Transition to chaos in lid-driven square cavity flow  

作　　者：Tao Wang Tiegang Liu 王涛;刘铁钢(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;LMIB and School of Mathematical Sciences,Beihang University,Beijing 100191,China)

机构地区：[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

出　　处：《Chinese Physics B》2021年第12期291-300,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.12162001);the Natural Science Foundation of Ningxia(Grant No.2019AAC03129);the Construction Project of First-Class Disciplines in Ningxia Higher Education(Grant No.NXYLXK2017B09)。

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 

分 类 号：O241.3[理学—计算数学] O415.5[理学—数学]