2017/02/15 by Jian-Zhou Zhu, Zhu, Jian-Zhou
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fluid Dynamics and Turbulent Flows #Phase Equilibria and Thermodynamics #math-ph #math.MP #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1702.04447
this and previous versions contain some technical error which will be fixed a bit later; closely relevant remarks concerning the virtual velocity are given in the appendix (A.2) of jfm14hydrochirality paper arXiv:1303.3823 and in the pof18Lie paper arXiv:1709.03356 Sec. III
arxiv created 2018/03/28 · arxiv updated 2018/03/29
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 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.