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題 名 | 熱擴散紊流場之重整化研究(2)--廣義熱擴散方程式與廣義混合流方程式=Renormalization Analysis of Turbulent Thermal-Diffusion Flow (Ⅱ) |
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作 者 | 林炳旭; 張建成; | 書刊名 | 國立臺灣大學工程學刊 |
卷 期 | 75 1999.02[民88.02] |
頁 次 | 頁1-29 |
分類號 | 440.137 |
關鍵詞 | 換尺操作; 重整化; 紊流模式; 熱擴散; 平均場; 混合式; 相變; Scaling analysis; Renormalization; Thermal-diffusion; Mean field; Phase transition; |
語 文 | 中文(Chinese) |
中文摘要 | 此部份承續第一部份之重整化分析,並加以推廣,得到一個三維之廣 義擴散模式下的相變化圖 (phase diagram) 此處除了z之外,新一個微分次冪參 數 蛂C相變化圖被劃分成五個不等的空間,第一區到第三區表現正規擴散行 為,第四區出現超擴散模式,其中第一區的範圍固定,其餘四區的範圍會隨著 微分冪次因子的大小而變,其中第五區中的擴散模式無法尋得一好的逼近模式, 所以是一個擴散模式不可局部界定的區域;將此結果與Avellaneda和Majda [2~4] 的理論結果比較發現,在正規擴散範圍內我們的尺度分析結果在微分冪次因子 區近於1時為平穩的,沒有出現激變性的不穩定性 (catastrophically unstable), 而在超擴散範圍內兩者理論是相容的;此外,於文中計算分析混合流方程式的 相變化,所考慮之混合流方程式仍以廣義模式呈現,在此模式下是必須處理具 有源項的廣義擴散方程,為了尋求其顯著極限,在做法上,先透過格林積分等 式來處理此源項,再藉助Kac公式去對應出其顯著極限模式,所得結果為一個 三維的相變化圖,其中不同相的區域範圍與廣義擴散方程式者相同。 |
英文摘要 | This part continues the renormalization analysis of Part I and makes substantial extension of it. Besides ??and z, the new added parameter is a fractional power ??of the differential operator; the resulting equation is called the generalized thermal-diffusion equation. The main result is a generalized phase diagram in the ??z-??space, which is divided to five regions according to the mean diffusion model obtained. The region I is fixed in the parameter space, while the other four regions depend on the fractional power ?? The behaviors in region I ~ III are normal-diffusion, while in IV, we have super-diffusion; however, region V is one where a local diffusion model cannot be well defined. Compared to the results of Avellaneda and Majda [2~4], it is found that (1) our scaling analysis for super-diffusion would yield results consistent with theirs as the fractional power ??tends to 1, while (2) contrary to their results, our scaling analysis shows a smooth transition instead of a catastrophical instability. In addition, this part deals with the problem of phase transition for a generalized model equation of mixed conduction and diffusion. The distinguished feature of the generalized model is a source term which can be handled with an appropriately chosen Green's function. Kac's formula is then employed to help carrying out the renormalization analysis; this yield also a three-dimensional phase diagram in the parameter space. The phase diagram is identical to that obtained for the generalized thermal- diffusion equation. |
本系統中英文摘要資訊取自各篇刊載內容。