平衡渦旋模型之熱與動量動力效率

Abstract

觀測資料顯示眼牆置換(ERC) 過程會產生不同的結果。Kuo et al. (2009) 發現在置換過程結束後， 大約28% 的颱風會繼續增強。Yang et al. (2013) 針對雙眼牆置換完成後的演化，發展出四個分類。他們指出不同分類的颱風在強度的演化上有明顯的不同，於T-V圖中亦具有不同的演化路徑。 Hack and Schubert (1986) 提出熱動力效率eta (r; z; t) 之概念。此物理量能夠定量描述總位能(P) 轉換到總動能(P) 之能量轉換速率(C)，並以加熱(Q) 最為量度基準。該文獻指出儘管總加熱量(H) 維持一樣，不同的渦漩結構會產生極為不同的轉換效率。在此研究中，我們將利用熱動力效率，來測試單雙眼牆颱風Francis (2004) 之轉換效率反應。我們發現外眼牆在動力上能夠透過減少羅士比長度而提高渦漩的能量轉換效率達50% 至400%，而改變內外眼牆之加熱率比重(從1 : 2 至2 : 1) 則可以強化能量轉換效率達100% 至600%。 除了此研究主要使用的圓柱座標外，本論文也推導在準地轉理論(卡式座標)，卡式座標，球座標與淺水模型之動力效率，可供參考與應用於其他尺度平衡動力研究之用。

The observation data shows that the eyewall replacement cycle (ERC) results in different consequences. Kuo et al. (2009) found that approximately 28% of typhoons strengthen after the formation of secondary eyewall. Yang et al. (2013) developed four categories to classify the situations after the formation. They found these four categories exhibit different behaviors on intensity and routes on T-V diagram. 'Dynamic efficiency of heat' eta (r; z; t)) developed by Hack and Schubert (1986) is to examine the effect of heating on the energy conversion rate (C) converting total potential energy (P) into total kinetic energy (K) They also pointed out that efficiencies vary under different vortex structures while total heating remains the same. In this study, we would apply dynamic efficiencies to examine the response of concentric eyewall cyclone Francis (2004). We find that the presence of outer eyewall enhances the efficiency response by approximately 50% to 400% through reducing Rossby length (lambda_R) while changing the heating ratio between inner and outer eyewalls from 1 : 2 to 2 : 1 enhances the efficiency by 100% to 600% (total heating is fixed). Apart from cylindrical coordinates, we also derive the dynamic efficiencies in quasi-geostrophic theory (Cartesian coordinates), Cartesian coordinates, spherical coordinates, and shallow water model for potentially application to other balance dynamics in different scales.