驱动模式对具有库源平衡的黏性流体中空间反射时间反演联合对称性的影响

陈曦; Yu Whitney; Joglekar Yogesh N; 郑友取; 许友生; 吴锋民

doi:10.7498/aps.63.060206

摘要

满足空间反射时间反演parity and time-reversal（PT）联合对称性的库源平衡宏观开放系统近几年成为一个研究热点. 本文将PT对称性引入到动力学系统，用格子玻尔兹曼方法求解Navier-Stokes方程，发现在二维黏性流体中，如果进口和出口的条件完全等同，在低雷诺数流动中，流场的PT对称函数（ρ）随雷诺数（Re）的增高以 ρn ～ Ren 指数增长. 用三种不同的速度剖面来驱动流体，计算流场达到稳定状态时的PT对称性. 结果发现，进出口平衡的黏性管流中，ρn ～ Ren 的规律在三种驱动模式中出现，表明流场的PT 对称性是由流体本身决定的，与驱动模式没有关系，从此论证所得到的指数率的谱适性.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
浙江师范大学物理系, 金华 321004;

2.
Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis (IUPUI), Indiana USA 46202;

3.
Department of Physics, Indiana University-Purdue University Indianapolis (IUPUI), Indiana USA 46202;

4.
浙江科技学院, 杭州 310023

基金项目: 国家自然科学基金重点项目（批准号：10932010）、国家自然科学基金（批准号：11072229，11072220，U1262109，11079029，61274099）和美国（the National Science Foundation DMR-1054020（YJ）.）资助的课题.

Authors and contacts

1.
Department of Physics, Zhejiang Normal University, Jinhua 321004, China;

2.
Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis (IUPUI), Indiana 46202, USA;

3.
Department of Physics, Indiana University-Purdue University Indianapolis (IUPUI), Indiana 46202, USA;

4.
Zhejing University of Science and Technology, Hangzhou 310023, China

Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10932010), the National Natural Science Foundation of China (Grant Nos. 11072229, 11072220, U1262109, 11079029, 61274099), and the National Science Foundation DMR-1054020 (YJ).

参考文献

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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]
[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]
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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

施引文献

[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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