A comparative investigation of the hydrodynamic instability development on the shock-driven square and rectangular light gas bubbles is carried out numerically. In contrast to the square bubble, both horizontally and vertically aligned rectangular bubbles with different aspect ratios are taken into consideration, highlighting the impacts of aspect ratios on interface morphology, vorticity production, and bubble deformation. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. The results show that the aspect ratio of rectangular bubbles has a considerable impact on the evolution of interface morphology in comparison with a square bubble. In horizontal-aligned rectangular bubbles, two secondary vortex rings connected to the primary vortex ring are produced by raising the aspect ratio. While in vertical-aligned rectangular bubbles, two re-entrant jets are seen close to the top and bottom boundaries of the upstream interface with increasing aspect ratio. The baroclinic vorticity generation affects the deformation of the bubble interface and accelerates the turbulent mixing. Notably, the complexity of the vorticity field keeps growing as the aspect ratio does in horizontal-aligned rectangular bubbles, and the trends are reversed in the vertical-aligned rectangular bubbles. Further, these aspect ratio effects also lead to the different mechanisms of the interface characteristics, including the upstream and downstream distances, width, and height. Finally, the temporal evolution of spatially integrated fields, including average vorticity, vorticity production terms, and enstrophy are analyzed in depth to investigate the impact of aspect ratio on the flow structure.

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 the interface of two gases accelerated by a shock wave
,”
Fluid Dyn.
4
,
101
(
1972
).
3.
H.
von Helmholtz
,
Über discontinuirliche Flüssigkeits-Bewegungen
(
Akademie der Wissenschaften zu
,
Berlin
,
1868
).
4.
L.
Kelvin
, “
On the motion of free solids through a liquid
,”
Philos. Mag.
42
,
362
377
(
1871
).
5.
L.
Rayleigh
, “
Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density
,”
Proc. London Math. Soc.
s1-14
,
170
177
(
1882
).
6.
G.
Taylor
, “
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
,”
Proc. R. Soc. London, Ser. A
201
,
192
196
(
1950
).
7.
W. D.
Arnett
,
J. N.
Bahcall
,
R. P.
Kirshner
, and
S. E.
Woosley
, “
Supernova 1987A
,”
Annu. Rev. Astron. Astrophys.
2
,
629
700
(
1989
).
8.
J.
Lindl
,
O.
Landen
,
J.
Edwards
,
E.
Moses
, and
N.
Team
, “
Review of the National Ignition Campaign 2009–2012
,”
Phys. Plasmas
21
,
020501
(
2014
).
9.
J.
Yang
,
T.
Kubota
, and
E. E.
Zukoski
, “
Applications of shock-induced mixing to supersonic combustion
,”
AIAA J.
31
,
854
862
(
1993
).
10.
W. G.
Zeng
,
J. H.
Pan
,
Y. T.
Sun
, and
Y. X.
Ren
, “
Turbulent mixing and energy transfer of reshocked heavy gas curtain
,”
Phys. Fluids
30
,
064106
(
2018
).
11.
M.
Brouillette
, “
The Richtmyer–Meshkov instability
,”
Annu. Rev. Fluid Mech.
34
,
445
(
2002
).
12.
Y.
Zhou
, “
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I
,”
Phys. Rep.
720–722
,
1
136
(
2017
).
13.
Y.
Zhou
, “
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II
,”
Phys. Rep.
723–725
,
1
160
(
2017
).
14.
Y.
Zhou
 et al, “
Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities
,”
Phys. Plasmas
26
,
080901
(
2019
).
15.
Y.
Zhou
,
R. J.
Williams
,
P.
Ramaprabhu
,
M.
Groom
,
B.
Thornber
,
A.
Hillier
,
W.
Mostert
,
B.
Rollin
,
S.
Balachandar
,
P. D.
Powell
,
A.
Mahalov
, and
N.
Attal
, “
Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales
,”
Physica D
423
,
132838
(
2021
).
16.
G. I.
Bell
, “
Taylor instability on cylinders and spheres in the small amplitude approximation
,” Technical Report No. LA-1321 (LANL,
1951
).
17.
M. S.
Plesset
, “
On the stability of fluid flows with spherical symmetry
,”
J. Appl. Phys.
25
,
96
(
1954
).
18.
