A numerical simulation of two-dimensional compressible Navier-Stokes equations using a high-order weighted essentially nonoscillatory finite difference shock capturing scheme is carried out in this paper, to study the effect of shock waves on the development of Rayleigh-Taylor instability. Shocks with different Mach numbers are introduced ahead or behind the Rayleigh-Taylor interface, and their effect on the transition to instability is demonstrated and compared. It is observed that shock waves can speed up the transition to instability for the Rayleigh-Taylor interface significantly. Stronger shocks are more effective in this speed-up process.
REFERENCES
1.
2.
3.
S.
Chandrasekhar
, Hydrodynamic and Hydromagnetic Stability
(Oxford University Press
, Oxford
, 1961
).4.
5.
C. L.
Gardner
, J.
Glimm
, O.
McBryan
, R.
Menikoff
, D. H.
Sharp
, and Q.
Zhang
, Phys. Fluids
31
, 447
(1988
).6.
Y.-N.
Young
, H.
Tufo
, A.
Dubey
, and R.
Rosner
, J. Fluid Mech.
447
, 377
(2001
).7.
Y.
Zhou
, H. F.
Robey
, and A. C.
Buckingham
, Phys. Rev. E
67
, 056305
(2003
).8.
L.
Smarr
, J. R.
Wilson
, R. P.
Barton
, and R. L.
Bowers
, Astrophys. J.
246
, 515
(1981
).9.
W. D.
Arnett
, J. N.
Bahcall
, R. T.
Kirshner
, and S. E.
Woosley
, Annu. Rev. Astron. Astrophys.
27
, 629
(1989
).10.
J.
Lindl
, Internal Confinement Fusion: The Quest for Ignition and Energy Gain
(Springer
, New York
, 1997
).11.
Y.
Zhou
, B. A.
Remington
, H. F.
Robey
et al., Phys. Plasmas
10
, 1883
(2003
).12.
Y.
Zhou
, R.
Rubinstein
, D.
Eliason
, and W.
Cabot
, Astron. Astrophys.
405
, 379
(2003
).13.
Y.
Zhou
, G.
Zimmerman
, and E.
Burke
, Phys. Rev. E
65
, 056303
(2002
).14.
G. F.
Carnevale
, P.
Orlandi
, Y.
Zhou
, and R. C.
Kloosterziel
, J. Fluid Mech.
457
, 181
(2002
).15.
G.
Pacitto
, C.
Flament
, J.-C.
Bacri
, and M.
Widom
, Phys. Rev. E
62
, 7941
(2000
).16.
C.
Mügler
and S.
Gauthier
, Phys. Fluids
12
, 1783
(2000
).17.
D.
Balsara
and C.-W.
Shu
, J. Comput. Phys.
160
, 405
(2000
).18.
C.-W.
Shu
and S.
Osher
, J. Comput. Phys.
77
, 439
(1988
).19.
G.
Jiang
and C.-W.
Shu
, J. Comput. Phys.
126
, 202
(1996
).20.
Y.-T.
Zhang
, J.
Shi
, C.-W.
Shu
, and Y.
Zhou
, Phys. Rev. E
68
, 046709
(2003
).21.
J.
Shi
, Y.-T.
Zhang
, and C.-W.
Shu
, J. Comput. Phys.
186
, 690
(2003
).22.
T. S.
Lundgren
, “A free vortex method with weak viscous effects
,” in Mathematic Aspects of Vortex Dynamics
, edited by R. E.
Caflish
(SIAM
, Philadelphia, 1989
).23.
J. Z.
Wu
, Phys. Fluids
7
, 2375
(1995
).24.
G.
Tryggvason
, J. Comput. Phys.
75
, 253
(1988
).25.
Th.
von Karman
, “On the foundation of high speed aerodynamics
,” in General Theory of High Speed Aerodynamics
, edited by W. R.
Sears
(Princeton University Press
, Princeton, NJ
, 1954
).26.
M. J.
Lighthill
, J. Fluid Mech.
2
, 1
(1956
).27.
© 2006 American Institute of Physics.
2006
American Institute of Physics
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