World Journal of Mechanics, 2012, 2, 152-161
doi:10.4236/wjm.2012.23018 Published Online June 2012 (http://www.SciRP.org/journal/wjm)
Evolution of Hydrodynamic Instability on Planar Jelly
Interface Driven by Explosion*
Tao Wang, Jingsong Bai, Wenbin Huang, Yang Jiang, Liyong Zou, Ping Li, Duowang Tan
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China
Received April 26, 2012; revised May 20, 2012; accepted May 30, 2012
ABSTRACT
A high precision numerical algorithm MVPPM (multi-viscous-fluid piecewise parabolic method) is proposed and ap-
plied to study the multi-viscous-fluid dynamics problems. Three planar jelly experiments with periodic cosine perturba-
tion on the initial interface have been conducted and numerically simulated by MVPPM. Good agreement between ex-
perimental and numerical results has been achieved, including the shape of jelly interface, the displacements of front
face of jelly layer, bubble top and spike head. The effects of initial conditions (including amplitude and wave length of
perturbation, thickness of jelly layer, etc.) on the evolution of the jelly interface have been numerically analyzed. It is
found that the key affecting factors are the perturbation amplitude and thickness of jelly layer. The hydrodynamic insta-
bility on double planar jelly layers driven by explosion has been investigated numerically to examine their laws of evo-
lution, and an interesting phenomenon is observed.
Keywords: MVPPM; Jelly; Hydrodynamic Instability; Explosion
1. Introduction
The hydrodynamic interfacial instability is a very impor-
tant physical phenomenon in a variety of man-made ap-
plications and natural phenomena such as inertial con-
finement fusion (ICF), high-speed combustion and as-
trophysics (i.e. supernova explosion). It can induce the
turbulent mixing in the late times and has gained much
attention for many years. According to the acting force
on an interface between two different fluids, the hydro-
dynamic interfacial instability can be classified as the
Richtmyer-Meshkov [1,2], Rayleigh-Taylor [3,4] and Kel-
vin-Helmholtz instability [5] (RMI, RTI and KHI), in
which the interface experiences an impulsive accelera-
tion (such as shock wave), a constant acceleration (gra-
vity, for example) or a shear stress.
Various experiments [6-11] have been designed to
study the interfacial instability. However, it is difficult to
generate a well-defined and well-controlled, sharp initial
interface between two fluids. One solution has been to
initially separate two fluids using a thin membrane, then
the membrane is broken into small pieces by the passing
shock wave. However, these membrane fragments can
influence the flow, and it is difficult to assess the effects
of the broken fragments on the development of the inter-
facial instability. Other experiments have attempted to
avoid the effects of membranes by implementing systems
in which the heavy gas is inserted into the test section
from a container by a jet at the upper wall of shock tube,
and flows out by an opposite center-to-center hole, the
initial interface shaped with the jet is created [12-16].
However, because the diffusion coefficients of gases are
large, this membraneless technique generates a thick dif-
fusive interface. It will cause the uncertainty of initial
conditions of interface, and they are often backward es-
timated by numerical simulations [17,18]. Another novel
technique, which is developed by VNIIEF [19], is that
the jelly interface is driven by the mixtures of C2H2 and
O2 explosion. On one hand, the jelly has a sufficient
strength allowing to fabricate the shells and layers of
complicated form in no need of any membrane and to
resist the deformation caused by gravity. On the other
hand, it also has a good transparency to observe the
hydrodynamic process of interface development easily.
LLNL had done some studying works of jelly ring inter-
face [20-22].
With the help of modern computers, numerical simula-
tion has become a very useful and powerful means to
study the interfacial instability. It allows us to examine
the data in detail far beyond the capability of experiments.
Many new numerical results have been reported [23-28].
In this paper, the hydrodynamic instability on planar jelly
interface driven by explosion is studied by experiments
and numerical simulations using the high precision nu-
*The authors thank supports from the National Natural Science Founda-
tion of China (Grant No. 11072228, 11002129).

