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Chin. Phys. B, 2021, Vol. 30(12): 120508    DOI: 10.1088/1674-1056/ac3226
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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
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.
Keywords:  unsteady lid-driven square cavity flows      chaos      time series analysis      third Hopf bifurcation  
Received:  26 August 2021      Revised:  08 October 2021      Accepted manuscript online:  22 October 2021
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 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).
Corresponding Authors:  Tiegang Liu     E-mail:

Cite this article: 

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

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