论文标题
最大渗透湍流能光谱的缩放
Scaling of the Maximum-Entropy Turbulence Energy Spectra
论文作者
论文摘要
根据最大熵原理得出的湍流能谱函数的对数正态分类型，在包括雷诺数（雷诺数）的根湍流变量方面被证明是可参数化的。首先将光谱函数与许多实验数据集进行比较，显示了整个能量和长度（波数）尺度的非常紧密的一致性。当雷诺数增加时，峰值波数（M）和宽度参数（C2）分别规定了光谱位置和扩展，其中C2具有〜1/REM依赖性。能量量表以乘法因子进行调整。从这个角度来看，当分别为两个和三维湍流的尺度范围增加，频谱宽度的增加，从k-3到K-5/3的惯性尺度从两维转变为频谱宽度的增加时，从K-3到K-5/3的惯性缩放被解释为光谱宽度的增加。通道流中各个位置的能量光谱也使用相同的函数再现，这表明在局部均衡的任何地方都适用。因此，基于少量缩放参数，可以使用最大透镜形式形式规定完整的能量光谱。
The log-normal type of turbulence energy spectral function, derived from the maximum entropy principle, is shown to be parameterizable in terms of root turbulence variables including the Reynolds number. The spectral function is first compared with a number of experimental data sets, showing a very close agreement across the entire energy and length (wavenumber) scales. The peak wavenumber (m) and the width parameter (C2) prescribe the spectral location and broadening, respectively, when the Reynolds number increases, where C2 has ~ 1/Rem dependence. The energy scale is adjusted with a multiplicative factor. In this perspective, the inertial scaling from k-3 to k-5/3 when the flow transitions from two- to three-dimensions is explained as the increase in spectral width since the range of scales increases as Re1/6 and Re3/4 for two and three-dimensional turbulence, respectively. Energy spectra at various locations in channel flows are also reproduced using the same function, indicating applicability wherever local equilibrium is achieved. Therefore, based on a small number of scaling parameters the full energy spectra can be prescribed using the maximum-entropy formalism.
