葉超雄臺灣大學:土木工程學研究所利岳聲Li, Yueh-ShengYueh-ShengLi2010-06-302018-07-092010-06-302018-07-092009U0001-0408200922180300http://ntur.lib.ntu.edu.tw//handle/246246/187723颱風，颶風或龍捲風等旋轉風系會造成嚴重災害，大氣學家或氣象學家，著重在其生成原因，這些風系對大地應有影響，即使非常細微，也是值得探討的。 本文即以波動學領域中的半無限域問題分析方法，分析不動颱(颶)風對大地所造成之可能之影響，其一為風壓在無限域表面造成之扭剪效應，另一為氣壓場造成之垂直壓力效應。為接近真實情況，本文特別以Jelesnianski發表的風場及壓力場作為施加的外力，其外力作用場皆涵蓋整個無限域表面，也與過去半無限域問題有所不同。 扭剪效應部份，配合一些假設及前人研究之不動颱(颶)風場，再利用積分表工具書找到部份脈衝型態外力之解析解，不足部份則以Durbin法數值解補足，同時也驗證了解析解的可信度；在此部份，階躍型態外力所造成之半無限域表面效應，也以Durbin法求出數值解。 垂壓效應部份，也以解析解與數值解相互搭配，進而求得脈衝型態外力的半無限域表面反應，並從中發現颱(颶)風對大地並不產生雷利波的效應。其中Mitra無法處理半無限域中核心半徑內區域，也成功地以數值法解決。 本文最終目的，是希望藉由介紹這樣的研究，提供對於旋轉風系力學行為感興趣者與彈性波動學研究者一個跨越兩門科學的方向，進而研究出更多的成果。Typhoons, hurricanes or tornadoes, such as cyclostrophic winds can cause serious disasters. Atmospheric scientists, or meteorologists, focus on the reasons for their generation, but in fact these winds should impact the earth and ground. Even if it is very subtle, it is also worthy to explore. The method of analyzing the half-space problem in the elastic-wave-propagation science is used in this thesis to analyze the possible effects on the earth and ground induced by typhoons or hurricanes. One is thought as the torsional-shear effect induced by the wind stress. Another is the vertical-pressure effect induced by the air pressure of the storms. This thesis features that the wind field and air pressure field studied and published by Jelesnianski are used as the loads in order to simulate the real situation and differs from previous research of the half-space problems because the loads act on whole surface of the half-space. Regarding the torsonal-shear-effect part, the analytic solutions which don’t cover the whole half-space are found out by using the tool books of integral tables and some hypothesis. The partial solutions are made up by using the Durbin method which has also been used to prove that the analytic solutions are correct. The numerical solutions of the responses on the surface of the half-space induced by the unit-step loads are also obtained by the Durbin method. The analytic and numerical methods are also collocated to analyze the surface responses of the half-space induced by the impulsive loads within in the vertical-pressure-effect paragraph in which the Rayleigh-wave motion doesn’t appear. The response in the partial area of the half-space that Mitra did not analyze are also solved by the numerical method in this part. The ultimate goal of this thesis is providing those who want to know more about the mechanical behavior of cyclostrophic winds or elastic waves science researchers with a direction to connect the two kinds of science, then more results may be explored in the future.口試委員會審定書 i 謝 ii 要 iiibstract iv一章 緒 論 - 1 -.1 研究動機 - 1 -.2 研究目的 - 1 -.3 本文內容 - 2 -.4 文獻探討 - 2 -二章 無限域表面扭剪廣義通解 - 4 -.1 基本方程式 - 4 -.2 積分轉換域 - 5 -.3 邊界條件 - 8 -.4 轉換域解與時域積分式通解 - 9 -三章 擬不動颱(颶)風風場 - 11 -.1 基本條件假設 - 11 -.2 解題步驟 - 12 -.3 Durbin數值法 - 15 -.3.1 Hankel 逆轉換 - 15 -.3.2 數值結果比較 - 16 -.3.3 階躍型態外力數值解 - 17 -.4 結果討論 - 18 -四章 半無限域表面垂直壓力廣義通解 - 20 -.1 基本方程式 - 20 -.2 積分轉換域 - 21 -.3 邊界條件 - 22 -.4 轉換域解與時域積分式通解 - 23 -五章 擬不動颱(颶)風壓力場 - 25 -.1 基本條件假設 - 25 -.2 解題步驟 - 26 -.2.1 之貢獻 - 27 -.2.2 之貢獻 - 35 -.2.3 Hypergeometric函數 之貢獻 - 38 -.3 結果討論 - 39 -.3.1 各別結果討論 - 39 -.3.2 總變位結果討論(圖5-E,5-F,5-G,5-H) - 41 -六章 結論與研究展望 - 42 -.1 結論： - 42 -.2 為來研究與展望 - 43 -目錄： 2-1 圓柱座標示意圖 - 44 -3-1 半徑與風速關係圖 - 45 -3-2 風速與半徑正交示意圖 - 45 -3-3a 解析解及數值解變位圖 - 46 -3-3b 解析解及數據解變位圖 - 46 -3-3c 2變位圖 - 47 -3-4a 1變位圖 - 48 -3-4b 3變位圖 - 48 -3-5a 解析解及數值解變位圖 - 49 -3-5b 解析解及數值解變位圖 - 49 -3-5c 變位圖 - 50 -列A 相同半徑位置不同 數值解變位圖 - 51 -列B 相同 不同半徑位置解析解變位圖 - 54 -列C 相同半徑位置，不同深度數值解變位圖 - 56 -列D 無限域表面各半徑位置階躍數值解變位圖 - 59 -5-1 圍線積分於 複數平面示意圖 - 60 -5-A,B 貢獻 - 61 -5-C 貢獻 - 66 -5-D Hypergeometric 函數 之貢獻 - 69 -5-E~5-H全變位圖 - 71 -錄 A Durbin法簡介 - 75 -錄 B Clenshaw-Curtis 法則簡介 - 84 -錄 C (5-7)式推導 - 86 -考文獻： - 88 -2089250 bytesapplication/pdfen-US颱風颶風龍捲風旋轉風系半無限域波動學扭剪垂直壓力Durbintyphoonhurricanetornadocyclostrophic windhalf-spacedynamicelasticitytorsionalshearvertical pressure[SDGs]SDG11thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187723/1/ntu-98-R96521228-1.pdf