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- 阻塞研究--第一部份:魔子(Modon)穩定度之分析
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題 名 | 阻塞研究--第一部份:魔子(Modon)穩定度之分析 |
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作 者 | 洪志誠; 林和; | 書刊名 | 大氣科學 |
卷 期 | 22:2 1994.06[民83.06] |
頁 次 | 頁297-318 |
分類號 | 328.2 |
關鍵詞 | 阻塞; 瞬變擾動; 魔子; 有界的; 李亞普諾夫直接法; 均向性; Blocking; Transient eddies; Modon; Bounded; Liapunov direct method; Isotropy; |
語 文 | 中文(Chinese) |
中文摘要 | 阻塞研究中,魔子(Modon)結構是區域理論較嚴謹的一支,數值實驗及觀測皆獲得有力支持。此外,瞬變擾動(2-8天)維持阻塞的生命,亦獲得不少觀測證據。本文嚐試結合這兩支研究於一爐,從理論,數值實驗及觀測三方面探討其可行性及局限。 若將魔子視為阻塞的零階近似(zero-order approximation)解,假設魔子動力結構之穩定性是阻塞持續的主要原因。而次一階(first-order)的瞬變渦流對阻塞應為穩定擾動,魔子分流場可以有效率得吸收瞬變渦流之能量,抵抗摩擦消耗,延長阻塞生命。由於瞬變渦流在魔子的初期演化屬於初始值問題,同時包括連續波譜(continuous spectrum)與離散正模(discrete normal mode)的演化。我們將以李亞普諾夫(Liapunov)直接法分析魔子穩定度,找出穩定的充要條件。 若假設擾動為均向,根據阿諾(1965)理論,以李亞普諾夫函數二次變分(δ²L)是否為負定鑑定穩定度。計算得到魔子不穩定的臨界波長大約4000公里,依此標準瞬變渦流屬於穩定類型的擾動。當擾動為非均向,我們首先以擾動的能譜重心決定擾動的非均向性([9465]定義見內文),然後從數值實驗歸納得到,對相同平均尺度(δ²L<0)之擾動,如果非均向性大於1([9465]>1)為不穩定;小於1([9465]<1)為漸進穩定;等於1([9465]=1)為中性穩定。能譜分析顯示瞬變渦流的非均向性小於1,滿足穩定的條件。 |
英文摘要 | In blocking studies, the modon theory is one of the more rigorous approachs along the line of local structure. It was supported convincingly by the results from the numerical experiments and observations. On the other side, the maintainency of blocking needs the feedback mechanism of transient eddies (2-8 days). These are also evidences supported the transient-eddy theory. In this paper we tried to merge these two theories into one consistent conjecture. We investigated theoretical, numerical and observational aspects, explored the feasibility and limitation of our hypothesis. The modon solution is treated as the zero-order approximation of blocking structure. The longevity of moden will be accounted entirely from the view of stability analysis. The transient eddies, the first-order approximation are incapable of drawing energy from the main structure. On the contrary, if asymptotically stable condition is satisfied, the confluence of modon flow can drain the eddies energy very effectively. By compensating the dissipation, and it's existence will be extended. The downstream variation of modon solution destroys Hermitianity, hence it calls to consider both discrete modal solution and continuous spectrum. The stability study becomes an initial-value problem. We took the Liapunov approach, to find the necessary and sufficient conditions for modon's stability. Suppose initial disturbances are isotropic, following Arnold's theory, the second variation of Liapunov function provides the stability criterion. The critical wave length for unstable eddies is near 400km. The isotropic eddises shorter than this length cannot destabilize the modon. But if the disturbances are anisotropic, the anisotropy can be measured by a parameter ε (see context), decided by the weighting of energy spectrum, it is found that, even when the eddies with the same averaged scale, the flow becomes unstable when ε>1, neutral stable when ε=1 and stable when ε<0. |
本系統中英文摘要資訊取自各篇刊載內容。