T. WANG ET AL. 153
merical algorithm MVPPM, which is developed by com-
bining the volume of fluid (VOF) methodology and
piecewise parabolic method (PPM). Three planar jelly
experiments with different periodic cosine perturbations
on the initial interface have been conducted at the Na-
tional Key Laboratory of Shock Wave and Detonation
Physics (LSD). The effects of initial conditions (include-
ing amplitude and wave length of perturbation, thickness
of jelly layer, etc.) on the evolution of the jelly interface
have been analyzed numerically by MVPPM. Then the
hydrodynamic instability on double planar jelly layers
driven by explosion has been investigated numerically.
2. Numerical Algorithm
2.1. Governing Equations
When considering the viscosity and heat-conduction, the
governing equations for multi-viscous-fluid can be writ-
ten as follows in tensor notation:

 
0
01,2,,
j
j
ji ij
i
jij
1
j
ji
j
jj
ss
jj
u
tx
uu
up
tx xx
uE puu
q
E
tx x
YY
us
tx




ij
j
x
N










  

 



 







,p
(1)
Here, i and j represent the three directions of x, y, z re-
spectively; are the fluid density,
velocity and pressure; E is the total energy per unit mass;
N is the types of fluid,

, ,
k
u kij  
()
s
Y is the volume fraction of the
th
s
fluid and satisfies() 1
s
Y

; ij

is the Newtonian
fluid viscosity stress tensor:
2
3
j
ik
ij ij
ji k
u
uu
xx x
 
 





 







(2)
where
 is the fluid viscosity; qj is the energy flux per
unit time and space,
j
j
qTx

 ,  is the efficient
heat-conduction coefficient, T is the temperature.
The equation of state is the “Stiffen Gas” form as:

1πpe

   (3)
For gas,
 is the ratio of specific heat, and  = 0; for
liquid and elastic closed-grained material described by
impacting Hugoniot curve,
 is the fitting constant of
material,  is constant with viscous stress tensor dimen-
sion; e is the specific internal energy.
2.2. Algorithm
The physical process, as described by Equation (1), can
be decomposed into three sub-processes, i.e., the calcula-
tions of inviscid flux, viscous flux and heat flux by op-
erator splitting technique, and it is split up into two equa-
tions as follows:

 
0
0
0
01,2,,
j
j
ji
i
ji
jj
j
ss
jj
u
tx
uu
up
txx
uE pu
E
tx
YY
us
tx













 







1 N






(4)

()
0
01,2,,
ij
i
j
iij
j
jj
s
t
u
tx
u
q
E
txx
YsN
t
















 
 

1




(5)
The inviscid flux is calculated by PPM for multi-fluids
to solve Equation (4), and the PPM of two-step La-
grange-Remapping algorithm in one time step can be
divided into four steps: 1) the piecewise parabolic inter-
polation of physical quantities; 2) solving the Riemann
problems approximately; 3) marching of the Lagrange
equations; 4) remapping the physical quantities back to
the stationary Euler meshes. Then the viscous flux and
heat flux are calculated based on the computation of in-
viscid flux by using second-order spatial center differ-
ence and two-step Runge-Kutta time marching to solve
Equation (5). The detailed description of numerical algo-
rithm is referred in Ref. [29].
3. Results and Discussions
3.1. Planar Jelly Experiment and Its Numerical
Simulations
The planar jelly experiment was carried out at LSD. The
experimental equipment is illustrated in Figure 1, in
which the inner cross section is 40 mm  40 mm. The red
part is the jelly layer. The cavity (driver section with
length of LE = 75 mm) below jelly layer is filled with the
mixture of C2H2 and O2 at one atm. The gaseous mixture
detonates through discharge, and the instantaneous pres-
sure of explosive products (EP) is measured to be 18 atm,
the Mach number of shock wave after explosion is about

