Navier-Stokes equation: irreversibility turbulence and ensembles equivalence
Abstract
The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fields depending on a parameter R (Reynolds number). It is proposed that other equations could lead to -- exactly -- the same distributions via a mechanism closely analogous to the coincidence of the canonical and microcanonical averages of local observables in the statistical mechanics thermodynamic limit (proposed, here, to correspond to the limit in which the UV cut-off N, regularizing the equations, is removed to infinity).
Keywords
Cite
@article{arxiv.1902.09610,
title = {Navier-Stokes equation: irreversibility turbulence and ensembles equivalence},
author = {Giovanni Gallavotti},
journal= {arXiv preprint arXiv:1902.09610},
year = {2019}
}
Comments
4 figures 4 pages. in V.2 FIG 2 and 3 are replaced and footnote 7 im improved. A code error implied incorrect scalings in Fig.2 and 3. V.3 is modified to take into account typos remarked