Richtmyer–Meshkov instability (RMI) occurs when a shock wave impulsively accelerates a perturbed density interface between different fluids. The present work investigates the suppression of RMI of double interfaces in terms of linear analysis in cylindrical geometry. An exponential increase/decrease in a growth rate is related to the Rayleigh–Taylor instability that occurs without a magnetic field as the lighter fluid penetrates the heavier one. The research program of inertial confinement fusion is one of the advanced applications where fluid mixing is the main mechanize of producing energy. The investigations represent the effects of different Atwood numbers or magnetic strengths on the suppression of the instabilities. Three different cases are considered with the hydrodynamics and magnetohydrodynamics (MHD). In the MHD case, the instability's growth rate reduces proportion to the Atwood ratios or the strength of the magnetic field. Two waves are interfering and running parallel and anti-parallel to the interfaces and transport the generated vorticity at the interfaces, causing the perturbed interfaces' growth rate to oscillate in time, which is the essential suppression mechanism.

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
,”
Pure Appl. Math.
4
,
101
104
(
1969
).
3.
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
).
4.
J.
Kane
,
R.
Drake
, and
B.
Remington
, “
An evaluation of the Richtmyer-Meshkov instability in supernova remnant formation
,”
Astrophys. J.
511
,
335
(
1999
).
5.
Y.
Kuramitsu
,
Y.
Sakawa
,
T.
Morita
,
S.
Dono
,
H.
Aoki
,
H.
Tanji
,
C. D.
Gregory
,
J. N.
Waugh
,
B.
Loupias
,
M.
Koenig
 et al, “
Formation of density inhomogeneity in laser produced plasmas for a test bed of magnetic field amplification in supernova remnants
,”
Astrophys. Space Sci.
336
,
269
272
(
2011
).
6.
J.
Yang
,
T.
Kubota
, and
E. E.
Zukoski
, “
Applications of shock-induced mixing to supersonic combustion
,”
AIAA J.
31
,
854
862
(
1993
).
7.
T. H.
Johnson
, “
Inertial confinement fusion: Review and perspective
,”
Proc. IEEE
72
,
548
594
(
1984
).
8.
R.
Betti
and
O. A.
Hurricane
, “
Inertial-confinement fusion with lasers
,”
Nat. Phys.
12
,
435
448
(
2016
).
9.
J.
Lindl
,
O.
Landen
,
J.
Edwards
,
E.
Moses
,
N.
Team
 et al, “
Review of the national ignition campaign 2009–2012
,”
Phys. Plasmas
21
,
020501
(
2014
).
10.
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
).
11.
V.
Wheatley
,
R.
Samtaney
, and
D. I.
Pullin
, “
The Richtmyer-Meshkov instability in magnetohydrodynamics
,”
Phys. Fluids
21
,
082102
(
2009
).
12.
K. O.
Mikaelian
, “
Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells
,”
Phys. Fluids
17
,
094105
(
2005
).
13.
K. O.
Mikaelian
, “
Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells
,”
Phys. Rev. A
42
,
3400
(
1990
).
14.
A.
Bakhsh
,
S.
Gao
,
R.
Samtaney
, and
V.
Wheatley
, “
Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics
,”
Phys. Fluids
28
,
034106
(
2016
).
15.
A.
Bakhsh
and
R.
Samtaney
, “
Linear analysis of converging Richtmyer-Meshkov instability in the presence of an azimuthal magnetic field
,”
J. Fluids Eng.
140
,
050901
(
2018
).
16.
H.-H.
Zhang
,
C.
Zheng
,
N.
Aubry
,
W.-T.
Wu
, and
Z.-H.
Chen
, “
Numerical analysis of Richtmyer–Meshkov instability of circular density interface in presence of transverse magnetic field
,”
Phys. Fluids
32
,
116104
(
2020
).
17.
V.
Wheatley
,
D. I.
Pullin
, and
R.
Samtaney
, “
Stability of an impulsively accelerated density interface in magnetohydrodynamics
,”
Phys. Rev. Lett.
95
,
125002
(
2005
).
18.
A.
Bakhsh
and
R.
Samtaney
, “
Incompressible models of magnetohydrodynamic Richtmyer-Meshkov instability in cylindrical geometry
,”
Phys. Rev. Fluids
4
,
063906
(
2019
).
19.
W.
Mostert
,
V.
Wheatley
,
R.
Samtaney
, and
D. I.
Pullin
, “
Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability
,”
Phys. Fluids
27
,
104102
(
2015
).
20.
W.
Mostert
,
V.
Wheatley
,
R.
Samtaney
, and
D. I.
Pullin
, “
Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics
,”
Phys. Fluids
26
,
126102
(
2014
).
21.
R.
Samtaney
, “
A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics
,”
J. Comput. Phys.
228
,
6773
6783
(
2009
).
22.
Y.
Li
,
R.
Samtaney
, and
V.
Wheatley
, “
The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics
,”
Matter Radiat. Extremes
3
,
207
218
(
2018
).
23.
D.
Pullin
,
W.
Mostert
,
V.
Wheatley
, and
R.
Samtaney
, “
Converging cylindrical shocks in ideal magnetohydrodynamics
,”
Phys. Fluids
26
,
097103
(
2014
).
24.
R.
Samtaney
, “
Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field
,”
Phys. Fluids
15
,
L53
L56
(
2003
).
25.
V.
Wheatley
,
D. I.
Pullin
, and
R.
Samtaney
, “
Regular shock refraction at an oblique planar density interface in magnetohydrodynamics
,”
J. Fluid Mech.
522
,
179
214
(
2005
).
26.
V.
Wheatley
,
R.
Samtaney
,
D. I.
Pullin
, and
R. M.
Gehre
, “
The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics
,”
Phys. Fluids
26
,
016102
(
2014
).
27.
Y.
Yang
,
Q.
Zhang
, and
D. H.
Sharp
, “
Small amplitude theory of Richtmyer–Meshkov instability
,”
Phys. Fluids
6
,
1856
1873
(
1994
).
28.
C.
Weber
,
N.
Haehn
,
J.
Oakley
,
M.
Anderson
, and
R.
Bonazza
, “
Richtmyer–Meshkov instability on a low Atwood number interface after reshock
,”
Shock Waves
22
,
317
325
(
2012
).
You do not currently have access to this content.