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In this paper, Layzers model which has a simple velocity potential, and Zufirias model are extended to the case of non-ideal fluids, and the effects of surface tension on Rayleigh-Taylor instability are investigated. Firstly, the analytical expressions for the asymptotic bubble velocity and curvature are obtained in the two models. Secondly, the effects of surface tension on Rayleigh-Taylor instability are studied systematically. Finally, the two models are compared with each other and the comparisons with numerical simulation are made as well. The results indicate that the surface tension depresses the bubble velocity, but does not affect the bubble curvature. The Layzers model with the simple velocity potential gives a smaller bubble velocity than that predicted by the Layzers model with a complex velocity potential. But the bubble velocity predicted by the Layzers model with the simple velocity potential is larger than that obtained by Zufirias model. Both Layzers models lead to the same bubble velocity when the Atwood number is A = 1.
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Keywords:
- Rayleigh-Taylor instability /
- surface tension /
- Layzer /
- s model
[1] Rayleigh L 1883 Proc. London Math. Soc. 14 170
[2] Taylor G I 1950 Proc. R. Soc. London Ser. A 201 192
[3] Buchler J R, Livio M, Colgate S A 1980 Space Science Rev. 27 571
[4] Keskinen M J, Ossakow S L, Szuszczewicz E P, Holmes J C 1981 J. Geophys. Res. 86 5785
[5] Jia G, Xiong J, Dong J Q, Xie Z Y, Wu J 2012 Chin. Phys. B 21 095202
[6] Rayleigh L 1900 Scientific Papers II (Cambridge: Cambridge University Press) p200
[7] Inogamov N A, Abarzhi S I 1995 Physica D 87 339
[8] Abarzhi S I 1999 Phys. Rev. E 59 1729
[9] Layzer D 1955 Astrophys. J. 122 1
[10] Oron D, Arazi L, Kartoon D, Rikanati A, Alon U, Shvarts D 2001 Phys. Plasmas 8 2883
[11] Alon U 1995 Phys. Rev. Lett. 74 534
[12] Dimonte G 2000 Phys. Plasmas 7 2255
[13] Dimonte G, Schneider M 2000 Phys. Fluids 12 304
[14] Mikaelian K O 1998 Phys. Rev. Lett. 80 508
[15] Zufiria J A 1988 Phys. Fluids 31 440
[16] Zhang Q1998 Phys. Rev. Lett. 81 3391
[17] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[18] Sohn S I 2003 Phys. Rev. E 67 026301
[19] Sohn S I 2004 Phys. Rev. E 70 045301(R)
[20] LeLevier R, Lasher G J, Bjorklund F 1955 Effect of a density gradient on Taylor instability (Lawrence Livermore Laboratory report UCRL-4459)
[21] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 61 075207]
[22] Zhang Y, Ding N 2008 Chin. Phys. B 17 2994
[23] Cao Y G, Guo H Z, Zhang Z F, Sun Z H, Chow W K 2011 J. Phys. A: Math. Theor. 44 275501
[24] Huo X H, Wang L F, Tao Y S, Li Y J 2013 Acta Phys. Sin. 62 144705 (in Chinese) [霍新贺, 王立峰, 陶烨晟, 李英骏 2013 62 144705]
[25] Chen X M, Fried E 2006 J. Fluid Mech. 560 395
[26] Mitcher M, Landshoff R K M 1964 Phys. Fluids 7 862
[27] Wolf G H 1969 Z. Physik 227 291
[28] Sun L 2008 Chin. Phys. Lett. 25 1343
[29] Wang L F, Ye W H, Fan Z F, Li Y J 2009 Acta Phys. Sin. 58 4787 (in Chinese) [王立锋, 叶文华, 范征锋, 李英骏 2009 58 4787]
[30] Liu Y L, Zhang A M, Wang S P, Tian Z L 2012 Acta Phys. Sin. 61 224702 (in Chinese) [刘云龙, 张阿曼, 王诗平, 田昭丽 2012 61 224702]
[31] Young Y N, Ham F E 2006 J. Turbul. 7 1
[32] Sohn S I 2009 Phys. Rev. E 80 055302(R)
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[1] Rayleigh L 1883 Proc. London Math. Soc. 14 170
[2] Taylor G I 1950 Proc. R. Soc. London Ser. A 201 192
[3] Buchler J R, Livio M, Colgate S A 1980 Space Science Rev. 27 571
[4] Keskinen M J, Ossakow S L, Szuszczewicz E P, Holmes J C 1981 J. Geophys. Res. 86 5785
[5] Jia G, Xiong J, Dong J Q, Xie Z Y, Wu J 2012 Chin. Phys. B 21 095202
[6] Rayleigh L 1900 Scientific Papers II (Cambridge: Cambridge University Press) p200
[7] Inogamov N A, Abarzhi S I 1995 Physica D 87 339
[8] Abarzhi S I 1999 Phys. Rev. E 59 1729
[9] Layzer D 1955 Astrophys. J. 122 1
[10] Oron D, Arazi L, Kartoon D, Rikanati A, Alon U, Shvarts D 2001 Phys. Plasmas 8 2883
[11] Alon U 1995 Phys. Rev. Lett. 74 534
[12] Dimonte G 2000 Phys. Plasmas 7 2255
[13] Dimonte G, Schneider M 2000 Phys. Fluids 12 304
[14] Mikaelian K O 1998 Phys. Rev. Lett. 80 508
[15] Zufiria J A 1988 Phys. Fluids 31 440
[16] Zhang Q1998 Phys. Rev. Lett. 81 3391
[17] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[18] Sohn S I 2003 Phys. Rev. E 67 026301
[19] Sohn S I 2004 Phys. Rev. E 70 045301(R)
[20] LeLevier R, Lasher G J, Bjorklund F 1955 Effect of a density gradient on Taylor instability (Lawrence Livermore Laboratory report UCRL-4459)
[21] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 61 075207]
[22] Zhang Y, Ding N 2008 Chin. Phys. B 17 2994
[23] Cao Y G, Guo H Z, Zhang Z F, Sun Z H, Chow W K 2011 J. Phys. A: Math. Theor. 44 275501
[24] Huo X H, Wang L F, Tao Y S, Li Y J 2013 Acta Phys. Sin. 62 144705 (in Chinese) [霍新贺, 王立峰, 陶烨晟, 李英骏 2013 62 144705]
[25] Chen X M, Fried E 2006 J. Fluid Mech. 560 395
[26] Mitcher M, Landshoff R K M 1964 Phys. Fluids 7 862
[27] Wolf G H 1969 Z. Physik 227 291
[28] Sun L 2008 Chin. Phys. Lett. 25 1343
[29] Wang L F, Ye W H, Fan Z F, Li Y J 2009 Acta Phys. Sin. 58 4787 (in Chinese) [王立锋, 叶文华, 范征锋, 李英骏 2009 58 4787]
[30] Liu Y L, Zhang A M, Wang S P, Tian Z L 2012 Acta Phys. Sin. 61 224702 (in Chinese) [刘云龙, 张阿曼, 王诗平, 田昭丽 2012 61 224702]
[31] Young Y N, Ham F E 2006 J. Turbul. 7 1
[32] Sohn S I 2009 Phys. Rev. E 80 055302(R)
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