Epi-two-dimensional fluid flow: A new topological paradigm for dimensionality
Epi-two-dimensional fluid flow: A new topological paradigm for dimensionality
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外延二维流体流动：一种新的维度拓扑范式
DOI：
10.1103/physrevlett.119.244501
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发表时间：
2017
影响因子：
8.6
通讯作者：
Z. Yoshida and P. J. Morrison
中科院分区：
文献类型：
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作者：
Z. Yoshida and P. J. Morrison
虽然已知将二维（2D）和三维（3D）流体流分开的各种基本差异，但尚不清楚它们如何相关。传统上，降维是由一个先验几何框架来证明的;即，二维流动在一些几何约束下发生，例如浅度。然而，对3D流的更深入的研究经常发现存在没有这种约束的局部2D样结构，其中2D样行为可以通过涡线的可积性或消失的局部螺旋度来识别。在这里，我们提出了一个新的范式的流结构，通过引入一个中间类，称为epi-two-dimensional流，从而建立一个拓扑之间的桥梁2D和3D流。epi-2D特性是局部的，并且在服从理想（无粘和正压）力学的流体元素中被保留;局部epi-2D流可以被视为携带广义拟能作为其电荷的“粒子”。有限的粘度可能会导致两个epi-2D粒子的“融合”，从它们的电荷产生螺旋性，从而产生3D流动。
While a variety of fundamental differences are known to separate two-dimensional (2D) and three-dimensional (3D) fluid flows, it is not well understood how they are related. Conventionally, dimensional reduction is justified by ana priorigeometrical framework; i.e., 2D flows occur under some geometrical constraint such as shallowness. However, deeper inquiry into 3D flow often finds the presence of local 2D-like structures without such a constraint, where 2D-like behavior may be identified by the integrability of vortex lines or vanishing local helicity. Here we propose a new paradigm of flow structure by introducing an intermediate class, termed epi-two-dimensional flow, and thereby build a topological bridge between 2D and 3D flows. The epi-2D property is local and is preserved in fluid elements obeying ideal (inviscid and barotropic) mechanics; a local epi-2D flow may be regarded as a “particle” carrying a generalized enstrophy as its charge. A finite viscosity may cause “fusion” of two epi-2D particles, generating helicity from their charges giving rise to 3D flow.