T. WANG ET AL. 154
Jelly Layer
Figure 1. Experimental equipment.
3.592. One solid layer (plexiglass with thickness of 3 mm)
overlays the jelly layer, which keeps the planeness of
front face of jelly layer when it is moving. The upper part
of tube opens out to the atmosphere. The process of de-
velopment of jelly layer is visualized by a high speed
photography (Photron FASTCAM-APX RS). The Sche-
matic of experimental data acquisition process is dis-
played in Figure 2, the xenon lamp is used as the illumi-
nation, the camera is located at opposite position of lamp,
the computer and camera are connected with the ignition
device by the synchronous machine, the experimental
images are actually integrated ones. The full resolution of
camera is 1024  1024 pixel arrays with 10 bits per pixel.
The frame rate can vary in the range between 50 Hz and
250,000 Hz, and it is set to be 30,000 fps in our experi-
ment. The exposure time of camera is 2 s.
The jelly consists of gelatin water solution with the
concentration 3.5%. Therefore, its initial density is about
1000 kg/m3, and the Atwood number is about 0.998. The
initial properties of jelly and explosive products are listed
in Tabl e 1 . Three periodic initial cosine perturbations are
set on the EP/jelly interface. The amplitudes and wave
lengths are:
1)
 = 0.5 mm,  = 8 mm;
2)
 = 1.0 mm,  = 8 mm;
3)
 = 1.0 mm,  = 5 mm.
The schematic of computational model is shown in
Figure 3. The grid resolution is 0.2 mm.
Because the process of GEM explosion is very transi-
tory, so it is neglected and completes momently in our si-
mulations. The jelly layer is shocked by the gaseous
mixture explosion, and the hydrodynamic interfacial in-
stability happens at the EP/jelly interface. Figure 4
shows the time evolvement of jelly interface for the per-
turbation of
 = 1.0 mm and  = 8 mm, the left and right
columns are experimental and numerical results, respec-
tively. It can be seen that the periodic initial cosine per-
turbation develops into structures shaped with bubble and
spike regularly and gradually. Numerical results agree
Lamp
Jelly Layer
Camera
Figure 2. Schematic of experimental data acquisition process.
Figure 3. Schematic of computational model.
Table 1. Initial properties of jelly and explosive produc ts.
Material
 (kg/m3)p (atm)  (Pas)   (MPa)
Jelly 1000 1.0 1.002 × 10 P–3 7.0 300
Explosive
Products 1.38 18.0 1.776 × 10 P–5 2.5 0.0
well with the experimental ones qualitatively, including
the shape of jelly interface, the positions of bubble top
and spike head. Quantitative analysis between experi-
ments and numerical simulations has been done by com-
parison of three geometric characteristic variables. These
geometric characteristic variables are the displacements
of front face of jelly layer X1, bubble top X2 and spike
head X3 relative to the initial equilibrium position of
perturbation (white line), and is displayed in Figure 5.
These experimental quantitative data of geometric char-
acteristic variables are obtained by processing digitally
the photographic images. Figure 6 shows the time histo-
ries of X1, X2 and X3 for three kinds of initial perturba-
tions. The comparison between numerical simulations
and experiments reveals that good agreements are achi-
eved except the displacement of spike head X3 at the late
times. The errors may be resulted by the inaccurate mea-
surements in experiments, because sometimes it is too
difficult to determine the interface exactly, especially at
the late times. In addition, the growth rates (slope of
curve) of displacements X1, X2 and X3 all increases with
time gradually, and the bubble grows faster.

