The second Hopf bifurcation in lid-driven square cavity

doi:10.1088/1674-1056/ab6b15

Abstract To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical simulations. In this paper, we study the characteristics of the second Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme recently developed by us. We numerically identify the critical Reynolds number of the second Hopf bifurcation located in the interval of (11093.75,11094.3604) by bisection. In addition, we find that there are two dominant frequencies in its spectral diagram when the flow is in the status of the second Hopf bifurcation, while only one dominant frequency is identified if the flow is in the first Hopf bifurcation via the Fourier analysis. More interestingly, the flow phase portrait of velocity components is found to make transition from a regular elliptical closed form for the first Hopf bifurcation to a non-elliptical closed form with self-intersection for the second Hopf bifurcation. Such characteristics disclose flow in a quasi-periodic state when the second Hopf bifurcation occurs.

Keywords: unsteady lid-driven cavity flows second Hopf bifurcation critical Reynolds number numerical simulation

Received: 05 October 2019
Revised: 03 December 2019
Accepted manuscript online:

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	05.70.Jk	(Critical point phenomena)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11601013 and 91530325).

Corresponding Authors: Tiegang Liu
E-mail: liutg@buaa.edu.cn

Cite this article:

Tao Wang(王涛), Tiegang Liu(刘铁钢), Zheng Wang(王正) The second Hopf bifurcation in lid-driven square cavity 2020 Chin. Phys. B 29 030503

[1]	Kawaguti M 1961 J. Phys. Soc. Jpn. 16 2307
[2]	Erturk E 2006 Int. J. Numer. Meth. Fluids 50 421
[3]	Das M K and Kanna P 2007 International Journal of Numerical Methods for Heat and Fluid Flow 17 799
[4]	Erturk E 2009 Int. J. Numer. Meth. Fluids 60 275
[5]	Tang J S, Zhao M H, Han F and Zhang L 2011 Chin. Phys. B 20 020504
[6]	Nuriev A N, Egorov A G and Zaitseva O N 2016 Fluid Dyn. Res. 48 61405
[7]	Fang L and Ge M W 2017 Chin. Phys. Lett. 34 030501
[8]	Hou S, Zou Q, Chen S, Doolen G and Cogley A C 1995 J. Comput. Phys. 118 329
[9]	Poliashenko M and Aidun A 1995 J. Comput. Phys. 121 246
[10]	Bruneau C H and Saad M 2006 Comput. Fluids 35 326
[11]	Fortin A, Jardak M, Gervais J and Pierre R 1997 Int. J. Numer. Method Fluids 24 1185
[12]	Cazemier W, Verstappen R and Veldman A 1998 Phys. Fluids 10 1685
[13]	Auteri F, Parolini N and Quartapelle L 2002 J. Comput. Phys. 183 1
[14]	Wang T and Liu T G 2019 Numer. Math.: Theory, Methods and Applications 12 312
[15]	Spotz W F 1998 Int. J. Numer. Method Fluids 28 737
[16]	Shu C W and Osher S 1988 J. Comput. Phys. 77 439
[17]	Tian Z F, Liang X and Yu P 2011 Int. J. Numer. Method Eng. 88 511