J. R.
Fincke
,
N. E.
Lanier
,
S. H.
Batha
,
R. M.
Hueckstaedt
,
G. R.
Magelssen
,
S. D.
Rothman
,
K. W.
Parker
, and
C. J.
Horsfield
, “
Postponement of saturation of the Richtmyer–Meshkov instability in a convergent geometry
,”
Phys. Rev. Lett.
93
,
115003
(
2004
).
19.
M.
Lombardini
,
D. I.
Pullin
, and
D. I.
Meiron
, “
Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth
,”
J. Fluid Mech.
748
,
85
112
(
2014
).
20.
J. W.
Jacobs
,
D. L.
Klein
,
D. G.
Jenkins
, and
R. F.
Benjamin
, “
Instability growth patterns of a shock-accelerated thin fluid layer
,”
Phys. Rev. Lett.
70
,
583
(
1993
).
21.
J. W.
Jacobs
,
D. G.
Jenkins
,
D. L.
Klein
, and
R. F.
Benjamin
, “
Nonlinear growth of the shock-accelerated instability of a thin fluid layer
,”
J. Fluid Mech.
295
,
23
42
(
1995
).
22.
M. T.
Henry de Frahan
,
P.
Movahed
, and
E.
Johnsen
, “
Numerical simulations of a shock interacting with successive interfaces using the discontinuous Galerkin method: The multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities
,”
Shock Waves
25
,
329
345
(
2015
).
23.
Y.
Liang
,
L.
Liu
,
Z.
Zhai
,
T.
Si
, and
C.-Y.
Wen
, “
Evolution of shock-accelerated heavy gas layer
,”
J. Fluid Mech.
886
,
A7
(
2020
).
24.
Y.
Liang
and
X.
Luo
, “
On shock-induced heavy-fluid-layer evolution
,”
J. Fluid Mech.
920
,
A13
(
2021
).
25.
Y.
Liang
and
X.
Luo
, “
Shock-induced dual-layer evolution
,”
J. Fluid Mech.
929
,
R3
(
2021
).
26.
Y.
Liang
and
X.
Luo
, “
On shock-induced evolution of a gas layer with two fast/slow interfaces
,”
J. Fluid Mech.
939
,
A16
(
2022
).
27.
Y.
Liang
and
X.
Luo
, “
On shock-induced light-fluid-layer evolution
,”
J. Fluid Mech.
933
,
A10
(
2022
).
28.
Y.
Liang
, “
The phase effect on the Richtmyer–Meshkov instability of a fluid layer
,”
Phys. Fluids
34
,
034106
(
2022
).
29.
G. H.
Markstein
, “
A shock-tube study of flame front-pressure wave interaction
,” in
6th International Symposium on Combustion
(
Elsevier
,
1957
), Vol.
6
, p.
387
.
30.
G.
Rudinger
and
L. M.
Somers
, “
Behaviour of small regions of different gases carried in accelerated gas flows
,”
J. Fluid Mech.
7
,
161
176
(
1960
).
31.
J. F.
Haas
and
B.
Sturtevant
, “
Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities
,”
J. Fluid Mech.
181
,
41
(
1987
).
32.
J. W.
Jacobs
, “
Shock-induced mixing of a light-gas cylinder
,”
J. Fluid Mech.
234
,
629
(
1992
).
33.
J. W.
Jacobs
, “
The dynamics of shock accelerated light and heavy gas cylinders
,”
Phys. Fluids A
5
,
2239
(
1993
).
34.
G.
Layes
,
G.
Jourdan
, and
L.
Houas
, “
Distortion of a spherical gaseous interface accelerated by a plane shock wave
,”
Phys. Rev. Lett.
91
,
174502
(
2003
).
35.
L.
Guillaume
,
J.
Georges
, and
H.
Lazhar
, “
Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity
,”
Phys. Fluids
17
(
2
),
028103
(
2005
).
36.
S. H. R.
Hosseini
and
K.
Takayama
, “
Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves
,”
Phys. Fluids
17
,
084101
(
2005
).
37.
D.
Ranjan
,
J. H. J.
Niederhaus
,
J. G.
Oakley
,
M. H.
Anderson
,
R.
Bonazza
, and
J. A.
Greenough
, “
Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations
,”
Phys. Fluids
20
,
036101
(
2008
).
