论文标题
识别能量在湍流中消散的多型套件
Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluid
论文作者
论文摘要
巴黎和弗里奇（Parisi and Frisch）的作品所说明的流体湍流的丰富多重分子特性与三维纳维尔 - 斯托克斯方程的Leray弱解明显相关。直接从这种对应关系中可以发现，能量消散的集合，$ \ mathbb {f} _ {m} $，具有一系列尺寸$ \ dim = 3/m $（$ 1 \ leq m \ leq \ leq \ leq \ infty $），以及子kolmogorov upptersipation uppersever inversever unverse colvers unvevers unverse calleper unvewers $ l l l或1 re^{3/（1+ \ dim）} $ spanning $ re^{3/4} $ to $ re^{3} $。相应地，使用$ - \ twothirds \ leq h_ {min} \ leq \ leq \ third $ cosey $ h \ geq h_ {min} $必须服从$ h \ geq h_ {min} $。
The rich multifractal properties of fluid turbulence illustrated by the work of Parisi and Frisch are related explicitly to Leray's weak solutions of the three-dimensional Navier-Stokes equations. Directly from this correspondence it is found that the set on which energy dissipates, $\mathbb{F}_{m}$, has a range of dimensions $\Dim=3/m$ ($1 \leq m \leq \infty$), and a corresponding range of sub-Kolmogorov dissipation inverse length scales $Lη_{m}^{-1} \leq Re^{3/(1+\Dim)}$ spanning $Re^{3/4}$ to $Re^{3}$. Correspondingly, the multifractal model scaling parameter $h$, must obey $h \geq h_{min}$ with $-\twothirds \leq h_{min} \leq \third$.
