论文标题
平面线性流的几何形状
The geometry of planar linear flows
论文作者
论文摘要
我们确定不可压缩的平面线性流，这些流量是众所周知的单参数家族的概括，其特征在于平面延伸与（平面外）涡度的比例。后者的“规范”家族分别分别为椭圆形和双曲线线性流，分别用封闭和开放的流线分类为相对于延伸与涡度的比率较小或大于统一性。统一是简单剪切流的边际情况。新颖的流动具有平面外扩展，但是流线可能仍然是封闭或开放的，使组织在三维参数空间中允许组织进入“怪异”椭圆形和多重流动流的区域，并通过简单的寄生虫流动线的变性线性流的表面分离出来，具有简单的shear的概括。我们讨论对各种流体机械场景的影响。
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into elliptic and hyperbolic linear flows with closed and open streamlines, respectively, corresponding to the extension-to-vorticity ratio being less or greater than unity; unity being the marginal case of simple shear flow. The novel flows possess an out-of-plane extension, but the streamlines may nevertheless be closed or open, allowing for an organization, in a three-dimensional parameter space, into regions of `eccentric' elliptic and hyperbolic flows, separated by a surface of degenerate linear flows with parabolic streamlines that are generalizations of simple shear. We discuss implications for various fluid mechanical scenarios.
