论文标题
Godbillon-Veave不变，作为拓扑涡度压缩和理想流体中稳定流动的阻塞
The Godbillon-Vey Invariant as Topological Vorticity Compression and Obstruction to Steady Flow in Ideal Fluids
论文作者
论文摘要
如果理想流体的涡度场与叶面相切，则会出现其他保护定律。对于一类零螺旋的涡流场，叶叶的Godbillon-Vey（GV）被定义，被证明是纯粹的涡流的不变性，成为了流动的高阶螺旋型不变性。 GV非零可以使全球拓扑流程构成稳定流动的拓扑障碍，并且以特定形式的局部阻塞。 GV被解释为涡旋线的螺旋压缩和拉伸。如果GV的值由一组杰出的封闭涡流线确定，则给出示例。
If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV non-zero gives both a global topological obstruction to steady flow and, in a particular form, a local obstruction. GV is interpreted as helical compression and stretching of vortex lines. Examples are given where the value of GV is determined by a set of distinguished closed vortex lines.