38.
Z.
Zhai
,
T.
Si
,
X.
Luo
, and
J.
Yang
, “
On the evolution of spherical gas interfaces accelerated by a planar shock wave
,”
Phys. Fluids
23
(
8
),
084104
(
2011
).
39.
T.
Si
,
Z.
Zhai
, and
X.
Luo
, “
Experimental study of Richtmyer–Meshkov instability in a cylindrical converging shock tube
,”
Phys. Fluids
32
,
343
351
(
2014
).
40.
J.
Ding
,
T.
Si
,
M.
Chen
,
Z.
Zhai
,
X.
Lu
, and
X.
Luo
, “
On the interaction of a planar shock with a three-dimensional light gas cylinder
,”
J. Fluid Mech.
828
,
289
317
(
2017
).
41.
J. J.
Quirk
and
S.
Karni
, “
On the dynamics of a shock-bubble interaction
,”
J. Fluid Mech.
318
,
129
(
1996
).
42.
A.
Bagabir
and
D.
Drikakis
, “
Mach number effects on shock-bubble interaction
,”
Shock Waves
11
(
3
),
209
(
2001
).
43.
J.
Giordano
and
Y.
Burtschell
, “
Richtmyer–Meshkov instability induced by shock-bubble interaction: Numerical and analytical studies with experimental validation
,”
Phys. Fluids
18
(
3
),
036102
(
2006
).
44.
J. H. J.
Niederhaus
,
J. A.
Greenough
,
J. G.
Oakley
,
D.
Ranjan
,
M. H.
Anderson
, and
R. A.
Bonazza
, “
A computational parameter study for the three-dimensional shock-bubble interaction
,”
J. Fluid Mech.
594
,
85
(
2008
).
45.
S. K.
Shankar
,
S.
Kawai
, and
S. K.
Lele
, “
Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder
,”
Phys. Fluids
23
,
024102
(
2011
).
46.
B.
Rybakin
and
V.
Goryachev
, “
The supersonic shock wave interaction with low-density gas bubble
,”
Acta Astronaut.
94
,
749
753
(
2014
).
47.
Z.
Wang
,
B.
Yu
,
H.
Chen
,
B.
Zhang
, and
H.
Liu
, “
Scaling vortex breakdown mechanism based on viscous effect in shock cylindrical bubble interaction
,”
Phys. Fluids
30
,
126103
(
2018
).
48.
A.
Kundu
, “
Numerical simulation of a shock–helium bubble interaction
,”
Shock Waves
31
,
19
30
(
2021
).
49.
S.
Singh
and
M.
Battiato
, “
Behavior of a shock-accelerated heavy cylindrical bubble under nonequilibrium conditions of diatomic and polyatomic gases
,”
Phys. Rev. Fluids
6
,
044001
(
2021
).
50.
S.
Singh
,
M.
Battiato
, and
R. S.
Myong
, “
Impact of the bulk viscosity on flow morphology of shock-bubble interaction in diatomic and polyatomic gases
,”
Phys. Fluids
33
,
066103
(
2021
).
51.
J. M.
Picone
and
J. P.
Boris
, “
Vorticity generation by shock propagation through bubbles in a gas
,”
J. Fluid Mech.
189
,
23
51
(
1988
).
52.
J.
Yang
,
T.
Kubota
, and
E. E.
Zukoski
, “
A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity
,”
J. Fluid Mech.
258
,
217
244
(
1994
).
53.
R.
Samtaney
and
N. J.
Zabusky
, “
On shock polar analysis and analytical expressions for vorticity deposition in shock-accelerated density-stratified interfaces
,”
Phys. Fluids A
5
(
6
),
1285
1287
(
1993
).
54.
R.
Samtaney
and
N. J.
Zabusky
, “
Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: Models and scaling laws
,”
J. Fluid Mech.
269
,
45
78
(
1994
).
55.
D.
Li
,
G.
Wang
, and
B.
Guan
, “
On the circulation prediction of shock-accelerated elliptical heavy gas cylinder
,”
Phys. Fluids
31
(
5
),
056104
(
2019
).
56.
J.
Ray
,
R.
Samtaney
, and
N. J.
Zabusky
, “
Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times
,”
Phys. Fluids
12
,
707
716
(
2000
).
57.
J.
