-
The Rayleigh-Bénard convection in a binary fluid mixture is one of typical models for studying the nonlinear dynamics of nonequilibrium convection. In this paper, using the numerical simulations of the two-dimensional full equations of hydrodynamics, we study the bifurcation and evolution of patterns in the traveling wave convection in binary fluid mixtures with strong Soret effect (separation ratio Ψ=-0.60) in a rectangular cell. The system exhibits 5 types of traveling wave convection solutions with the increasing of reduced Rayleigh number r along the upper branch of the bifurcation curve. They are localized traveling wave convection, traveling wave convection with defects, traveling wave convection, undulation traveling wave convection, and stationary overturning convection. Second, the influence of separation ratio on convection solutions is investigated. By comparing the convection solutions with strong Soret effect (Ψ=-0.60) with those of weakly Soret effect (Ψ=-0.11), we find that those with strong Soret effect are richer. Because of the complexity in convection with strong Soret effect, the convection solutions at Ψ=-0.60 are different from those at Ψ=-0.20, -0.4.
-
Keywords:
- Soret effect /
- Rayleigh-Bé /
- nard convection /
- numerical simulation /
- binary fluid mixture
[1] Chandrasekhar S 1961 Hydrodynamics and Hydromagnetic Stability (Oxford: Clarendon Press) pp126-146
[2] Getling A V 1998 Rayleigh-Bénard Convection (London: World Scientific) pp98-112
[3] Ning L Z 2006 Rayleigh-Bénard Convection in a Binary Fluid Mixture with and without Lateral Flow (Xi'an: Northwest A & F University Press) pp112-134
[4] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 998
[5] Barten W, Lucke M, Kamps M 1991 Phys. Rev. Lett. 66 2621
[6] Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5636
[7] Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5662
[8] Yahata H 1991 Prog. Theor. Phys. 85 933
[9] Yahata H 1989 Prog. Theor. Phys. (Suppl.) 99 493
[10] Batiste O, Knobloch E, Alonso A, Mercader I 2006 J. Fluid Mech. 560 149
[11] Batiste O, Knobloch E, Mercader I, Net M 2001 Phys. Rev. E 65 016303
[12] Futterer C 2003 Theor. Comput. Fluid Dyn. 16 467
[13] Ryskin A, Mller H W, Pleiner H 2003 Phys. Rev. E 67 046302
[14] Ning L Z, Zhou Y, Wang S Y, Li G D, Zhang S Y, Zhou Q 2010 Chin. J. Hydrodyn. 25 299 (in Chinese) [宁利中, 周洋, 王思怡, 李国栋, 张淑芸, 周倩 2010 水动力学研究与进展 25 299]
[15] Ning L Z, Qi X, Yu L, Zhou Y, Wang S Y, Li G D 2010 J. Basic Sci. Eng. 18 281 (in Chinese) [宁利中, 齐昕, 余荔, 周洋, 王思怡, 李国栋 2010 应用基础和工程科学学报 18 281]
[16] Ning L Z, Harada Y, Yahata H 1996 Prog. Theor. Phys. 96 669
[17] Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 97 831
[18] Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 98 551
[19] Ning L Z, Harada Y, Yahata H, Li J Z 2001 Prog. Theor. Phys. 106 503
[20] Ning L Z, Harada Y, Yahata H, Li J Z 2001 J. Hydrodyn. 13 65
[21] Ning L Z, Qi X, Harada Y, Yahata H 2006 J. Hydrodyn. 18 199
[22] Ning L Z, Qi X, Zhou Y, Yu L 2009 Acta Phys. Sin. 58 2528 (in Chinese)[宁利中, 齐昕, 周洋, 余荔 2009 58 2528]
[23] Ning L Z, Harada Y, Yahata H, Li J Z 2000 J. Hydrodyn. 12 20
