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Structures of nonlinear disturbances arising from shear flow instabilities

由剪切流不稳定性引起的非线性扰动的结构

基本信息

批准号：
12650062
负责人：
NAGATA Masato
金额：
$ 2.24万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

As an example of typical shear flows we consider internally heated convective flows in an inclined channel with two parallel plates of infinite extent. The strength of the shear is parameterized by the Grashof number which measures the intensity of the homogeneously distributed heat source. The stability of the basic shear flow, that can have two inflectional points in its velocity profile, Is examined and subsequent nonlinear states are followed numerically. In the case of vertical orientation of the channel, the secondary flow in a form of two-dimensional traveling transverse vortices emerges from the basic state via a Hopf bifurcation regardless of the value of the Prandtl number, Pr, of the fluid, as the Grashof number is increased. We find that as the Grashof number is further increased the secondary flow loses its stability also in a Hopf bifurcation for the fluid with Pr=0 so that the tertiary flow is represented by three-dimensionality in space and quasi-periodicity in time. In the case of water (Pr=7.0) the secondary instability is described by a quasi-periodic mode as in the case of the fluid with Pr=0, whereas the instability is characterized by a phase-locked mode in the case of air (Pr=0.71).The extension of the investigation to cases with inclined orientation of the channel shows that perturbations in the form of longitudinal vortices, in contrast to the transverse vortices in the vertical orientation, are most dangerous for a wide range of the value of inclination angles. The most surprising finding is that the inclination of the channel angle by one degree from the vertical orientation is enough to change the spatial structure of disturbances which are responsible for the instability of the basic state.

作为典型的剪切流的例子，我们考虑内部加热的对流在倾斜通道中的两个平行的无限延伸的板。剪切强度由Grashof数参数化，Grashof数测量均匀分布的热源的强度。基本剪切流的稳定性，可以有两个拐点，在其速度分布，检查和随后的非线性状态的数值。在垂直方向的通道的情况下，二次流的形式的二维旅行横向涡出现从基本状态通过一个霍普夫分叉的流体的普朗特数，Pr的值无关，作为Grashof数的增加。我们发现，作为Grashof数进一步增加的二次流失去其稳定性也在一个Hopf分支的流体与Pr=0，使三级流是由三维空间和准周期性的时间。在水的情况下当Pr=7.0时，二次不稳定性与Pr=0时的流体一样由准周期模描述，而在空气中，二次不稳定性由锁相模描述（Pr=0.71）。对通道倾斜情况的研究表明，纵向涡形式的扰动，与垂直方向上的横向涡流相反，对于大范围的倾斜角值来说是最危险的。最令人惊讶的发现是，通道角度从垂直方向倾斜一度足以改变扰动的空间结构，这是造成基态不稳定的原因。