T. WANG ET AL. 155
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 4. Time evolving of the jelly interface (  = 1.0 mm, 
= 8 mm, left column: experiments, right column: simula-
tions). (a) t = 0.0 ms; (b) t = 0.1 ms; (c) t = 0.2 ms; (d) t = 0.3
ms; (e) t = 0.4 ms; (f) t = 0.5 ms; (g) t = 0.6 ms; (h) t = 0.7 ms;
(i) t = 0.8 ms.
X
3
X
2
X
1
Figure 5. Schematic of displacements X1, X2, X3.
3.2. Numerical Analysis of the Effects of Initial
Conditions on the Evolving of Jelly Interface
In order to analyze the effects of initial conditions, in-
cluding the amplitude and wave length of perturbation,
thickness of jelly layer and width of explosion driver
section, on the evolvement of jelly interface, sixteen
models with different initial conditions have been calcu-
lated numerically by MVPPM based on the model in Sec.
3.1. The sixteen models have been divided into four
groups according to the initial perturbation and listed in
Table 2. Numerical images show that these jelly inter-
faces have a similar process of development. We define
the width of mixing zone, W, as the distance between
bubble top and spike head, i.e. W = X2 – X3. Another
quantity, S, is the displacement of front face of jelly layer
relative to its initial position. The effects of initial condi-
tions on the evolution of the jelly interface are mainly
analyzed by the comparisons of the width of mixing
zone.
Figures 7(a)-(d) give the width of mixing zone vs.
time for the models with same initial perturbation and
different thickness of jelly layer and width of explosion
driver section. Figures 7(e)-(h) give the width of mixing
zone vs. time for the models with different initial pertur-
bation and same thickness of jelly layer and width of
explosion driver section. By the comparison, the follow-
ing observations can be obtained. Firstly, the thickness of
jelly layer has a major effect on the evolution of jelly
interface, the width of mixing zone increases much faster

T. WANG ET AL. 156
(a) (b) (c)
Figure 6. Time histories of X1, X2 and X3 ((a)  = 0.5 mm,  = 8 mm; (b)  = 1.0 mm,  = 8 mm; (c)  = 1.0 mm,  = 5 mm).
Figure 7. Width of mixing zone vs. time for different models. (a)  = 0.5 mm,  = 8 mm; (b)  = 0.5 mm,  = 5 mm; (c)  = 1.0
mm,  = 8 mm; (d)  = 1.0 mm,  = 5 mm; (e) LE = 50 mm, LG = 20 mm; (f) LE = 70 mm, LG = 20 mm; (g) LE = 50 mm, LG =
10 mm; (h) LE = 70 mm, LG = 10 mm.

T. WANG ET AL. 157
Table 2. Model parameters of single jelly layer.
Serial
Number
LE
(mm)
LG
(mm)
Perturbation
(mm)
1-1 50 20
1-2 70 20
1-3 50 10
1-4 70 10
y = 0.5cos(2x/8)
2-1 50 20
2-2 70 20
2-3 50 10
2-4 70 10
y = 0.5cos(2x/5)
3-1 50 20
3-2 70 20
3-3 50 10
3-4 70 10
y = 1.0cos(2x/8)
4-1 50 20
4-2 70 20
4-3 50 10
4-4 70 10
y = 1.0cos(2x/5)
when the thickness of jelly layer is smaller. Secondly, the
width of explosion driver section has a relatively smaller
effect on the evolution of jelly interface, especially when
the thickness of jelly layer is larger. Thirdly, the ampli-
tude of initial perturbation also has a major effect on the
evolution of jelly interface, and the width of mixing zone
grows faster when the amplitude is larger. Lastly, the
wave length of initial perturbation has a less effect on the
evolution of jelly interface. Figure 8 gives the width of
mixing zone vs. the displacement of front face of jelly
layer relative to its initial position for different models. It
can be seen that the width of mixing zone changes line-
arly with the displacement of front face of jelly layer, i.e.,
the spatial growth rate of the width of mixing zone is a
constant. Therefore, the key affecting factors on the evo-
lution of jelly interface are the amplitude of initial per-
turbation and the thickness of jelly layer.
3.3. Hydrodynamic Instability on Double Planar
Jelly Layers
In this section, the hydrodynamic instability on double
planar jelly layer is numerically simulated. The objective
is to study how the double planar jelly layers evolve
Figure 8. Width of mixing zone vs. the displacement of front face of jelly layer relative to its initial position for different mod-
els. (a)  = 0.5 mm,  = 8 mm; (b)  = 0.5 mm,  = 5 mm; (c)  = 1.0 mm,  = 8 mm; (d)  = 1.0 mm,  = 5 mm.

