Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

作     者：Zhimin CHEN W.G.PRICE Zhimin CHEN;W.G.PRICE

作者机构：School of Mathematics and StatisticsShenzhen UniversityShenzhen 518060Guangdong ProvinceChina Ship ScienceUniversity of SouthamptonSouthampton SO171BJU.K. 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2023年第44卷第3期

页      面：447-458页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Project supported by the National Natural Science Foundation of China(No.11571240) the Shenzhen Natural Science Fund of China(the Stable Support Plan Program No.20220805175116001) 

主　　题：two-dimensional(2D)Navier-Stokes equation non-parallel square vortex flow primary bifurcation secondary steady-state flow secondary time-periodic flow 

摘      要：In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is *** energy dissipation of the flow is controlled by the viscosity and linear *** latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed *** basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise *** N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=*** this reason,this study focuses on the instability of the square eddy flow of nine *** is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction ***,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory *** Hopf bifurcation phenomenon has not been observed in earlier investigations.