A Study of Dynamical Expression of Turbulence Using K-L Expansion and Stochastic Differential Eqation

首先研究了风洞的湍流边界层是否为正则二维湍流，证实了其具有完全二维的平均速度分布和脉动速度分布。由于KL-Expansion需要多个点的同时数据，我们构建了24通道热线风速仪，其线性度由超级计算机获得。我们还制作了24根探头，每根探头的直径约为1 mm，约为泰勒微尺度。利用该探头测量了湍流边界层中的多点相关，并计算了KL展开的基础。由该展开式可以重建瞬时速度分布，这对于识别中间结构是有用的，但对于空间结构识别是有问题的。其次，采用随机微分方程组模拟湍流。我们使用分数布朗噪声作为随机项，并成功地获得了-5/3谱和间歇性。为了比较概率密度，引入了Kullback散度，并首次证明了它对湍流的有效性。采用三维pdf方法对管流中的湍流扩散进行了数值模拟，并与实验结果进行了比较。结果表明，该模型与实验结果具有较好的自相似性，并确定了截面浓度分布。

Firstly the turbulent boundary layr of our wind tunnel is investigated whether it is canonical two dimensional turbulent flow or not and we confirmed it has complete two dimensionality of mean and fluctuating velosity distributions. Since KL-expansion needs multi points same time data, we constructed 24-channels hot wire anemometers of which linearity is obtained using super computer. Also we made a 24 wires probe, each wire having disetance 1mm which is approximately Taylor microscale. Using this probe the multi points correlation in the turbulent boundary layr is measured and the basis of KL-expansion is calculated. From this expansion instantaneous velocity distribution can be reconstructed and it shows usefulness to identify temral structure but problems for spatial structure identification. Secondary a stochastic differential eqation is assumed to simulate turbulence. We used fractional Brownian noise for the stochastic term and suceeded to obtain -5/3 spectrum and intermittency. In order to compare probability densities Kullback divergence is introduced and it is shown its effectiveness for the turbulence for the first time. Thirdry pdf method is applied for the simulation of turbulent diffusion in pipe flow and compared the experimental results. It shows self-similality in agreement with the experiment and it determined concentration distribution in sections.