Bai
,
L.
Zou
,
T.
Wang
,
K.
Liu
,
W.
Huang
,
J.
Liu
,
P.
Li
,
D.
Tan
, and
C.
Liu
, “
Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders
,”
Phys. Rev. E
82
,
056318
(
2010
).
58.
P. Y.
Georgievskiy
,
V. A.
Levin
, and
O. G.
Sutyrin
, “
Interaction of a shock with elliptical gas bubbles
,”
Shock Waves
25
,
357
369
(
2015
).
59.
L.
Zou
,
S.
Liao
,
C.
Liu
,
Y.
Wang
, and
Z.
Zhai
, “
Aspect ratio effect on shock-accelerated elliptic gas cylinders
,”
Phys. Fluids
28
,
036101
(
2016
).
60.
J.
Chen
,
F.
Qu
,
X.
Wu
,
Z.
Wang
, and
J.
Bai
, “
Numerical study of interactions between shock waves and a circular or elliptic bubble in air medium
,”
Phys. Fluids
33
,
043301
(
2021
).
61.
C.
Tomkins
,
K.
Prestridge
,
P.
Rightley
,
P.
Vorobieff
, and
R.
Benjamin
, “
Flow morphologies of two shock-accelerated unstable gas cylinders
,”
J. Visualization
5
,
273
283
(
2002
).
62.
C.
Tomkins
,
K.
Prestridge
,
P.
Rightley
,
M.
Marr-Lyon
,
P.
Vorobieff
, and
R.
Benjamin
, “
A quantitative study of the interaction of two Richtmyer–Meshkov-unstable gas cylinders
,”
Phys. Fluids
15
,
986
1004
(
2003
).
63.
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
).
64.
Z.
Zhai
,
J.
Ou
, and
J.
Ding
, “
Coupling effect on shocked double-gas cylinder evolution
,”
Phys. Fluids
31
,
096104
(
2019
).
65.
K. R.
Bates
,
N.
Nikiforakis
, and
D.
Holder
, “
Richtmyer-Meshkov instability induced by the interaction of a shock wave with a rectangular block of
SF6,”
Phys. Fluids
19
,
036101
(
2007
).
66.
Z.
Zhai
,
M.
Wang
,
T.
Si
, and
X.
Luo
, “
On the interaction of a planar shock with a light polygonal interface
,”
J. Fluid Mech.
757
,
800
816
(
2014
).
67.
X.
Luo
,
M.
Wang
,
T.
Si
, and
Z.
Zhai
, “
On the interaction of a planar shock with an SF6 polygon
,”
J. Fluid Mech.
773
,
366
394
(
2015
).
68.
D.
Igra
and
O.
Igra
, “
Numerical investigation of the interaction between a planar shock wave with square and triangular bubbles containing different gases
,”
Phys. Fluids
30
,
056104
(
2018
).
69.
D.
Igra
and
O.
Igra
, “
Shock wave interaction with a polygonal bubble containing two different gases, a numerical investigation
,”
J. Fluid Mech.
889
,
1
20
(
2020
).
70.
S.
Singh
, “
Role of Atwood number on flow morphology of a planar shock-accelerated square bubble: A numerical study
,”
Phys. Fluids
32
,
126112
(
2020
).
71.
S.
Singh
, “
Contribution of Mach number to the evolution of the Richtmyer–Meshkov instability induced by a shock-accelerated square light bubble
,”
Phys. Rev. Fluids
6
,
104001
(
2021
).
72.
S.
Singh
, “
Numerical investigation of thermal non-equilibrium effects of diatomic and polyatomic gases on the shock-accelerated square light bubble using a mixed-type modal discontinuous Galerkin method
,”
Int. J. Heat Mass Transfer
179
,
121708
(
2021
).
73.
S.
Singh
and
M.
Battiato
, “
Numerical simulations of Richtmyer–Meshkov instability of SF6 square bubble in diatomic and polyatomic gases
,”
Comput. Fluids
242
,
105502
(
2022
).
74.
J. R.
Lindner
, “
Microbubbles in medical imaging: Current applications and future directions
,”
Nat. Rev. Drug Discovery
3
,
527
533
(
2004
).
75.
G.
Sinibaldi
,
A.
Occhicone
,
P. F.
Alves
,
D.
