论文标题
通过分形强迫诱导二维湍流的反向级联反向级联
Inducing intermittency in the inverse cascade of two dimensional turbulence by a fractal forcing
论文作者
论文摘要
我们证明，就像在三维湍流的正向级联中一样，由于能量耗散的集中在一组小于三个小于三个小于三个的分形尺寸中，由于能量耗散的浓度浓度（缺乏自相似度），如果二维湍流的逆级联反向级联也可能缺乏二维湍流，这也可能表现出较小的毛线限制，而不是限制了两者的缩小范围。使用相同的强迫长度尺度但不同的分形尺寸$ d $的不同强迫函数对二维湍流进行了一系列数值模拟，该功能与经典$ d = 2 $ case doint vortex case $ d = 0 $不同。结果表明，由于强迫的分形维度从$ d = 2 $降低，因此自相似性丢失并出现间歇性，而不同结构函数的缩放$ \ langle |ΔU_\ |^p | \ rangle \ propto r^{ζ_P} $与维度分析预测$ζ_P= p/3 $不同。因此，本模型提供了一个独特的示例，即间歇性受到控制，因此可以散发光线并为多骨湍流模型提供测试床。
We demonstrate that like in the forward cascade of three dimensional turbulence that displays intermittency (lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two dimensional turbulence are examined, using different forcing functions of the same forcing length-scale but different fractal dimension $D$ that varies from the classical $D=2$ case to the point vortex case $D=0$. It is shown that as the fractal dimension of the forcing is decreased from $D=2$, the self-similarity is lost and intermittency appears, with the scaling of the different structure functions $\langle |δu_\|^p| \rangle\propto r^{ζ_p}$ differs from the dimensional analysis prediction $ζ_p=p/3$. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multi-fractal models of turbulence.