T. WANG ET AL. 158
driven by explosion. The schematic of computational
model is shown in Figure 9. The thicknesses of jelly
layer 1 and 2 are all 20 mm, and denoted by LG1 and
LG2 respectively. The jelly layer 1 has a periodic initial
cosine perturbation on the EP/Jelly interface. The closed
region between jelly layer 1 and 2 is filled with air at one
atm. Eight models with different initial conditions have
been calculated numerically and divided into two groups
according as the jelly layer 2 has or has not periodic ini-
tial cosine perturbation. The model parameters are listed
in Table 3.
Figures 10 and 11 give the numerical evolving images
of double planar jelly layers when the jelly layer 2 has
(1-1) and has not (2-1) periodic initial cosine perturba-
tion respectively. It can be seen that the jelly layer 1
moves rightwards driven by gaseous mixture explosion,
and the jelly interface 1 developed into the structures
shaped with bubble and spike regularly and gradually.
When the jelly layer 1 moves rightwards, the jelly layer 2
holds still, the jelly interface 2 has no any development,
and the closed air is compressed. When the closed air is
compressed to a degree, it starts to rebound. On the re-
bound, an interesting phenomenon happens on the jelly
interface 1, which is that some new spikes are growing at
the bubble top in the same direction (Figures 10(f)-(i)
and Figures 11(f)-(i)). These new spikes grow much
faster than their neighbors whose growing reduces obvi-
ously, and the original bubbles are split up into two ones
symmetrically. The development of jelly interface 2 has a
great difference on the rebound of closed air, whether it
has initial perturbation. If jelly interface 2 has a periodic
initial cosine perturbation, it will conglutinate with the
jelly layer 1 at the perturbation crest, and the closed re-
gion is separated into several small regions, which are
stretched gradually (Figures 10(e)-(i)); otherwise the jelly
interface 2 has no any perturbation development, it can
not conglutinate with the jelly layer 1, and the jelly layer
2 moves rightwards driven by the compressed closed air
as a whole (Figures 11(e)-(i)). The numerical simula-
tions for other models show the same evolving laws.
Figure 12 shows the schematic of the mixing zone
width of jelly interface 1. Figure 13 shows the width of
mixing zone of jelly interface 1 vs. time for different mo-
dels. Several conclusions can be obtained. Firstly, under
the driver of gaseous mixture explosion, the width of
mixing zone of jelly interface 1 increases to an extremum
gradually, so does its growth rate (slope of curve). At the
intervals, the closed air is always compressed. After
reaching the extremum, the width of mixing zone ex-
periences a short-term negative growth, this is because
the rebound of compressed closed air constrains its
growth, then such effect of constraint weakens until dis-
appearance, and the width of mixing zone increases again.
Secondly, for the models with same initial perturbation
on jelly interface 1 and 2 (It can be treated as the ampli-
tude to be zero that jelly interface 2 has no initial
Table 3. Model parameters of double jelly layer.
Perturbation (mm)
Serial Number LE (mm) LG1 (mm) LA (mm)LG2 (mm)Jelly layer 1 Jelly layer 2
1-1 50 20
1-2 70 20
1-3 50 30
1-4 70 30
y = 0.5cos(2x/8) y = 0.5cos(2x/5)
2-1 50 20
2-2 70 20
2-3 50 30
2-4 70
20
30
20
y = 0.5cos(2x/8) None
Air
C
2
H
2
+O
2
18 atm
Jelly
layer
1
Jelly
layer
2
L
G2 L
E
40 mm
L
G1
Figure 9. Schematic of computational model of double planar jelly layers.

