktev
,
A.
,
2010
, “
Measurement of Spectral Characteristics of the Turbulent Mixing Zone
,”
J. Appl. Mech. Tech. Phys.
,
51
(
3
), pp.
299
307
.10.1007/s10808-010-0041-y
19.
Niederhaus
,
J.
,
Ranjan
,
D.
,
Oakley
,
J.
,
Anderson
,
M.
,
Greenough
,
J.
, and
Bonazza
,
R.
,
2009
, “
Computations in 3D for Shock-Induced Distortion of a Light Spherical Gas Inhomogeneity
,”
Shock Waves
,
Springer
,
New York
, pp.
1169
1174
.
20.
Haehn
,
N.
,
Weber
,
C.
,
Oakley
,
J.
,
Anderson
,
M.
,
Ranjan
,
D.
, and
Bonazza
,
R.
,
2011
, “
Experimental Investigation of a Twice-Shocked Spherical Gas Inhomogeneity With Particle Image Velocimetry
,”
Shock Waves
,
21
(
3
), pp.
225
231
.10.1007/s00193-011-0299-x
21.
Ranjan
,
D.
,
Anderson
,
M.
,
Oakley
,
J.
, and
Bonazza
,
R.
,
2005
, “
Experimental Investigation of a Strongly Shocked Gas Bubble
,”
Phys. Rev. Lett.
,
94
(
18
), p.
184507
.10.1103/PhysRevLett.94.184507
22.
Ranjan
,
D.
,
Niederhaus
,
J.
,
Motl
,
B.
,
Anderson
,
M.
,
Oakley
,
J.
, and
Bonazza
,
R.
,
2007
, “
Experimental Investigation of Primary and Secondary Features in High-Mach-Number Shock-Bubble Interaction
,”
Phys. Rev. Lett.
,
98
(
2
), p.
024502
.10.1103/PhysRevLett.98.024502
23.
Ranjan
,
D.
,
Niederhaus
,
J.
,
Oakley
,
J.
,
Anderson
,
M.
,
Greenough
,
J.
, and
Bonazza
,
R.
,
2008
, “
Experimental and Numerical Investigation of Shock-Induced Distortion of a Spherical Gas Inhomogeneity
,”
Phys. Scr.
,
2008
,
014020
.10.1088/0031-8949/2008/T132/014020
24.
Jacobs
,
J.
,
1992
, “
Shock-Induced Mixing of a Light-Gas Cylinder
,”
J. Fluid Mech.
,
234
, pp.
629
649
.10.1017/S0022112092000946
25.
Balasubramanian
,
S.
,
Orlicz
,
G.
,
Prestridge
,
K.
, and
Balakumar
,
B.
,
2012
, “
Experimental Study of Initial Condition Dependence on Richtmyer-Meshkov Instability in the Presence of Reshock
,”
Phys. Fluids
,
24
, p.
034103
.10.1063/1.3693152
26.
Prestridge
,
K.
,
Vorobieff
,
P.
,
Rightley
,
P.
, and
Benjamin
,
R.
,
2000
, “
Validation of an Instability Growth Model Using Particle Image Velocimetry Measurements
,”
Phys. Rev. Lett.
,
84
(
19
), pp.
4353
4356
.10.1103/PhysRevLett.84.4353
27.
Mikaelian
,
K. O.
,
1996
, “
Numerical Simulations of Richtmyer–Meshkov Instabilities in Finite-Thickness Fluid Layers
,”
Phys. Fluids
,
8
, pp.
1269
1292
.10.1063/1.868898
28.
Motl
,
B.
,
Oakley
,
J.
,
Ranjan
,
D.
,
Weber
,
C.
,
Anderson
,
M.
, and
Bonazza
,
R.
,
2009
, “
Experimental Validation of a Richtmyer–Meshkov Scaling Law Over Large Density Ratio and Shock Strength Ranges
,”
Phys. Fluids
,
21
, p.
126102
.10.1063/1.3280364
29.
