Transition to chaos in lid-driven square cavity flow

doi:10.1088/1674-1056/ac3226

中国物理B ›› 2021, Vol. 30 ›› Issue (12): 120508-120508.doi: 10.1088/1674-1056/ac3226

Transition to chaos in lid-driven square cavity flow

Tao Wang(王涛)¹ and Tiegang Liu(刘铁钢)^2,†

1 School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China;
2 LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China

收稿日期:2021-08-26 修回日期:2021-10-08 接受日期:2021-10-22 出版日期:2021-11-15 发布日期:2021-11-20
通讯作者: Tiegang Liu E-mail:liutg@buaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12162001), the Natural Science Foundation of Ningxia (Grant No. 2019AAC03129), and the Construction Project of First-Class Disciplines in Ningxia Higher Education (Grant No. NXYLXK2017B09).

Transition to chaos in lid-driven square cavity flow

Tao Wang(王涛)¹ and Tiegang Liu(刘铁钢)^2,†

1 School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China;
2 LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China

Received:2021-08-26 Revised:2021-10-08 Accepted:2021-10-22 Online:2021-11-15 Published:2021-11-20
Contact: Tiegang Liu E-mail:liutg@buaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12162001), the Natural Science Foundation of Ningxia (Grant No. 2019AAC03129), and the Construction Project of First-Class Disciplines in Ningxia Higher Education (Grant No. NXYLXK2017B09).

摘要/Abstract

摘要： To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.

关键词: unsteady lid-driven square cavity flows, chaos, time series analysis, third Hopf bifurcation

Abstract: To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.

Key words: unsteady lid-driven square cavity flows, chaos, time series analysis, third Hopf bifurcation

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

05.70.Jk (Critical point phenomena)

Tao Wang(王涛) and Tiegang Liu(刘铁钢). Transition to chaos in lid-driven square cavity flow[J]. 中国物理B, 2021, 30(12): 120508-120508.

Tao Wang(王涛) and Tiegang Liu(刘铁钢). Transition to chaos in lid-driven square cavity flow[J]. Chin. Phys. B, 2021, 30(12): 120508-120508.

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Transition to chaos in lid-driven square cavity flow

Transition to chaos in lid-driven square cavity flow

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