中性流体和二流体等离子体非理想流动中的局部不变量
Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas
摘要：
局部结构，超出了众所周知的'冻结'的广义涡度的正压流动，双流体模型的等离子体流。更一般的非正压情况也被认为是。一个改进的欧拉方程[T. Tao，Ann. PDE \textbf{2}，9（2016）]也相应地从双流体模型的视角进行了分析和评论，重点是局部结构。而且，局部约束的高阶微分形式，如螺旋度，除其他外，找到简单的配方可能的应用建模的动态。因此，柯西不变量方程[N。贝斯和U。Frisch，J.Fluid \textbf{825}，412（2017）]可以在非理想流中找到实际应用。特别有趣的是，二维三分量（2D3C）或二维被动标量问题提出了一个局部不变的$Θ= 2θζ$，其中$θ$和$ζ$分别是“垂直速度”的标量值（或被动标量）和“垂直涡度”，可以被用作好像它是全球不变螺旋度的空间密度，提供了一个拉格朗日处方，以控制后者在某些情况下，研究其物理效应的快速旋转流（普遍存在于大气中的天体物理对象）与显着的2D3C涡模或纯二维被动标量。
英文摘要：
Local structures, beyond the well-known `frozen-in' to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, Ann. PDE \textbf{2}, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of two-fluid model, with emphasis on the local structures. And, the local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible applications in modelling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, J. Fluid Mech. \textbf{825}, 412 (2017)] may find practical application in non-ideal flows. Some formal examples are offered to outline the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant $Θ= 2θζ$, with $θ$ and $ζ$ being respectively the scalar value of the `vertical velocity' (or the passive scalar) and the `vertical vorticity', may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.
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