T. WANG ET AL. 159
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 10. Numerical time evolving images of double planar jelly layers (1-1). (a) t = 0.0 ms; (b) t = 0.2 ms; (c) t = 0.4 ms; (d) t
= 0.6 ms; (e) t = 0.8 ms; (f) t = 1.0 ms; (g) t = 1.2 ms; (h) t = 1.4 ms; (i) t = 1.6 ms.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 11. Numerical time evolving images of double planar jelly layers (2-1). (a) t = 0.0 ms; (b) t = 0.2 ms; (c) t = 0.4 ms; (d) t
= 0.6 ms; (e) t = 0.8 ms; (f) t = 1.0 ms; (g) t = 1.2 ms; (h) t = 1.4 ms; (i) t = 1.6 ms.
W
Figure. 12. Schematic of the mixing zone width of jelly in-
terface 1.
perturbation.), the width of explosion driver section al-
most can not affect the evolution of mixing zone before
the rebound of compressed closed air. But on its rebound,
the effect of width of explosion driver section enhances
gradually, the width of mixing zone of jelly interface 1
increases faster for models with the larger width of
explosion driver section. The width of closed air almost
can not influence the growth of mixing zone too before
its rebound. When the width of closed air is larger, it will

T. WANG ET AL. 160
Figure 13. Width of mixing zone of jelly interface 1 vs. time for different models. (a) y1 = 0.5cos(2x/8) & y2 = 0.5cos(2x/5);
(b) y1 = 0.5cos(2x/8) & y2 = 0; (c) LA = 20 mm; (d) LA = 30 mm.
pass through a long process of compression, and its re-
bound will lag behind. The width of mixing zone has a
greater difference on the rebound of compressed closed
air with a different size (Figures 13(a) and (b)). Thirdly,
for the models with same width of explosion driver sec
tion and closed air, the growth of mixing zone of jelly
interface 1 almost can not be influenced before the re-
bound of compressed closed air whether the jelly inter-
face 2 has initial perturbation. On the rebound, when the
closed region is greater, the growth of mixing zone of
jelly interface 1 has a larger difference whether the jelly
interface 2 has initial perturbation (Figures 13(c) and
(d)). Therefore, for the hydrodynamic instability on dou-
ble planar jelly layers driven by explosion, the key af-
fecting factors are the width of explosion driver section
and closed air, and the initial perturbation on the jelly
interface 2.
4. Conclusion
In this paper, the hydrodynamic instability on planar jelly
interface driven by explosion is studied by experiments
and numerical simulations. Three single layer of planar
jelly experiments with periodic initial cosine perturbation
conducted at LSD are numerically simulated by high
precision numerical algorithm MVPPM. There is good
agreement between experiments and numerics. Then se-
veral single jelly layer of models are numerically simu-
lated to analyze the effects of initial conditions (include-
ing amplitude and wave length of perturbation, thickness
of jelly layer and width of explosion driver section) on
the evolution of jelly interface. The key affecting factors
are the perturbation amplitude and thickness of the jelly
layer. The hydrodynamic instability on double planar
jelly layers driven by explosion has been investigated
numerically, in which the evolving law is greatly diffe-
rent from the one of single jelly layer, and the affecting
factors are more.
REFERENCES
[1] R. D. Richtmyer, “Taylor Instability in Shock Accelera-
tion of Compressible Fluids,” Communications on Pure
and Applied Mathematics, Vol. 13, No. 2, 1960, pp. 297-
319. doi:10.1002/cpa.3160130207
[2] E. E. Meshkov, “Instability of the Interface of Two Gases
Accelerated by a Shock Wave,” Soviet Fluid Dynamics,
Vol. 4, No. 5, 1969, pp. 101-104.
doi:10.1007/BF01015969
[3] G. I. Taylor, “The Instability of Liquid Surfaces When

