Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength
Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength
复制标题
平行板间泊肃叶流的分岔：大展向波长的三维解
DOI：
10.1007/bf00379917
复制
发表时间：
1995
影响因子：
2.5
通讯作者：
A. Mielke
中科院分区：
文献类型：
--
作者：
A. Afendikov;A. Mielke
应用“空间动力学”方法分析了平行板间三维泊泽维尔流的分岔问题。与经典研究相反，我们在流方向上施加周期为2π/α的时间周期性和空间周期性。然而，除了分岔解与基本流的均匀接近性外，我们没有对跨向的行为做任何假设。在一个抽象的背景下，展示了如何从经典的线性稳定性问题唯一地确定空间动力学分析的临界特征空间的维数。对于三维泊泽维尔问题，我们可以从纯二维问题的分析中找到所有相关系数。此外，我们能够精确地分析跨向压力梯度和相关的跨向质量通量的影响。对约简问题的研究表明，与Couette-Taylor问题一样，在展向上存在两种不同的2αp/β周期解（螺旋解和带状解），且两者在同一方向上分岔。
The “spatial dynamics” approach is applied to the analysis of bifurcations of the three-dimensional Poiseuille flow between parallel plates. In contrast to the classical studies, we impose time periodicity as well as spatial periodicity with period 2π/α in the streamwise direction. However, we make no assumptions on the behavior in the spanwise direction, except the uniform closeness of the bifurcating solution to the basic flow. In an abstract setting it is shown how the dimension of the critical eigenspace of the spatial dynamics analysis can be uniquely determined from the classical linear stability problem. For the three-dimensional Poiseuille problem we are able to find all relevant coefficients from the analysis of the purely two-dimensional problem. Moreover, we are able to analyze precisely the influence of a spanwise pressure gradient and the associated spanwise mass flux. The study of the reduced problem shows that there are two different kinds of solutions (spirals and ribbons) which are 2αp/β periodic in the spanwise direction, as in the Couette-Taylor problem, and both of them bifurcate in the same direction.