Three-dimensional wavelike equilibrium states in plane Poiseuille flow
Three-dimensional wavelike equilibrium states in plane Poiseuille flow
复制标题
平面泊肃叶流中的三维波状平衡态
DOI：
10.1017/s0022112091002653
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发表时间：
1991
影响因子：
3.7
通讯作者：
W. Koch
中科院分区：
文献类型：
--
作者：
U. Ehrenstein;W. Koch
为了寻求一个物理上更真实的过渡准则，研究了平面泊泽维尔流的前混沌分岔行为。利用Keller的伪弧长延拓方法计算了各种非线性时周期平衡解。重点研究了三维非线性行波型二次分叉分支。这些饱和平衡态源于中性锁相次级不稳定模式的非线性初级分岔面。利用对称性，只研究了对应于对称和反对称线性二次失稳模态的非线性二次分支。结果表明，一种新的仅包含偶数展向傅里叶模态的二次分岔解是特别重要的。这些解的平均数量在很大程度上受展向（0,2）模态支配，并通过研究双临界次级分岔发现，与在“尖峰”阶段过渡流动中观察到的结果有一定的相似之处。新溶液分支的摩擦系数在实验观测范围内，以平均流速定义的临界雷诺数降至1000左右，与实验基本一致。
In the quest for a physically more realistic transition criterion, the prechaotic bifurcation behaviour of plane Poiseuille flow is studied. Various classes of nonlinear time-periodic equilibrium solutions are computed via Keller's pseudo-arclength continuation method. In particular, attention is focused on three-dimensional nonlinear travelling-wave type secondary bifurcation branches. These saturated equilibrium states originate on the nonlinear primary bifurcation surface from neutral, phase-locked secondary instability modes. Taking advantage of symmetries, only those nonlinear secondary branches which correspond to symmetric and antisymmetric linear secondary instability modes are investigated. It appears that a new family of secondary bifurcation solutions which contains only even spanwise Fourier modes is particularly important. Dominated largely by the spanwise (0,2) mode and discovered by investigating bicritical secondary bifurcations, the mean quantities of these solutions show a certain resemblance to those observed in transitional flow during the ‘spike’ stage. The friction factor of this new solution branch is in the experimentally observed range and the critical Reynolds number, defined with the mean flow velocity, is reduced to about 1000 in general agreement with experiments.
DOI：
10.1146/annurev.fl.19.010187.002011
发表时间：
1987
期刊：
--
影响因子：
--
作者：
C. Canuto;M. Hussaini;A. Quarteroni;T. Zang
通讯作者：
C. Canuto;M. Hussaini;A. Quarteroni;T. Zang