论文标题
指数的饱和度和渐近的第四个湍流状态
The saturation of exponents and the asymptotic fourth state of turbulence
论文作者
论文摘要
关于均质和各向同性湍流的惯性范围的最新发现是缩放指数$ζ_n$的饱和，用于大$ n $，通过$ n $的结构函数定义为$ n $ aS $ s_ {n}（r）= \ overline = \ overline {（Δ_ru）{（δ_ru）我们专注于$Δ_Ru $的纵向结构在两个位置之间的$δ_ru $ $ $ $ $ $ $ $ $。在以前的论文（Phys。V。\ fluids 6，104604，2021）中，我们开发了一个用于$ζ_N$的理论，该理论与所有可靠数据的$ n $相符，并显示出可靠的$ N $，并显示了大型$ n $的饱和度。在这里，我们为四种不同的湍流状态（包括对应于大型$ n $的指数的饱和度对应的渐近式第四状态，包括$Δ_Ru $ $Δ_ru $的概率密度函数的表达式。这种饱和度意味着尺度分离是违反了强键耦合的准级流结构的，该结构的形式为长而薄（类似蠕虫的）长度$ l $和厚度$ l = o（l/re）$的结构。
A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents $ζ_n$ for large $n$, defined via structure functions of order $n$ as $S_{n}(r)=\overline{(δ_r u)^{n}}=A(n)r^{ζ_{n}}$. We focus on longitudinal structure functions for $δ_r u$ between two positions that are $r$ apart in the same direction. In a previous paper (Phys.\ Rev.\ Fluids 6, 104604, 2021), we developed a theory for $ζ_n$, which agrees with measurements for all $n$ for which reliable data are available, and shows saturation for large $n$. Here, we derive expressions for the probability density functions of $δ_r u$ for four different states of turbulence, including the asymptotic fourth state corresponding to the saturation of exponents for large $n$. This saturation means that the scale separation is violated in favor of a strongly-coupled quasi-ordered flow structures, which take the form of long and thin (worm-like) structures of length $L$ and thickness $l=O(L/Re)$.
