非理想系统的拓扑流体力学与虚拟冻结动力学
On topological fluid mechanics of non-ideal systems and virtual frozen-in dynamics
摘要：
欧拉和纳维尔-斯托克斯有不同的系统，它们具有螺旋度的动力学不变性，因此具有（弱）拓扑等价性，允许一种强的“冻结”（到，或者，双重地，由\textit{virtual}速度$V$“携带”）涡度公式，带有“逆亥姆霍兹定理”的味道。本文对具有动力学时间可逆性和螺旋度不变性的非理想（统计）拓扑流体力学（TFM），（1）Constantin-Iyer形式的Navier-Stokes方程，（2）我们自己的具有能量螺旋度约束的修正Navier-Stokes方程的Gallavotti-Cohen型动力学系综的推广，（3）Galerkin截断Euler方程作了评述.因此，理想的TFM与非理想流桥接。本文以一个伽辽金截断欧拉系统中的涡量虚（Lie-）载体为例，讨论了如何确定$V$的问题。
英文摘要：
Euler and Navier-Stokes have variant systems with dynamical invariance of helicity and thus (weak) topological equivalence, allowing a strong `frozen-in' (to, or, dually, `Lie-carried' by the \textit{virtual} velocity $V$) formulation of the vorticity with a flavor of `inverse Helmholtz theorem'. We remark on the non-ideal (statistical) topological fluid mechanics (TFM) for (1) the Constantin-Iyer formulation of Navier-Stokes, (2) our own extension of the Gallavotti-Cohen type dynamical ensembles of modified Navier-Stokes with energy-helicity constraints and (3) the Galerkin truncated Euler, as the typical case variants with dynamical time reversibility and helicity invariance. Ideal TFM is thus bridged with non-ideal flows. An example virtual (Lie-)carrier of the vorticity in a Galerkin-truncated Euler system is calculated to demonstrate the issue of determining $V$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
