论文标题
在湍流的局部能量通量上
On the local energy flux of turbulent flows
论文作者
论文摘要
我们使用直接的数值模拟并应用不同的低通滤波器研究了各向同性湍流流中的小尺度，我们将局部能量通量率$π_\ ell（\ bf x）$研究。检查了两个不同的过滤器，一个尖锐的傅立叶过滤器和一个高斯滤波器。计算针对不同过滤器和不同过滤量表的局部能量通量的概率密度函数（PDF）。结果表明，局部能量通量在很大程度上波动的数量既有负值和正值，这对于锋利的滤波器更为明显。这些波动的差异，偏度和峰度被证明随着滤波量表的降低而增加。此外，我们将$π_\ ell（\ bf x）$的关节pdf与本地过滤的应变率$ s_ \ ell $和endstrophy $ω__\ ell $。通量与菌株有良好的相关性，但与腹部没有良好的相关性。结果表明，其条件平均值尺度如$ <{π_\ ell}> _ s \ propto \ ell^2 s_ \ ell^{3} $支持Smagorinsky Eddy粘度模型。尽管如此，也需要对此值进行建模，但存在强烈的波动。我们讨论了结果对子网格量表模型的含义，并提出了新的建模方向。
We investigate the local energy flux rate $Π_\ell(\bf x)$ towards small scales in isotropic turbulent flows using direct numerical simulations and applying different low-pass filters. Two different filters are examined, a sharp Fourier filter and a Gaussian filter. The probability density function (pdf) of the local energy flux is calculated for the different filters and for different filtering scales. It is shown that the local energy flux is a largely fluctuating quantity taking both negative and positive values and this is more pronounced for the sharp filter. The variance, the skewness and the kurtosis of these fluctuations are shown to increase as the filtering scale is decreased. Furthermore we calculate the joint pdf of $Π_\ell(\bf x)$ with the local filtered strain rate $S_\ell$ and the enstrophy $Ω_\ell$. The flux shows a good correlation with the strain but not with the enstrophy. It is shown that its conditional mean value scales like $<{Π_\ell}>_S \propto \ell^2 S_\ell^{3} $ in support to the Smagorinsky eddy viscosity model. Nonetheless strong fluctuations exist around this value that also need to be modeled. We discuss the implications of our results for subgrid scale models, and propose new modelling directions.
