https://scholars.lib.ntu.edu.tw/handle/123456789/81350
標題: | 以重整群分析耦合場紊流模式(II) | 作者: | 張建成 | 關鍵字: | 重整群分析;磁流動力紊流;有效渦度黏滯性;磁阻;Renormalization group analysis;magnetohydrodynamic turbulence;effective eddy viscosity;magnetic resistivity | 公開日期: | 31-七月-2005 | 出版社: | 臺北市:國立臺灣大學應用力學研究所 | 摘要: | 本研究旨在以重整群分析方法研究不可壓縮之耦合磁流場紊流模式,在平均磁導相 較於平均流速為可忽略以及Alfven 效應成立的假設下,透過遞迴重整群程序而建構出 的重整群轉換,可以得到一具有換尺不變性的耦合磁流場方程組,此轉換的固定點在數 學上可被等價成渦漩黏滯力在Fourier 空間中的積微分方程組,藉由此積微分方程組的 求解,發現流場能量光譜與波數的-5/3 次方呈正比關係。而此關係式可進而推導 Kolmogorov 和Smagorinsky 係數與流場特徵波數的關係。 In this study, we continue with a recursive renormalization group (RG) analysis of incompressible turbulence, aiming at investigating various turbulent properties of three-dimensional magneto-hydrodynamics (MHD). In particular, we are able to locate the fixed point (i.e. the invariant effective eddy viscosity) of the RG transformation under the following conditions. (i) The mean magnetic induction is relatively weak compared to the mean flow velocity. (ii) The Alfv´en effect holds, that is, the fluctuating velocity and magnetic induction are nearly parallel and approximately equal in magnitude. It is found under these conditions that re-normalization does not incur an increment of the magnetic resistivity, while the coupling effect tends to reduce the invariant effective eddy viscosity. Both the velocity and magnetic energy spectra are shown to follow the Kolmogorov k−5/3 in the inertial subrange; this is consistent with some laboratory measurements and observations in astronomical physics. By assuming further that the velocity and magnetic induction share the same specified form of energy spectrum, we are able to determine the dependence of the (magnetic) Kolmogorov constant CK (CM) and the model constant CS of the Smagorinsky model for large-eddy simulation on some characteristic wavenumbers. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/21741 | 其他識別: | 932212E002037 | Rights: | 國立臺灣大學應用力學研究所 |
顯示於: | 應用力學研究所 |
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932212E002037.pdf | 228.44 kB | Adobe PDF | 檢視/開啟 |
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