[24] Ning L Z, Yu L, Yuan Z, Zhou Y 2009 Sci. China G 39 746 (in Chinese) [宁利中, 余荔, 袁喆, 周洋 2009 中国科学G 39 746]
[25] Ning L Z, Qi X, Yuan Z, Shi F 2008 J. Hydrodyn. 20 567
[26] Jung D, Lucke M 2002 Phys. Rev. Lett. 89 054502
[27] Buchel P, Lucke M 2000 Phys. Rev. E 61 3793
[28] Shen K, Zhang X 2002 Acta Phys. Sin. 51 2702 (in Chinese)[沈柯, 张旭 2002 51 2702]
[29] Zhang X, Shen K 2001 Acta Phys. Sin. 50 2116 (in Chinese)[张旭, 沈柯 2001 50 2116]
[30] Ni J, Liu H 2002 Physics 31 461 (in Chinese)[倪军, 刘华 2002 物理 31 461]
[31] Taraut A V, Smorodin B L, Lucke M 2012 New J. Phys. 14 093055
[32] Smorodin B L, Lucke M 2010 Phys. Rev. E 82 016310
-
[1] Chandrasekhar S 1961 Hydrodynamics and Hydromagnetic Stability (Oxford: Clarendon Press) pp126-146
[2] Getling A V 1998 Rayleigh-Bénard Convection (London: World Scientific) pp98-112
[3] Ning L Z 2006 Rayleigh-Bénard Convection in a Binary Fluid Mixture with and without Lateral Flow (Xi'an: Northwest A & F University Press) pp112-134
[4] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 998
[5] Barten W, Lucke M, Kamps M 1991 Phys. Rev. Lett. 66 2621
[6] Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5636
[7] Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5662
[8] Yahata H 1991 Prog. Theor. Phys. 85 933
[9] Yahata H 1989 Prog. Theor. Phys. (Suppl.) 99 493
[10] Batiste O, Knobloch E, Alonso A, Mercader I 2006 J. Fluid Mech. 560 149
[11] Batiste O, Knobloch E, Mercader I, Net M 2001 Phys. Rev. E 65 016303
[12] Futterer C 2003 Theor. Comput. Fluid Dyn. 16 467
[13] Ryskin A, Mller H W, Pleiner H 2003 Phys. Rev. E 67 046302
[14] Ning L Z, Zhou Y, Wang S Y, Li G D, Zhang S Y, Zhou Q 2010 Chin. J. Hydrodyn. 25 299 (in Chinese) [宁利中, 周洋, 王思怡, 李国栋, 张淑芸, 周倩 2010 水动力学研究与进展 25 299]
[15] Ning L Z, Qi X, Yu L, Zhou Y, Wang S Y, Li G D 2010 J. Basic Sci. Eng. 18 281 (in Chinese) [宁利中, 齐昕, 余荔, 周洋, 王思怡, 李国栋 2010 应用基础和工程科学学报 18 281]
[16] Ning L Z, Harada Y, Yahata H 1996 Prog. Theor. Phys. 96 669
[17] Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 97 831
[18] Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 98 551
[19] Ning L Z, Harada Y, Yahata H, Li J Z 2001 Prog. Theor. Phys. 106 503
[20] Ning L Z, Harada Y, Yahata H, Li J Z 2001 J. Hydrodyn. 13 65
[21] Ning L Z, Qi X, Harada Y, Yahata H 2006 J. Hydrodyn. 18 199
[22] Ning L Z, Qi X, Zhou Y, Yu L 2009 Acta Phys. Sin. 58 2528 (in Chinese)[宁利中, 齐昕, 周洋, 余荔 2009 58 2528]
[23] Ning L Z, Harada Y, Yahata H, Li J Z 2000 J. Hydrodyn. 12 20
[24] Ning L Z, Yu L, Yuan Z, Zhou Y 2009 Sci. China G 39 746 (in Chinese) [宁利中, 余荔, 袁喆, 周洋 2009 中国科学G 39 746]
[25] Ning L Z, Qi X, Yuan Z, Shi F 2008 J. Hydrodyn. 20 567
[26] Jung D, Lucke M 2002 Phys. Rev. Lett. 89 054502
[27] Buchel P, Lucke M 2000 Phys. Rev. E 61 3793
[28] Shen K, Zhang X 2002 Acta Phys. Sin. 51 2702 (in Chinese)[沈柯, 张旭 2002 51 2702]
[29] Zhang X, Shen K 2001 Acta Phys. Sin. 50 2116 (in Chinese)[张旭, 沈柯 2001 50 2116]
[30] Ni J, Liu H 2002 Physics 31 461 (in Chinese)[倪军, 刘华 2002 物理 31 461]
[31] Taraut A V, Smorodin B L, Lucke M 2012 New J. Phys. 14 093055
[32] Smorodin B L, Lucke M 2010 Phys. Rev. E 82 016310
Catalog
Metrics
- Abstract views: 6314
- PDF Downloads: 439
- Cited By: 0
下载:
