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題 名 | 熱擴散紊流場之重整化研究(1)--隨機微分方程式與廣義Kolmogoroff模型=Renormalization Analysis of Turbulent Thermal-Diffusion Flow(Ⅰ) |
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作 者 | 張建成; 林炳旭; | 書刊名 | 國立臺灣大學工程學刊 |
卷 期 | 74 1998.10[民87.10] |
頁 次 | 頁1-41 |
分類號 | 440.137 |
關鍵詞 | 重整化; 紊流模式; 熱擴散; 平均場; Renormalization; Turbulence models; Thermal-diffusion; Mean field; |
語 文 | 中文(Chinese) |
中文摘要 | 本文主旨在推導紊流場中大尺度及長時間觀察下之各種可能平均場的擴散模式,所考慮的流場為不可壓縮且為單一流向者,紊流模式則為Kolmogorov統計場的推廣形式。文中採用隨機微分方程式的技巧來求解拋物線型偏微分方程式,並將解以Wiener測度表現, 再對其作顯著極限(distinguished limit)上的重整分析,以求得不同尺度觀察下各種可能出現的擴散模式,及其出現之範圍;在數學物理上,擴散行為可解釋為布朗運動,這是一個隨機過程,藉此觀點,可以建構正確的隨機微分方程式,透過隨機微分方程式的表現,我們可以計算各種不同的空尺度下的擴散均行為;其行為的決定由紊流場的二個參數,一為ε:用以量度紅外線發散的速率,另一為z:用以量度紊流場的相關尺度。本文精要地給出必備的知識並為第二部份作準備工作,且整理了Avellaneda和Majda [4] 在紊流場中擴散行為模式的重整化研究。 |
英文摘要 | The article aims to study various diffusion models for turbulent thermal transport at appropriate time and length scales. The flow is assumed to be incompressible and unidirectional, while the turbulence model is rather general that it includes the Kolmogorov spectrum as a special point. For this purpose, renormalization analysis has been carried out with the help of functional representation of the temperature field in terms of the solution to an SDE (stochastic differential equation). From the theory of probability, diffusion behavior may be interpreted as Brownian motion of particles, which enables probabilistic representation of the solution to the turbulent thermal-diffusion equation. Distinguished limits are then obtained by analyzing the solution to yield various diffusion models for the mean temperature fields, depending upon the parameter ε, which measures the rate of infrared divergence and the parameter z, which measures the correlation of the turbulent velocity field. In this part Ⅰ we give a concise account of the necessary background, review some recent work of Avellaneda & Majda [4], and prepare for the further study in part Ⅱ. |
本系統中英文摘要資訊取自各篇刊載內容。