Collins
,
B.
, and
Jacobs
,
J.
,
2002
, “
Plif Flow Visualization and Measurements of the Richtmyer-Meshkov Instability of an Air/SF6 Interface
,”
J. Fluid Mech.
,
464
, pp.
113
136
.10.1017/S0022112002008844
30.
Schilling
,
O.
,
Latini
,
M.
, and
Don
,
W. S.
,
2007
, “
Physics of Reshock and Mixing in Single-Mode Richtmyer-Meshkov Instability
,”
Phys. Rev. E
,
76
(
2
), p.
026319
.10.1103/PhysRevE.76.026319
31.
Long
,
C.
,
Krivets
,
V.
,
Greenough
,
J.
, and
Jacobs
,
J.
,
2009
, “
Shock Tube Experiments and Numerical Simulation of the Single-Mode, Three-Dimensional Richtmyer–Meshkov Instability
,”
Phys. Fluids
,
21
, p.
114104
.10.1063/1.3263705
32.
Haas
,
J.-F.
,
1995
, “
Experiments and Simulations on Shock Waves in Non-Homogeneous Gases
,”
Shock Waves @ Marseille IV
,
Springer
,
New York
, pp.
27
36
.
33.
Sturtevant
,
B.
,
1989
, “
Rayleigh-Taylor Instability in Compressible Fluids
,” Lawrence Livermore National Laboratory, Livermore, CA, California Institute of Technology, Pasadena, CA, Graduate Aeronautical Labs, Technical Report.
34.
Jahn
,
R. G.
,
1956
, “
The Refraction of Shock Waves at a Gaseous Interface
,”
J. Fluid Mech.
,
1
(
5
), pp.
457
489
.10.1017/S0022112056000299
35.
Abd-El-Fattah
,
A.
,
Henderson
,
L. F.
, and
Lozzi
,
A.
,
1976
, “
Precursor Shock Waves at a Slow Fast Gas Interface
,”
J. Fluid Mech.
,
76
(
1
), pp.
157
176
.10.1017/S0022112076003182
36.
Abd-El-Fattah
,
A.
, and
Henderson
,
L.
,
1978
, “
Shock Waves at a Fast-Slow Gas Interface
,”
J. Fluid Mech.
,
86
(
1
), pp.
15
32
.10.1017/S0022112078000981
37.
Samtaney
,
R.
, and
Zabusky
,
N. J.
,
1994
, “
Circulation Deposition on Shock-Accelerated Planar and Curved Density-Stratified Interfaces: Models and Scaling Laws
,”
J. Fluid Mech.
,
269
, pp.
45
78
.10.1017/S0022112094001485
38.
Zhang
,
S.
,
Peng
,
G.
, and
Zabusky
,
N.
,
2005
, “
Vortex Dynamics and Baroclinically Forced Inhomogeneous Turbulence for Shock Planar Heavy Curtain Interactions
,”
J. Turbulence
,
6
, pp.
1
29
.10.1080/14685240500054882
39.
Mikaelian
,
K. O.
,
2005
, “
Richtmyer–Meshkov Instability of Arbitrary Shapes
,”
Phys. Fluids
,
17
, p.
034101
.10.1063/1.1848547
40.
Smith
,
A.
,
Holder
,
D.
,
Barton
,
C.
,
Morris
,
A.
, and
Youngs
,
D.
,
2001
, “
Shock Tube Experiments on Richtmyer-Meshkov Instability Across a Chevron Profiled Interface
,” AWE, Local Organizing Committee.
41.
McFarland
,
J. A.
,
Greenough
,
J. A.
, and
Ranjan
,
D.
,
2011
, “
Computational Parametric Study of a Richtmyer-Meshkov Instability for an Inclined Interface
,”
Phys. Rev. E
,
84
(
2
), p.
026303
.10.1103/PhysRevE.84.026303
42.
McFarland
,
J. A.
,
Greenough
,
J. A.
, and
Ranjan
,
D.
