We investigate the linear stability of both positive and negative Atwood ratio interfaces accelerated either by a fast magnetosonic or hydrodynamic shock in cylindrical geometry. For the magnetohydrodynamic (MHD) case, we examine the role of an initial seed azimuthal magnetic field on the growth rate of the perturbation. In the absence of a magnetic field, the Richtmyer–Meshkov growth is followed by an exponentially increasing growth associated with the Rayleigh–Taylor instability (RTI). In the MHD case, the growth rate of the instability reduces in proportion to the strength of the applied magnetic field. The suppression mechanism is associated with the interference of two waves running parallel and antiparallel to the interface that transport vorticity and cause the growth rate to oscillate in time with nearly a zero mean value.

References

References
1.
Richtmyer
,
R. D.
,
1960
, “
Taylor Instability in Shock Acceleration of Compressible Fluids
,”
Commun. Pure Appl. Math.
,
13
(
2
), pp.
297
319
.
2.
Meshkov
,
E. E.
,
1969
, “
Instability of the Interface of Two Gases Accelerated by a Shock Wave
,”
Pure Appl. Math.
,
4
(
5
), pp.
101
104
.
3.
Arnett
,
D.
,
2000
, “
The Role of Mixing in Astrophysics
,”
Astrophys. J., Suppl. Ser.
,
127
(
2
), pp.
213
217
.
4.
Yang
,
J.
,
Kubota
,
T.
, and
Zukoski
,
E. E.
,
1993
, “
Applications of Shock-Induced Mixing to Supersonic Combustion
,”
AIAA J.
,
31
(
5
), pp.
854
862
.
5.
Brouillette
,
M.
,
2002
, “
The Richtmyer–Meshkov Instability
,”
Annu. Rev. Fluid Mech.
,
34
, pp.
445
468
.
6.
Lindl
,
J.
,
1995
, “
Development of the Indirect-Drive Approach to Inertial Confinement Fusion and the Target Physics Basis for Ignition and Gain
,”
Phys. Plasmas
,
2
(
11
), pp.
3933
4024
.
7.
Holmes
,
R. L.
,
Dimonte
,
G.
,
Fryxell
,
B.
,
Gittings
,
M. L.
,
Grove
,
J. W.
,
Schneider
,
M.
,
Sharp
,
D. H.
,
Velikovich
,
A. L.
,
Weaver
,
R. P.
, and
Zhang
,
Q.
,
1999
, “
Richtmyer–Meshkov Instability Growth: Experiment, Simulation and Theory
,”
J. Fluid Mech.
,
389
, pp.
55
79
.
8.
Lindl
,
J. D.
,
Mccrory
,
R. L.
, and
Campbell
,
E. M.
,
1992
, “
Progress Toward Ignition and Burn Propagation in Inertial Confinement Fusion
,”
Phys. Today
,
45
(
9
), pp.
32
40
.
9.
Lindl
,
J.
,
Landen
,
O.
,
Edwards
,
J.
,
Moses
,
E.
, and NIC Team,
2014
, “
Review of the National Ignition Campaign 2009–2012
,”
Phys. Plasmas
,
21
(
2
), p.
020501
.
10.
Samtaney
,
R.
,
2003
, “
Suppression of the Richtmyer–Meshkov Instability in the Presence of a Magnetic Field
,”
Phys. Fluids
,
15
(
8
), pp.
L53
L56
.
11.
Wheatley
,
V.
,
Pullin
,
D. I.
, and
Samtaney
,
R.
,
2005
, “
Stability of an Impulsively Accelerated Density Interface in Magnetohydrodynamics
,”
Phys. Rev. Lett.
,
95
, p.
125002
.
12.
Wheatley
,
V.
,
Samtaney
,
R.
, and
Pullin
,
D. I.
,
2009
, “
The Richtmyer–Meshkov Instability in Magnetohydrodynamics
,”
Phys. Fluids
,
21
(
8
), p.
082102
.
13.
Qiu
,
Z.
,
Wu
,
Z.
,
Cao
,
J.
, and
Li
,
D.
,
2008
, “
Effects of Transverse Magnetic Field and Viscosity on the Richtmyer–Meshkov Instability
,”
Phys. Plasmas
,
15
(
4
), p.
42305
.
14.
Cao
,
J.
,
Wu
,
Z.
,
Ren
,
H.
, and
Li
,
D.
,
2008
, “
Effects of Shear Flow and Transverse Magnetic Field on Richtmyer–Meshkov Instability
,”
Phys. Plasmas
,
15
(
4
), p.
042102
.
15.
Levy
,
Y.
,
Jaouen
,
S.
, and
Canaud
,
B.
