论文标题
全面发育的湍流中间歇性的体积理论
Volumetric theory of intermittency in fully developed turbulence
论文作者
论文摘要
这项研究介绍了一个新的体积平坦因子系列，从而对完全发达的湍流中的间歇性现象进行了严格的参数描述。这些数量收集了有关每个比例$ \ ell $在速度字段中最“活跃”部分的信息，并允许一个人定义一个尺寸函数$ p \ to d_p $，该函数将间歇性校正恢复到结构指数$ζ_P$以显式方式。特别是，可以以系统和严格的方式回收弗里氏多纹状体形式主义的预测。 在此框架内，我们确定在给定比例$ \ ell $的速度字段中最有能力的部分的活动区域。明确定义了构成活性的阈值。在我们以前的联合工作\ cite {ph-paper}中，活跃区域已被证明是可以观察到的，并证明可以将能量级联的浓度捕获为$ \ ell \ to 0 $，in \ cite {cs2014}。 我们介绍了几个在理论上允许的限制内显示任意多重频谱的场的示例。同时，我们证明了使用概率论证的使用，即预计随机字段将在限制$ \ ell \ to 0 $的情况下产生经典的K41频谱。与K41理论的间歇性偏差也以任何有限尺度估算。 最后，我们对引入对象进行了详细的信息理论分析。特别是，我们根据体积因子，阈值和活动区域来量化给定源场的浓度。
This study introduces a new family of volumetric flatness factors which give a rigorous parametric description of the phenomenon of intermittency in fully developed turbulent flows. These quantities gather information about the most "active" part of a velocity field at each scale $\ell$, and allows one to define a dimension function $p \to D_p$ that recovers intermittency correction to the structure exponents $ζ_p$ in an explicit way. In particular, the predictions of the Frisch-Parisi multifractal formalism can be recovered in a systematic and rigorous way. Within this framework we identify active regions that carry the most energetic part of a velocity field at a given scale $\ell$. A threshold for what constitutes to be active is defined explicitly. Active regions have proven to be experimentally observable in our previous joint work \cite{Ph-paper}, and shown to capture concentration of the energy cascade as $\ell \to 0$, in \cite{CS2014}. We present several examples of fields which exhibit arbitrary multifractal spectrum within theoretically permitted limitations. At the same time we demonstrate with the use of a probabilistic argument that a random field is expected to produce the classical K41 spectrum in the limit $\ell\to 0$. Intermittent deviations from K41 theory are estimated at any finite scale also. Lastly, we present a detailed information-theoretic analysis of the introduced objects. In particular, we quantify concentration of a given source-field in terms of the volume factors, thresholds, and active regions.