,
2013
, “
Investigation of the Initial Perturbation Amplitude for the Inclined Interface Richtmyer-Meshkov Instability
,”
Phys. Scr.
,
2013
, p.
014014
.10.1088/0031-8949/2013/T155/014014
43.
Hill
,
D.
,
Pantano
,
C.
, and
Pullin
,
D.
,
2006
, “
Large-Eddy Simulation and Multiscale Modelling of a Richtmyer-Meshkov Instability With Reshock
,”
J. Fluid Mech.
,
557
, pp.
29
62
.10.1017/S0022112006009475
44.
Latini
,
M.
,
Schilling
,
O.
, and
Don
,
W. S.
,
2007
, “
Effects of Weno Flux Reconstruction Order and Spatial Resolution on Reshocked Two-Dimensional Richtmyer–Meshkov Instability
,”
J. Comput. Phys.
,
221
(
2
), pp.
805
836
.10.1016/j.jcp.2006.06.051
45.
Wilkins
,
M. L.
,
1963
, “
Calculation of Elastic-Plastic Flow
,” California University Livermore Radiation Laboratory, Report No. UCRL 7322.
46.
Kolev
,
T. V.
, and
Rieben
,
R.
,
2009
, “
A Tensor Artificial Viscosity Using a Finite Element Approach
,”
J. Comput. Phys.
,
228
(
22
), pp.
8336
8366
.10.1016/j.jcp.2009.08.010
47.
Sharp
,
R.
,
1978
, “
Hemp Advection Model
,” Lawrence Livermore Lab, Livermore, CA, Technical Report.
48.
Berger
,
M. J.
, and
Oliger
,
J.
,
1984
, “
Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations
,”
J. Comput. Phys.
,
53
(
3
), pp.
484
512
.10.1016/0021-9991(84)90073-1
49.
Berger
,
M. J.
, and
Colella
,
P.
,
1989
, “
Local Adaptive Mesh Refinement for Shock Hydrodynamics
,”
J. Comput. Phys.
,
82
(
1
), pp.
64
84
.10.1016/0021-9991(89)90035-1
50.
Morgan
,
R.
,
Aure
,
R.
,
Stockero
,
J.
,
Greenough
,
J.
,
Cabot
,
W.
,
Likhatchev
,
O.
, and
Jacobs
,
J.
,
2012
.
“On the Late-Time Growth of the 2D Richtmyer-Meshkov Instability in Shock Tube Experiments,”
J. Fluid Mech.
,
712
, pp.
354
383
.10.1017/jfm.2012.426
51.
Gilliland
,
E.
,
1934
, “
Diffusion Coefficients in Gaseous Systems
,”
Ind. Eng. Chem.
,
26
(
6
), pp.
681
685
.10.1021/ie50294a020
52.
Poling
,
B.
,
Prausnitz
,
J.
, and
O'Connell
,
J. P.
,
2001
,
The Properties of Gases and Liquids
,
5th ed.
,
McGraw-Hill
,
New York
.
53.
Cook
,
A. W.
,
2009
. “
Enthalpy Diffusion in Multicomponent Flows
,”
Phys. Fluids
,
21
, p.
055109
.10.1063/1.3139305
54.
Tomkins
,
C.
,
Kumar
,
S.
,
Orlicz
,
G.
, and
Prestridge
,
K.
,
2008
, “
An Experimental Investigation of Mixing Mechanisms in Shock-Accelerated Flow
,”
J. Fluid Mech.
,
611
, pp.
131
150
.10.1017/S0022112008002723
55.
Peng
,
G.
,
Zabusky
,
N. J.
, and
Zhang
,
S.
,
2003
, “
Vortex-Accelerated Secondary Baroclinic Vorticity Deposition and Late-Intermediate Time Dynamics of a Two-Dimensional Richtmyer–Meshkov Interface
,”
Phys. Fluids
,
15
, pp.
3730
3744
.10.1063/1.1621628
You do not currently have access to this content.