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We generalize the Layzer's bubble model to the cases of two-dimensional and three-dimensional analytical models of an arbitrary interface Atwood number and obtain self-consistent equations. The generalized model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime. The asymptotic bubble velocities are obtained for the Rayleigh-Taylor(RT) and Richtmyer-Meshkov(RM) instabilities. We also report on the two-dimensional and the three-dimensional analytical expressions for the evolution of the RT bubble velocity.
[1] Lord Rayleigh 1900 Scientific Papers (Vol. Π) (Cambridge, England: Cambridge University Press) p200
[2] Richtmyer R D 1960 Commum Pure Appl. Math. 13 297
[3] Ye W H, Zhang W Y, He X T 2002 Phys. Rev. E 65 57401
[4] Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
[5] Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Sciences 2001 Frontiers in High Energy Density Physics (Washington DC: Academic)
[6] Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025202
[7] Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 49 726]
[8] Wang L F, Ye W H , Li Y J 2008 Acta Phys. Sin. 57 3038 (in Chinese) [王立锋, 叶文华, 李英骏 2008 57 3038]
[9] Wang L F, Ye W H, Li Y J, Meng L M 2008 Chin. Phys. B 17 3792
[10] Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Physics of Plasmas 17 122706
[11] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[12] Stefano Atzeni 2003 Inertial Fusion Beam plasma interaction, hydrodynamics, dense plasma physics (Oxford: Clarendon Press) p286
[13] Sung-Ik Sohn 2003 Phys. Rev. E 67 26301
[14] Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL 90 15001
[15] Jacobs J W, Catton I 1988 J. Fluid Mech. 187 329
[16] Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 042103
[17] Wang Li Feng, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203
[18] Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 052305
[19] Layzer D 1955 Astrophys. J. 122 1
[20] Abarzhi S I, Nishihara K, Glimm J 2003 Phys. Lett. A 317 470
[21] Ramaprabhu P, Guy Dimonte 2005 Phys. Rev. E 71 036314
[22] Karning O. Mikaelian 2003 Phys. Rev. E 67 026319
[23] Ramaprabhu P, Guy Dimonte, Young Y N, Calder A C, Fryxell B 2006 Phys. Rev. E 74 066308
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[1] Lord Rayleigh 1900 Scientific Papers (Vol. Π) (Cambridge, England: Cambridge University Press) p200
[2] Richtmyer R D 1960 Commum Pure Appl. Math. 13 297
[3] Ye W H, Zhang W Y, He X T 2002 Phys. Rev. E 65 57401
[4] Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
[5] Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Sciences 2001 Frontiers in High Energy Density Physics (Washington DC: Academic)
[6] Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025202
[7] Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 49 726]
[8] Wang L F, Ye W H , Li Y J 2008 Acta Phys. Sin. 57 3038 (in Chinese) [王立锋, 叶文华, 李英骏 2008 57 3038]
[9] Wang L F, Ye W H, Li Y J, Meng L M 2008 Chin. Phys. B 17 3792
[10] Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Physics of Plasmas 17 122706
[11] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[12] Stefano Atzeni 2003 Inertial Fusion Beam plasma interaction, hydrodynamics, dense plasma physics (Oxford: Clarendon Press) p286
[13] Sung-Ik Sohn 2003 Phys. Rev. E 67 26301
[14] Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL 90 15001
[15] Jacobs J W, Catton I 1988 J. Fluid Mech. 187 329
[16] Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 042103
[17] Wang Li Feng, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203
[18] Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 052305
[19] Layzer D 1955 Astrophys. J. 122 1
[20] Abarzhi S I, Nishihara K, Glimm J 2003 Phys. Lett. A 317 470
[21] Ramaprabhu P, Guy Dimonte 2005 Phys. Rev. E 71 036314
[22] Karning O. Mikaelian 2003 Phys. Rev. E 67 026319
[23] Ramaprabhu P, Guy Dimonte, Young Y N, Calder A C, Fryxell B 2006 Phys. Rev. E 74 066308
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