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研究生:許天耀
研究生(外文):Tien-Yiao Hsu
論文名稱:平衡渦旋模型之熱與動量動力效率
論文名稱(外文):Dynamic Efficiency of Heat and Momentum in Balanced Vortex Model
指導教授:郭鴻基郭鴻基引用關係
口試委員:游政谷黃彥婷楊明仁
口試日期:2015-07-16
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:大氣科學研究所
學門:自然科學學門
學類:大氣科學學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:82
中文關鍵詞:平衡渦漩熱動力效率動量動力效率雙眼牆
外文關鍵詞:balanced vortexdynamic efficiency of heatdynamic efficiency of momentumconcentric eyewalldouble eyewall
相關次數:
  • 被引用被引用:1
  • 點閱點閱:134
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
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.

口試委員會審定書 ii
誌謝 iii
摘要 iv
Abstract v
1 Introduction 1
2 Formulation 3
2.1 Efficiency in Quasi-geostrophic Theory 4
2.2 Efficiency in Cartesian Coordinates 9
2.3 Efficiency in Cylindrical Coordinates 15
2.4 Efficiency in Spherical Coordinates 21
2.5 Efficiency in Shallow Water Model 25
3 Numerical Method 29
4 Numerical Experiments 34
4.1 Diagnose Procedure 35
4.2 Vortex and Heating Settings 35
4.3 Single eyewall cyclone 37
4.4 Concentric eyewall cyclone 45
4.5 Eye with hub cloud 46
4.6 Internal structure of moat and outer eyewall 53
4.7 Position of maximum heating 54
4.8 Pre-existing baroclinity 54
4.9 Sensitivity of baroclinity on the operator 55
5 Summary 56
A Derivation of Quasi-Geostrophic equations 58
A.1 Perturbation Method 58
A.2 Balanced Condition 60
B Waves and the Eliassen-Sawyer Circulation Equation 63
C Boundary Conversion 71
D Similarity between cylindrical and spherical coordinates 72
E Application Programming Interface 77
Bibliography 81

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Hack, J. J., and W. H. Schubert, 1986: Nonlinear response of atmospheric vortices to heating by organized cumulus convection. J. Atmos. Sci., 43, 1559–1573.
Hack, J. J., W. H. Schubert, D. E. Stevens, and H.-C. Kuo, 1989: Response of the hadley circulation to convective forcing in the itcz. J. Atmos. Sci., 46, 2957–2973.
Holliday, C. R., and A. H. Thompson, 1979: Climatological characteristics of rapidly intensifying typhoons. J. Atmos. Sci., 107, 1022–1034.
Hoskins, B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29, 11–37.
Hoskins, B. J., and N. V. West, 1979: Baroclinic waves and frontogenesis. part ii: Uniform potential vorticity jet flows-cold and warm fronts. J. Atmos. Sci., 36, 1663–1680.
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Schubert, W. H., and B. D. McNoldy, 2010: Application of the concepts of rossby length and rossby depth to tropical cyclone dynamics. J. Adv. Model. Earth Syst., 2, 13pp., doi:10.3894/JAMES.2010.2.7.
Schubert, W. H., C. M. Rozoff, J. L. Vigh, B. D. McNoldy, and J. P. Kossin, 2007: On the distribution of subsidence in the hurricane eye. Quart. J. Roy. Meteor. Soc., 133, 595–605.
Shea, D. J., and W. M. Gray, 1973: The hurricane’s inner core retion, i: Symmetric and asymmetric structure. J. Atmos. Sci., 30, 1544–1564.
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Yang, Y.-T., E. A. Kuo, H.-C. Hendricks, and M. S. Peng, 2013: Structural and intensity changes of concentric eyewall typhoons in the western north pacific basin. Monthly Weather Review, 141, 2632–2648.

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