[1]	Quantitative measurement of the charge carrier concentration using dielectric force microscopy Junqi Lai(赖君奇), Bowen Chen(陈博文), Zhiwei Xing(邢志伟), Xuefei Li(李雪飞), Shulong Lu(陆书龙), Qi Chen(陈琪), and Liwei Chen(陈立桅). Chin. Phys. B, 2023, 32(3): 037202.
[2]	Micro-mechanism study of the effect of Cd-free buffer layers ZnXO (X=Mg/Sn) on the performance of flexible Cu₂ZnSn(S, Se)⁴ solar cell Caixia Zhang(张彩霞), Yaling Li(李雅玲), Beibei Lin(林蓓蓓), Jianlong Tang(唐建龙), Quanzhen Sun(孙全震), Weihao Xie(谢暐昊), Hui Deng(邓辉), Qiao Zheng(郑巧), and Shuying Cheng(程树英). Chin. Phys. B, 2023, 32(2): 028801.
[3]	Theoretical and experimental studies on high-power laser-induced thermal blooming effect in chamber with different gases Xiangyizheng Wu(吴祥议政), Jian Xu(徐健), Keling Gong(龚柯菱), Chongfeng Shao(邵崇峰), Yang Kou(寇洋), Yuxuan Zhang(张宇轩), Yong Bo(薄勇), and Qinjun Peng(彭钦军). Chin. Phys. B, 2022, 31(8): 086105.
[4]	Spatio-spectral dynamics of soliton pulsation with breathing behavior in the anomalous dispersion fiber laser Ying Han(韩颖), Bo Gao(高博), Jiayu Huo(霍佳雨), Chunyang Ma(马春阳), Ge Wu(吴戈),Yingying Li(李莹莹), Bingkun Chen(陈炳焜), Yubin Guo(郭玉彬), and Lie Liu(刘列). Chin. Phys. B, 2022, 31(7): 074208.
[5]	Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Chin. Phys. B, 2022, 31(6): 060201.
[6]	Characteristics of secondary electron emission from few layer graphene on silicon (111) surface Guo-Bao Feng(封国宝), Yun Li(李韵), Xiao-Jun Li(李小军), Gui-Bai Xie(谢贵柏), and Lu Liu(刘璐). Chin. Phys. B, 2022, 31(10): 107901.
[7]	Effects of Prandtl number in two-dimensional turbulent convection Jian-Chao He(何建超), Ming-Wei Fang(方明卫), Zhen-Yuan Gao(高振源), Shi-Di Huang(黄仕迪), and Yun Bao(包芸). Chin. Phys. B, 2021, 30(9): 094701.
[8]	Evolution of melt convection in a liquid metal driven by a pulsed electric current Yanyi Xu(徐燕祎), Yunhu Zhang(张云虎), Tianqing Zheng(郑天晴), Yongyong Gong(龚永勇), Changjiang Song(宋长江), Hongxing Zheng(郑红星), and Qijie Zhai(翟启杰). Chin. Phys. B, 2021, 30(8): 084701.
[9]	Effect of pressure and space between electrodes on the deposition of SiN_xH_y films in a capacitively coupled plasma reactor Meryem Grari, CifAllah Zoheir, Yasser Yousfi, and Abdelhak Benbrik. Chin. Phys. B, 2021, 30(5): 055205.
[10]	Numerical simulation of super-continuum laser propagation in turbulent atmosphere Ya-Qian Li(李雅倩), Wen-Yue Zhu (朱文越), and Xian-Mei Qian(钱仙妹). Chin. Phys. B, 2021, 30(3): 034201.
[11]	Asymmetric coherent rainbows induced by liquid convection Tingting Shi(施婷婷), Xuan Qian(钱轩), Tianjiao Sun(孙天娇), Li Cheng(程力), Runjiang Dou(窦润江), Liyuan Liu(刘力源), and Yang Ji(姬扬). Chin. Phys. B, 2021, 30(12): 124208.
[12]	Numerical simulation of chorus-driving acceleration of relativistic electrons at extremely low L-shell during geomagnetic storms Zhen-Xia Zhang(张振霞), Ruo-Xian Zhou(周若贤), Man Hua(花漫), Xin-Qiao Li(李新乔), Bin-Bin Ni(倪彬彬), and Ju-Tao Yang(杨巨涛). Chin. Phys. B, 2021, 30(10): 109401.
[13]	CO₂ emission control in new CM car-following model with feedback control of the optimal estimation of velocity difference under V2X environment Guang-Han Peng(彭光含), Rui Tang(汤瑞), Hua Kuang(邝华), Hui-Li Tan(谭惠丽), and Tao Chen(陈陶). Chin. Phys. B, 2021, 30(10): 108901.
[14]	Synchronization mechanism of clapping rhythms in mutual interacting individuals Shi-Lan Su(苏世兰), Jing-Hua Xiao(肖井华), Wei-Qing Liu(刘维清), and Ye Wu(吴晔). Chin. Phys. B, 2021, 30(1): 010505.
[15]	Optical properties of several ternary nanostructures Xiao-Long Tang(唐小龙), Xin-Lu Cheng(程新路), Hua-Liang Cao(曹华亮), and Hua-Dong Zeng(曾华东). Chin. Phys. B, 2021, 30(1): 017803.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

The second Hopf bifurcation in lid-driven square cavity

Cite this article:

Online attention