Caprini
,
L.
Marino
,
F.
Michelotti
, and
C. M.
Casciola
, “
Laser induced cavitation: Plasma generation and breakdown shockwave
,”
Phys. Fluids
31
,
103302
(
2019
).
76.
F.
Reuter
and
R.
Mettin
, “
Mechanisms of single bubble cleaning
,”
Ultrason. Sonochem.
29
,
550
562
(
2016
).
77.
N.
Qiu
,
W.
Zhou
,
B.
Che
,
D.
Wu
,
L.
Wang
, and
H.
Zhu
, “
Effects of microvortex generators on cavitation erosion by changing periodic shedding into new structures
,”
Phys. Fluids
32
,
104108
(
2020
).
78.
L. P.
Raj
,
S.
Singh
,
A.
Karchani
, and
R. S.
Myong
, “
A super-parallel mixed explicit discontinuous Galerkin method for the second-order Boltzmann-based constitutive models of rarefied and microscale gases
,”
Comput. Fluids.
157
,
146
163
(
2017
).
79.
S.
Singh
,
A.
Karchani
, and
R. S.
Myong
, “
Non-equilibrium effects of diatomic and polyatomic gases on the shock-vortex interaction based on the second-order constitutive model of the Boltzmann-Curtiss equation
,”
Phys. Fluids
30
,
016109
(
2018
).
80.
S.
Singh
and
M.
Battiato
, “
Effect of strong electric fields on material responses: The Bloch oscillation resonance in high field conductivities
,”
Materials
13
,
1070
(
2020
).
81.
S.
Singh
and
M.
Battiato
, “
Strongly out-of-equilibrium simulations for electron Boltzmann transport equation using modal discontinuous Galerkin approach
,”
Int. J. Appl. Comput. Math.
6
,
133
(
2020
).
82.
S.
Singh
and
M.
Battiato
, “
An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions
,”
Comput. Fluids
224
,
104972
(
2021
).
83.
S.
Singh
,
M.
Battiato
, and
V.
Kumar
, “
Spatiotemporal pattern formation in nonlinear coupled reaction-diffusion systems with a mixed-type modal discontinuous Galerkin approach
,” arXiv:2205.10755 (
2022
).
84.
T.
Chourushi
,
S.
Singh
,
V. A.
Sreekala
, and
R. S.
Myong
, “
Computational study of hypersonic rarefied gas flow over re-entry vehicles using the second-order Boltzmann-Curtiss constitutive model
,”
Int. J. Comput. Fluid Dyn.
35
,
566
593
(
2021
).
85.
S.
Singh
,
A.
Karchani
,
T.
Chourushi
, and
R. S.
Myong
, “
A three-dimensional modal discontinuous Galerkin method for the second-order Boltzmann-Curtiss-based constitutive model of rarefied and microscale gas flows
,”
J. Comput. Phys.
457
,
111052
(
2022
).
86.
E.
Johnsen
and
T.
Colonius
, “
Implementation of WENO schemes in compressible multicomponent flow problems
,”
J. Comput. Phys.
219
,
715
732
(
2006
).
87.
S.
Singh
, “
Development of a 3D discontinuous Galerkin method for the second-order Boltzmann-Curtiss based hydrodynamic models of diatomic and polyatomic gases
,” Ph.D. thesis (
Gyeongsang National University
,
South Korea
,
2018
).
88.
S.
Gottlieb
and
C.-W.
Shu
, “
Total variation diminishing Runge-Kutta schemes
,”
Math. Comput.
67
,
73
85
(
1998
).
89.
L.
Krivodonova
, “
Limiters for high-order discontinuous Galerkin methods
,”
J. Comput. Phys.
226
,
879
896
(
2007
).
90.
R.
Abgrall
and
S.
Karni
, “
Computations of compressible multifluid
,”
J. Comput. Phys.
169
,
594
623
(
2001
).
91.
A. M.
Abd-El-Fattah
and
L. F.
Henderson
, “
Shock waves at a slow-fast gas interface
,”
J. Fluid Mech.
89
,
79
95
(
1978
).
92.
D. H.
Edwards
,
P.
Fearnley
, and
M. A.
Nettleton
, “
Shock diffraction in channels with 90 bends
,”
J. Fluid Mech.
132
,
257
270
(
1983
).
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