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将具有简单速度势的Layzer模型和Zufiria模型推广至非理想流体情况, 并分别利用这两种模型研究了界面张力对Rayleigh-Taylor不稳定性的影响. 首先得到了两种模型下气泡的渐近速度和渐近曲率的解析表达式; 其次系统研究了界面张力对气泡的渐近速度和渐近曲率的影响; 最后将两种模型进行了比较, 并将气泡的渐近速度和数值模拟进行了比较. 研究表明: 界面张力压低了气泡的速度, 但对曲率没有影响; 利用简单速度势的Layzer模型所得的气泡的渐近速度比复杂速度势的Layzer模型的值小, 但是比Zufiria模型的值大; 当阿特伍德数等于1时, 简单速度势的Layzer模型和复杂速度势的Layzer模型给出的结果一致.
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关键词:
- Rayleigh-Taylor不稳定性 /
- 界面张力 /
- Layzer模型 /
- Zufiria模型
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.-
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
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[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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