國立臺灣大學應用力學研究所張建成2006-07-262018-06-292006-07-262018-06-292000-07-31http://ntur.lib.ntu.edu.tw//handle/246246/21587本研究旨在以重整群分析方法研究不可壓縮之紊流場，在大尺度渦漩與小尺度渦漩為統計之獨立的假設下，我們可以建立一個遞迴重整群的程序，而建構出重整群轉換，在此轉換下得到一具有換尺不變性的Navior-Stokes 方程，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式，藉由此積微分方程式的求解，發現渦漩黏滯力光譜與流場波數的-4/3 次方呈正比的關係，以及流場能量光譜與波數的-5/3 次方呈正比關係， 此外， 此解亦可進而推導出Smagorinsky 模型， 並且精確指出Smagorinsky 常數與隔點大小以及流場特徵波數的關係。The study starts with a brief review on recent development of renormalization group analysis for incompressible turbulence. It is found fruitful to take the simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A recursive renormalization procedure is then proposed for turbulence governed by the Navier-Stokes equation in an exact manner that a nonlinear triple term appearing in early treatment can be dispensed with in the present formulation. By employing the combined form of the scaling laws proposed respectively by Pao and Leslie \& Quarini for the energy spectrum, the relevant exponents for the spectrum are completely determined. Furthermore, the limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivation of the Smagorinsky model for large-eddy simulation of turbulent flow, which reveals the explicit dependence of the model constant on the cutoff size and other characteristic wavenumbers.application/pdf42209 bytesapplication/pdfzh-TW國立臺灣大學應用力學研究所紊流重整群渦漩黏滯力Kolmogorov 常數流場能量光譜大尺度渦漩模擬Smagorinsky 模型turbulencerenormalization groupeffective eddy viscosityKolmogorov constantenergy spectrumlarge-eddy simulationSmagorinsky model.reporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/21587/1/892212E002067.pdf