Fractal-generated turbulence
Fractal-generated turbulence
复制标题
分形产生的湍流
DOI：
10.1017/s0022112003007249
复制
发表时间：
2004
影响因子：
3.7
通讯作者：
J. C. Vassilicos
中科院分区：
文献类型：
--
作者：
B. Mazzi;J. C. Vassilicos
提出了一种适用于稳态、均匀和各向同性湍流直接数值模拟的分形强迫模型。这种强迫的功率谱是波数的幂律函数，其指数为正，是分形搅拌子的分形维数D_{f}$的增函数。对于受分维为D_f的完全自相似分形强迫作用的DNS湍流，得到了下列结果。(i)泰勒和Kolmogorov微尺度是成比例的，彼此和分形强迫的最小长度尺度。(ii)由于分形强迫产生非常不规则的速度场，积分长度尺度比DNS盒的尺寸L_B$小得多，并且是分形强迫范围的递减函数。(iii)在定性（但不是定量）协议与重整化群（RG）理论的湍流，更高的值$D_f$导致增加的能量在最高波数。(iv)能量谱、能量输入率谱和尺度间能量传递T（k）都与湍流均方根值成比例关系。速度$u '$和泰勒微尺度$\lambda$。(v)总耗散的80%以上发生在L_B ~ 1 ~ 2倍Taylor微尺度的分形强迫范围内。在这个范围内，$T（k）$可以忽略不计。(vi)$\lambda \，{\sim}\，\nu/u '$（其中$\nu$为运动粘度）、单位质量动能耗散率$\lambda\，{\sim}\，u'^{3}/\lambda \，{\sim}\，u '^{4}/\nu$以及速度导数偏度$S$在雷诺数和分形强迫范围同时增大的极限范围内与雷诺数无关。(vii)应变率张量的中间特征值平均为正，并且在分形强迫范围内的$T（k）$的值可以忽略不计，与仅在大尺度上强迫的湍流相比，伴随着$S$的较低值和局部压缩的显著减少。（viii）涡量、应变率张量本征向量和涡拉伸向量之间的几何对齐在性质上与湍流中一样，只在大尺度上受迫，但明显减弱。(ix)速度增量的p.d.f.s在柯尔莫哥洛夫和积分长度尺度之间的所有尺度上都是近似高斯的，尽管不是精确的。一些初步的DNS结果也给出了由分形强迫离散，而不是完全，自相似的湍流的情况下。
A model fractal forcing for direct numerical simulations (DNS) of stationary, homogeneous and isotropic turbulence is proposed. The power spectrum of this forcing is a power-law function of wavenumber with a positive exponent that is an increasing function of $D_{f}$, the fractal dimension of the fractal stirrer. The following results are obtained for DNS turbulence subjected to fully self-similar fractal forcing of fractal dimension $D_f$. (i) The Taylor and Kolmogorov microscales are proportional to each other and to the smallest length scale of the fractal forcing. (ii) The integral length scale is much smaller than the size $L_b$ of the DNS box and a decreasing function of the extent of the fractal forcing range because fractal forcing generates very irregular velocity fields. (iii) In qualitative (but not quantitative) agreement with renormalization group (RG) theories of turbulence, higher values of $D_f$ lead to increased energy at the highest wavenumbers. (iv) The energy and energy input rate spectra and the inter-scale energy transfer $T(k)$ all scale with the turbulence r.m.s. velocity $u'$ and the Taylor microscale $\lambda$. (v) More than 80% of the total dissipation occurs in the fractal forcing range of scales which extends from $L_b$ to about one to two times the Taylor microscale. In that range, $T(k)$ is negligible. (vi) $\lambda \,{\sim}\, \nu/u'$ (where $\nu$ is the kinematic viscosity), the kinetic energy dissipation rate per unit mass $\epsilon \,{\sim}\, u'^{3}/\lambda \,{\sim}\,u'^{4}/\nu$ and the velocity derivative skewness $S$ is independent of Reynolds number in the limit where the Reynolds number and the fractal forcing range are increased together. (vii) The intermediate eigenvalue of the strain rate tensor is on average positive, and the negligible values of $T(k)$ in the fractal forcing range are accompanied by lower values of $S$ and a significant reduction in local compression by comparison to turbulence forced only at the large scales. (viii) The geometrical alignments between vorticity, strain rate tensor eigenvectors and vortex stretching vector are qualitatively as in turbulence forced only at the large scales but significantly weakened. (ix) The p.d.f.s of velocity increments are approximately, though not exactly, Gaussian at all scales between the Kolmogorov and integral length scales. A few preliminary DNS results are also given for the case of turbulence generated by a fractal forcing that is discretely, as opposed to fully, self-similar.