Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori
Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori
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二维平面圆环上粘性不可压缩流体柯尔莫哥洛夫问题的分岔图
DOI：
10.1007/bf03167572
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发表时间：
1991
影响因子：
0.9
通讯作者：
M. Shōji
中科院分区：
文献类型：
--
作者：
Hisashi Okamoto;M. Shōji
本文考虑二维环面上粘性不可压缩流体运动的Kolmogorov问题。该问题是一个具有雷诺数和展弦比两个参数的分叉问题。以雷诺数为分叉参数，改变纵横比作为分叉参数，数值计算了分叉图。随着纵横比的变化，我们观察到转折点和二次分叉点出现或消失。当环面的长宽比满足一定条件时，还发现了Hopf分岔点。本文是该报告的改进和扩大版本[26]。本文纠正了[17，26]中的一些错误。
We consider Kolmogorov's problem of viscous incompressible fluid motions on two dimensional tori. The problem is a bifurcation problem with two parameters, the Reynolds number and the aspect ratio. Varying the aspect ratio as a splitting parameter, we compute numerically bifurcation diagrams with the Reynolds number as a bifurcation parameter. As the aspect ratio changes, we observe turning points and secondary bifurcation points appear or disappear. Furthermore, Hopf bifurcation points are also found when the aspect ratio of the torus satisfies a certain condition. This paper is an improved and enlarged version of the report [26]. Some errors in [17, 26] are corrected here.