,
2012
, “
Numerical Investigation of Magnetic Richtmyer–Meshkov Instability
,”
Laser Part. Beams
,
30
(
3
), pp.
415
419
.
16.
Wheatley
,
V.
,
Samtaney
,
R.
,
Pullin
,
D. I.
, and
Gehre
,
R. M.
,
2014
, “
The Transverse Field Richtmyer–Meshkov Instability in Magnetohydrodynamics
,”
Phys. Fluids
,
26
(
1
), p.
016102
.
17.
Zhang
,
Q.
, and
Graham
,
M. J.
,
1998
, “
A Numerical Study of Richtmyer–Meshkov Instability Driven by Cylindrical Shocks
,”
Phys. Fluids
,
10
(
4
), pp.
974
992
.
18.
Lombardini
,
M.
, and
Pullin
,
D. I.
,
2009
, “
Small-Amplitude Perturbations in the Three-Dimensional Cylindrical Richtmyer–Meshkov Instability
,”
Phys. Fluids
,
21
(
11
), p.
114103
.
19.
Mikaelian
,
K. O.
,
1990
, “
Rayleigh–Taylor and Richtmyer–Meshkov Instabilities and Mixing in Stratified Spherical Shells
,”
Phys. Rev. A
,
42
(
6
), pp.
3400
3420
.
20.
Mikaelian
,
K. O.
,
2005
, “
Rayleigh–Taylor and Richtmyer–Meshkov Instabilities and Mixing in Stratified Cylindrical Shells
,”
Phys. Fluids
,
17
(
9
), p.
094105
.
21.
Pullin
,
D. I.
,
Mostert
,
W.
,
Wheatley
,
V.
, and
Samtaney
,
R.
,
2014
, “
Converging Cylindrical Shocks in Ideal Magnetohydrodynamics
,”
Phys. Fluids
,
26
(
9
), p.
097103
.
22.
Whitham
,
G. B.
,
1958
, “
On the Propagation of Shock Waves Through Regions of Non-Uniform Area or Flow
,”
J. Fluid Mech.
,
4
(
4
), pp.
337
360
.
23.
Chisnell
,
R. F.
,
1998
, “
An Analytic Description of Converging Shock Waves
,”
J. Fluid Mech.
,
354
, pp.
357
375
.
24.
Mostert
,
W.
,
Pullin
,
D.
,
Samtaney
,
R.
, and
Wheatley
,
V.
,
2016
, “
Converging Cylindrical Magnetohydrodynamic Shock Collapse Onto a Power-Law-Varying Line Current
,”
J. Fluid Mech.
,
793
, pp.
414
443
.
25.
Mostert
,
W.
,
Wheatley
,
V.
,
Samtaney
,
R.
, and
Pullin
,
D. I.
,
2014
, “
Effects of Seed Magnetic Fields on Magnetohydrodynamic Implosion Structure and Dynamics
,”
Phys. Fluids
,
26
(
12
), p.
126102
.
26.
Mostert
,
W.
,
Wheatley
,
V.
,
Samtaney
,
R.
, and
Pullin
,
D.
,
2015
, “
Effects of Magnetic Fields on Magnetohydrodynamic Cylindrical and Spherical Richtmyer–Meshkov Instability
,”
Phys. Fluids
,
27
(
10
), p.
104102
.
27.
Bakhsh
,
A.
,
Gao
,
S.
,
Samtaney
,
R.
, and
Wheatley
,
V.
,
2016
, “
Linear Simulations of the Cylindrical Richtmyer–Meshkov Instability in Magnetohydrodynamics
,”
Phys. Fluids
,
28
(
3
), p.
034106
.
28.
Samtaney
,
R.
,
2009
, “
A Method to Simulate Linear Stability of Impulsively Accelerated Density Interfaces in Ideal-MHD and Gas Dynamics
,”
J. Comput. Phys.
,
228
(
18
), pp.
6773
6783
.
29.
Yang
,
Y.
,
Zhang
,
Q.
, and
Sharp
,
D. H.
,
1994
, “
Small Amplitude Theory of Richtmyer–Meshkov Instability
,”
Phys. Fluids
,
6
(
5
), pp.
1856
1873
.
30.
Meyer
,
K. A.
, and
Blewett
,
P. J.
,
1972
, “
Numerical Investigation of the Stability of a Shock-Accelerated Interface Between Two Fluids
,”
Phys. Fluids
,
15
(
5
), pp.
753
759
.
31.
Chandrasekhar
,
S.
,
1981
,
Hydrodynamic and Hydromagnetic Stability
(
Dover Classics of Science and Mathematics), Dover Publications
,
New York
, p.
1961
.
This content is only available via PDF.
You do not currently have access to this content.