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The evolution of bubble in Rayleigh-Taylor (RT) instability for non-ideal hydromagnetic fluid is investigated theoretically in this study. In a plane perpendicular to the magnetic field, the general governing equation describing the bubble evolution is derived by considering the influences of viscousity, surface tension and magnetic field. The numerical and asymptotic solutions of the bubble velocity in two-dimensional planar geometry are obtained under different conditions and the effects of fluid viscosity, surface tension and magnetic field on the bubble growth are then analyzed in detail. It is found that the bubble velocity is reduced by viscosity and surface tension, which indicates that viscosity and surface tension can suppress the RT instability. It is also observed that the influence of magnetic field on the RT instability is caused by its nonlinear part, and whether the RT instability can be suppressed or enhanced depends on the direction of the nonlinear part of magnetic field.
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Keywords:
- Rayleigh-Taylor instability /
- viscosity /
- surface tension /
- magnetic field
[1] Taylor G I 1950 Proc. R. Soc. London A 201 192
[2] Kilkenny J D, Glendinning S G, Haan S W, Hammel B A, Lindl J D, Munro D, Verdon C P 1994 Phys. Plasmas 1 1379
[3] [4] Cabot W H, Cook A W 2006 Nature Phys. 2 562
[5] [6] [7] Rayleigh L 1900 Scientific Papers (Vol. 2) (Cambridge: Cambridge University Press) pp200-207
[8] [9] Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon Press) pp441-453
[10] [11] Zhang W L, Wu Z W, Li D 2005 Phys. Plasmas 12 042106
[12] [13] Layzer D 1955 Astrophys. J. 122 1
[14] [15] Zufiria J 1998 Phys. Fluids 31 440
[16] [17] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[18] Sohn S I 2004 Phys. Rev. E 70 045301
[19] [20] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang T C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立峰, 叶文华, 张广财, 张天才, 张建成, 李英骏 2012 物理学报 61 075207]
[21] [22] Banerjee R, Mandal L, Khan M, Gupta M R 2013 Indian J. Phys. 87 929
[23] [24] [25] Sohn S I 2009 Phys. Rev. E 80 055302(R)
[26] Gupta M R, Banerjee R, Mandal L K, Bhar R, Pant H C, Khan M, Srivastava M K 2012 Indian J. Phys. 86 471
[27] [28] [29] 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 物理学报 62 144705]
[30] [31] Cao Y G, Guo H Z, Zhang Z F, Sun Z H, Chow W K 2011 J. Phys. A: Math. Theor. 44 275501
[32] Xia T J, Dong Y Q, Cao Y G 2013 Acta Phys. Sin. 62 214702 (in Chinese) [夏同军, 董永强, 曹义刚 2013 物理学报 62 214702]
[33] [34] Khan M, Mandal L, Banerjee R, Roy S, Gupta M R 2011 Nuclear Instruments and Methods in Physics Research A 653 2
[35] [36] Gupta M R, Mandal L, Roy S, Khan M 2010 Phys. Plasmas 17 012306
[37] -
[1] Taylor G I 1950 Proc. R. Soc. London A 201 192
[2] Kilkenny J D, Glendinning S G, Haan S W, Hammel B A, Lindl J D, Munro D, Verdon C P 1994 Phys. Plasmas 1 1379
[3] [4] Cabot W H, Cook A W 2006 Nature Phys. 2 562
[5] [6] [7] Rayleigh L 1900 Scientific Papers (Vol. 2) (Cambridge: Cambridge University Press) pp200-207
[8] [9] Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon Press) pp441-453
[10] [11] Zhang W L, Wu Z W, Li D 2005 Phys. Plasmas 12 042106
[12] [13] Layzer D 1955 Astrophys. J. 122 1
[14] [15] Zufiria J 1998 Phys. Fluids 31 440
[16] [17] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[18] Sohn S I 2004 Phys. Rev. E 70 045301
[19] [20] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang T C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立峰, 叶文华, 张广财, 张天才, 张建成, 李英骏 2012 物理学报 61 075207]
[21] [22] Banerjee R, Mandal L, Khan M, Gupta M R 2013 Indian J. Phys. 87 929
[23] [24] [25] Sohn S I 2009 Phys. Rev. E 80 055302(R)
[26] Gupta M R, Banerjee R, Mandal L K, Bhar R, Pant H C, Khan M, Srivastava M K 2012 Indian J. Phys. 86 471
[27] [28] [29] 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 物理学报 62 144705]
[30] [31] Cao Y G, Guo H Z, Zhang Z F, Sun Z H, Chow W K 2011 J. Phys. A: Math. Theor. 44 275501
[32] Xia T J, Dong Y Q, Cao Y G 2013 Acta Phys. Sin. 62 214702 (in Chinese) [夏同军, 董永强, 曹义刚 2013 物理学报 62 214702]
[33] [34] Khan M, Mandal L, Banerjee R, Roy S, Gupta M R 2011 Nuclear Instruments and Methods in Physics Research A 653 2
[35] [36] Gupta M R, Mandal L, Roy S, Khan M 2010 Phys. Plasmas 17 012306
[37]
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