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.

作为典型剪切流的示例，我们考虑具有两个无限延伸的平行板的倾斜通道中的内部加热对流。剪切强度由测量均匀分布热源强度的格拉霍夫数参数化。检查基本剪切流的稳定性（其速度分布中可能有两个拐点），并以数值方式跟踪随后的非线性状态。在通道垂直方向的情况下，无论流体的普朗特数 Pr 的值如何，二维行进横向涡旋形式的二次流都会通过 Hopf 分岔从基本状态中出现，如 Grashof数量增加。我们发现，随着格拉霍夫数的进一步增加，对于 Pr=0 的流体，二次流在 Hopf 分岔中也失去了稳定性，因此三次流在空间上呈现出三维性，在时间上呈现出准周期性。在水 (Pr=7.0) 的情况下，二次不稳定性由准周期模式描述，与 Pr=0 的流体情况一样，而在空气的情况下，不稳定性由锁相模式来表征 ( Pr=0.71）。将调查扩展到通道倾斜方向的情况表明，与垂直方向的横向涡流相比，纵向涡流形式的扰动对于多种情况来说是最危险的。倾斜角的值。最令人惊讶的发现是，通道角从垂直方向倾斜一度就足以改变扰动的空间结构，而扰动是造成基本态不稳定的原因。