T. WANG ET AL. 161
Accelerated in a Direction Perpendicular to Their Planes.
I,” Proceedings of the Royal Society A, Vol. 201, No.
1065, 1950, pp. 192-196. doi:10.1098/rspa.1950.0052
[4] D. H. Sharp, “An Overview of Rayleigh-Taylor Instabil-
ity,” Physica D, Vol. 12, No. 1-3, 1984, pp. 3-18.
doi:10.1016/0167-2789(84)90510-4
[5] S. Chandrasekhar, “Hydrodynamic and Hydromagnetic
Stability,” Oxford University Press, London, 1961.
[6] G. Dimonte and M. B. Schneider, “Turbulent Rayleigh-
Taylor Instability Experiments with Variable Accelera-
tion,” Physical Review E, Vol. 54, No. 4. 1996, pp. 3740-
3743. doi:10.1103/PhysRevE.54.3740
[7] Y. A. Kucherenko1, A. P. Pylaev, V. D. Murzakov, et al.,
“Experimental Study into the Asymptotic Stage of the
Separation of the Turbulized Mixtures in Gravitationally
Stable Mode,” In: R. Young, J. Glimm and B. Boston, Eds.,
Proceedings of the 5th International Workshop on Com-
pressible Turbulent Mixing, Stony Brook University Press,
New York, 1996.
[8] J. W. Jacobs and J. M. Sheeley, “Experimental Study of
Incompressible Richtmyer-Meshkov Instability,” Physics
of Fluids, Vol. 8, No. 2, 1996, pp. 405-415.
doi:10.1063/1.868794
[9] E. E. Meshkov, N. V. Nevmerzhitsky, V. A. Pavlovskii,
et al., “Jelly Technique Applications in Evolution Study
of Hydrodynamic Instabilities on Unstable Plane and Cy-
lindrical Surfaces,” In: R. Young, J. Glimm and B. Bos-
ton, Eds., Proceedings of the 5th International Workshop
on Compressible Turbulent Mixing, Stony Brook Univer-
sity Press, New York, 1996.
[10] L. Houas, G. Jourdan, L. Schwaederlé, et al., “A New Large
Cross-Section Shock Tube for Studies of Turbulent Mix-
ing Induced by Interfacial Hydrodynamic Instability,” Shock
Waves, Vol. 13, No. 5, 2003, pp. 431-434.
doi:10.1007/s00193-002-0173-y
[11] S. H. R. Hosseini and K. Takayama, “Experimental Study
of Richtmyer-Meshkov Instability Induced by Cylindrical
Shock Waves,” Physics of Fluids, Vol. 17, No. 8, 2005, p.
084101. doi:10.1063/1.1964916
[12] P. M. Rightley, P. Vorobieff, R. Martin, et al., “Experi-
mental Observations of the Mixing Transition in a Shock-
Accelerated Gas Curtain,” Physics of Fluids, Vol. 11, No.
1, 1999, pp. 186-200. doi:10.1063/1.869911
[13] B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, et al., “Si-
multaneous Particle-Image Velocimetry-Planar Laser-In-
duced Fluorescence Measurements of Richtmyer-Meshkov
instability Growth in a Gas Curtain with and without Re-
shock,” Physics of Fluids, Vol. 20, No. 12, 2008, p. 124103.
doi:10.1063/1.3041705
[14] J. W. Jacobs, “The Dynamics of Shock Accelerated Light
and Heavy Gas Cylinders,” Physics of Fluids, Vol. 5, No.
9, 1993, pp. 2239-2247. doi:10.1063/1.858562
[15] C. D. Tomkins, K. P. Prestridge, P. M. Rightley, et al., “A
Quantitative Study of the Interaction of Two Richtmyer-
Meshkov Unstable Gas Cylinders,” Physics of Fluids, Vol.
15, No. 4, 2003, pp. 986-1004. doi:10.1063/1.1555802
[16] S. Kumar, P. Vorobieff, G. Orlicz, et al., “Complex Flow
