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

本文首先对风洞湍流边界层是否为二维湍流进行了研究，证实了风洞湍流边界层具有完全二维的平均速度分布和脉动速度分布。由于KL展开式需要多点同时测量，我们构造了24通道热线风速计，并利用超级计算机实现了热线风速计的线性化。我们还制作了一个24线的探针，每根线的距离为1 mm，这大约是泰勒微米尺度。用该探头测量了湍流边界层中的多点关联，计算了KL展开的基。由该展开式可以重建瞬时速度分布，对识别三维结构是有用的，但对空间结构识别存在问题。其次，采用随机微分方程来模拟湍流.我们使用分数布朗噪声作为随机项，并将其用于连续性，以获得-5/3谱和连续性。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。本文采用三阶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。该模型具有与实验一致的自相似性，并确定了断面上的浓度分布。

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.