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In the past few years, the balanced sink and source macroscopic open system, which satisfies the parity and time-reversal symmetry, has become a research hot point. We introduce parity and time-reversal (PT) symmetry into fluid system by setting up balanced inflow and outflow in a two-dimensional channel. The flow is governed by Navier-Stokes equation and we use lattice Boltzmann method to solve them. Defining configuration-dependent asymmetric functions in velocity, kinetic energy density, and vorticity fields, we find that the PT function of the flow increases with the increase of the 2th power of Reynolds number i.e., ρn～ Ren. In this work, we use three different velocity profiles to drive the flow. It is demonstrated that in the three driven modes, the power-law schedule holds true. It is concluded that PT asymmetry of the viscous flow is determined by the flow dynamics not by the driven modes, thereby verifies the universality of the power-law scaling in viscous flow with balanced inflow and outflow.
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Keywords:
- balanced sink source /
- lattice Boltzmann method /
- parity and time-reversal symmetry /
- low Reynolds number
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[12] Ruter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192
[13] Feng L, Ayache M, Huang J, Xu Y L, Lu M H, Chen Y F, Fainman Y, Scherer A 2011 Science 333 729
[14] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U 2012 Nature 488 167
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[18] Kottos T 2010 Nat. Phys. 6 192
[19] Zheng M C, Christodoulides D N, Fleischmann R, Kottos T 2010 Phys. Rev. A 82 010103(R)
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[21] Wang C Y 1991 Ann. Rev. Fluid Mech. 23 159
[22] Yu W, Chen Xi, Xu Y S, Joglekar Y N 2014 Phys. Rev. E (in press)
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[26] Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
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[28] Wen B H, Liu H Y, Zhang C Y, Wang Q 2009 Chin. Phys. B 18 4353
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[31] He X, Luo L S 1997 Phys. Rev. E 55 R6333
[32] Bhatnagar P L, Gross E P, Krook M 1954 Phys. Rev. 94 511
[33] Chen H, Chen S, Matthaeus H W 1992 Phys. Rev. A 45 5339
[34] Qian Y H, d’Humieres D, Lallemand P 1992 Europhys. Lett. 17 479
[35] He X, Luo L S 1997 J. Stat. Phys. 88 927
[36] Skordos P A 1993 Phys. Rev. E 48 4823
[37] d’Humieres D, Ginzburg I, Krafczyk M, Lallemand P, Luo L S 2002 Philos. Trans. R. Soc. Lond. A 360 437
[38] Luo L S 2000 Phys. Rev. E 62 4982
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[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
[2] Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401
[3] Bender C M 2007 Rep. Prog. Phys. 70 947
[4] Mostafazadeh A 2010 Int. J. Geom. Meth. Mod. Phys. 7 1191
[5] Bendix O, Fleischmann R, Kottos T, Shapiro B 2009 Phys. Rev. Lett. 103 030402
[6] Jin L, Song Z 2009 Phys. Rev. A 80 052107
[7] Joglekar Y N, Scott D, Babbey M, Saxena A 2010 Phys. Rev. A 82 030103(R)
[8] Znojil M 2010 Phys. Rev. A 82 052113
[9] Znojil M 2011 Phys. Lett. A 375 3435
[10] Joglekar Y N, Saxena A 2011 Phys. Rev. A 83 050101(R)
[11] Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902
[12] Ruter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192
[13] Feng L, Ayache M, Huang J, Xu Y L, Lu M H, Chen Y F, Fainman Y, Scherer A 2011 Science 333 729
[14] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U 2012 Nature 488 167
[15] Schindler J, Li A, Zheng M C, Ellis F M, Kottos T 2011 Phys. Rev. A 84 040101(R)
[16] Bender C M, Berntson B K, Parker D, Samuel E 2013 Am. J. Phys. 81 173
[17] Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F, Scherer A 2013 Nat. Mater. 12 108
[18] Kottos T 2010 Nat. Phys. 6 192
[19] Zheng M C, Christodoulides D N, Fleischmann R, Kottos T 2010 Phys. Rev. A 82 010103(R)
[20] Wang C Y 1990 Acta Mech. 81 69
[21] Wang C Y 1991 Ann. Rev. Fluid Mech. 23 159
[22] Yu W, Chen Xi, Xu Y S, Joglekar Y N 2014 Phys. Rev. E (in press)
[23] Chen S, Doolen G D 1998 Ann. Rev. Fluid Mech. 30 329
[24] Aidun C K, Clausen J R 2010 Ann. Rev. Fluid Mech. 42 439
[25] Zeng J B, Li L J, Liao Q, Chen Q H, Cui W Z, Pan L M 2010 Acta Phys. Sin. 59 178 (in Chinese) [曾建邦, 李隆键, 廖全, 陈清华, 崔文智, 潘良明 2010 59 178]
[26] Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
[27] Wu W, Sun D K, Dai T, Zhu M F 2012 Acta Phys. Sin. 61 150501 (in Chinese) [吴伟, 孙东科, 戴挺, 朱鸣芳 2012 61 150501]
[28] Wen B H, Liu H Y, Zhang C Y, Wang Q 2009 Chin. Phys. B 18 4353
[29] Yu H D, Zhao K H 2000 Acta Phys. Sin. 49 816 (in Chinese) [余慧丹, 赵凯华 2000 49 816]
[30] Yu H D, Zhao K H 1999 Acta Phys. Sin. 48 1475 (in Chinese) [余慧丹, 赵凯华 1999 48 1475]
[31] He X, Luo L S 1997 Phys. Rev. E 55 R6333
[32] Bhatnagar P L, Gross E P, Krook M 1954 Phys. Rev. 94 511
[33] Chen H, Chen S, Matthaeus H W 1992 Phys. Rev. A 45 5339
[34] Qian Y H, d’Humieres D, Lallemand P 1992 Europhys. Lett. 17 479
[35] He X, Luo L S 1997 J. Stat. Phys. 88 927
[36] Skordos P A 1993 Phys. Rev. E 48 4823
[37] d’Humieres D, Ginzburg I, Krafczyk M, Lallemand P, Luo L S 2002 Philos. Trans. R. Soc. Lond. A 360 437
[38] Luo L S 2000 Phys. Rev. E 62 4982
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