Morphologies in shock-Accelerated Gaseous Flows,” Phy-
sica D, Vol. 235, No. 1-2, 2007, pp. 21-28.
doi:10.1016/j.physd.2007.04.023
[17] S. Gupta, S. Zhang and N. J. Zabusky, “Shock Interaction
with a Heavy Gas Cylinder: Emergence of Vortex Bilay-
ers and Vortex- Accelerated Baroclinic Circulation Gen-
eration,” Laser and Particle Beams, Vol. 24, No. 3, 2003,
pp. 443-448.
[18] S. Zhang, N. J. Zabusky, G. Z. Peng, et al., “Shock gases
Cylinder Interactions: Dynamically Validated Initial Con-
ditions Provide Excellent Agreement between Experiments
and Numerical Simulations to Late-Intermediate Time,”
Physics of Fluids, Vol. 16, No. 5, 2004, pp. 1203-1216.
doi:10.1063/1.1651483
[19] S. Andronov and E. E. Meshkov, “Computational and Ex-
perimental Studies of Hydro-Dynamic Instabilities and
Turbulent Mixing,” Los Alamos National Laboratory, Los
Alamos, 1995.
[20] B. Goodwin an S. Weir, “Rayleigh-Taylor Instability Ex-
periments in a Cylindrically Convergent Geometry,” Los
Alamos National Laboratory, Los Alamos, 1996.
[21] K. O. Mikaelian, “Rayleigh-Taylor and Richtmyer-Meshkov
Instabilities and Mixing in Stratified Spherical Shells,”
Physical Review A, Vol. 42, No. 6, 1990, pp. 3400-3420.
doi:10.1103/PhysRevA.42.3400
[22] K. O. Mikaelian, “Rayleigh-Taylor and Richtmyer-Meshkov
Instabilities and Mixing in Stratified Cylindrical Shells,”
Physics of Fluids, Vol. 17, No. 9, 2005, pp. 094105.
doi:10.1063/1.2046712
[23] N. C. Hearn, T. Plewa, R. P. Drake, et al., “Flash Code
Simulation of Rayleigh-Taylor and Richtmyer-Meshkov
Instabilitites in Laser-Driven Experiments,” Astrophysics
and Space Science, Vol. 307, No. 1-3, 2007, pp. 227-231.
doi:10.1007/s10509-006-9226-5
[24] H. Lee, H. Jin, Y. Yu, et al., “On Validation of Turbulent
Mixing Simulations for Rayleigh-Taylor Instability,” Phy-
sics of Fluids, Vol. 20, No. 1, 2008, p. 012102.
doi:10.1063/1.2832775
[25] A. Marocchino, S. Atzeni and A. Schiavi, “Numerical Stu-
dy of the Ablative Richtmyer-Meshkov Instability of La-
ser-Irradiated Deuterium and Deuterium-Tritium Targets,”
Physics of Plasmas, Vol. 17, No. 11, 2010, p. 112703.
doi:10.1063/1.3505112
[26] L. Biferale, F. Mantovani and M. Sbragaglia, “High Re-
solution Numerical Study of Rayleigh-Taylor Turbulence
Using a Thermal Lattice Boltzmann Scheme,” Physics of
Fluids, Vol. 22, No. 11, 2010, p. 115112.
doi:10.1063/1.3517295
[27] L. F. Wang, W. H. Ye, W. S. Don, et al., “Formation of
Large-Scale Structures in Ablative Kelvin-Helmholtz In-
stability,” Physics of Plasmas, Vol. 17, No. 12, 2010, p.
122308. doi:10.1063/1.3524550
[28] M. A. Ullah, W. B. Gao and D. K. Mao, “Numerical Simu-
lations of Richtmyer-Meshkov Instabilities Using Conser-
vative Front-Tracking Method,” Applied Mathematics and
Mechanics, Vol. 32, No. 1, 2011, pp. 119-132.
doi:10.1007/s10483-011-1399-x
[29] T. Wang, J. S. Bai, P. Li, et al., “The Numerical Study of
Shock-Induced Hydrodynamic Instability and Mixing,”
Chinese Physics B, Vol. 18, No. 3, 2009, pp. 1127-1135.
doi:10.1088/1674-1056/18/3/048