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

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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.