The local topology of stream- and vortex lines in turbulent flows
The local topology of stream- and vortex lines in turbulent flows
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DOI：
10.1063/1.4871097
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发表时间：
2014-04
影响因子：
4.6
通讯作者：
J. Boschung;P. Schaefer;N. Peters;C. Meneveau
中科院分区：
文献类型：
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作者：
J. Boschung;P. Schaefer;N. Peters;C. Meneveau
给定矢量场的切线，如流线或涡线，定义了一个局部单位矢量t，它指向直线方向的任何地方。线的局部行为由张量T= λ·t的本征值表征。在真实的特征值的情况下，t可以被解释为表面元素的法向量，其形状由T的特征值定义。这些特征值可以用来定义曲面的平均曲率−H和高斯曲率K。平均曲率−H描述了表面元素沿着磁力线面积的相对变化，是磁力线局部相对收敛或发散的度量。（H，K）的不同值决定了场线是收敛还是发散（椭圆凹面或椭圆凸面元素，稳定/不稳定节点），在一个主方向上收敛而在另一个主方向上发散（鞍形），还是向内或向外螺旋（稳定/不稳定焦点）。在湍流中，过多的局部场线拓扑结构是…
Tangent lines to a given vector field, such as streamlines or vortex lines, define a local unit vector t that points everywhere in the line's direction. The local behavior of the lines is characterized by the eigenvalues of the tensor T=∇·t. In case of real eigenvalues, t can be interpreted as a normal vector to a surface element, whose shape is defined by the eigenvalues of T. These eigenvalues can be used to define the mean curvature −H and the Gaussian curvature K of the surface. The mean curvature −H describes the relative change of the area of the surface element along the field line and is a measure for the local relative convergence or divergence of the lines. Different values of (H, K) determine whether field lines converge or diverge (elliptic concave or elliptic convex surface element, stable/unstable nodes), converge in one principal direction and diverge in another (saddle) or spiral inwards or outwards (stable/unstable focus). In turbulent flows, a plethora of local field line topologies are ...