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| 題 名 | Eulerian與Lagrangian方式之非旋轉性自由表面重力駐波之解間的互換=The Transformation between the Third-Order Eulerian and Lagrangian Solutions for Irrotational Standing Gravity Waves |
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| 作 者 | 陳陽益; 許弘莒; | 書刊名 | 海洋工程學刊 |
| 卷 期 | 8:2 2008.12[民97.12] |
| 頁 次 | 頁93-121 |
| 分類號 | 440.137 |
| 關鍵詞 | 重力駐波; 質點運動軌跡; Eulerian; Lagrangian; Standing gravity waves; Particle trajectory; |
| 語 文 | 中文(Chinese) |
| 中文摘要 | 本文以Eulerian與Lagrangian兩種方式,對於等深水中之非旋轉性重力駐波流場已求出之至三階的解,依同一顆流體質點在相同時間與位置處其流速值爲唯一與質量守恆,及在自由表面水位之Eulerian形式解與Lagrangian形式解之值爲同一等特性,來導述其間之互可轉換。藉由一系列連續的Taylor級數展開,於考量波動場中各流體質點之運動軌跡與運動週期下,將已知的Eulerian解轉換成完全未知的Lagrangian形式解。接著再將已有的Lagrangian解轉換成對應的Eulerian形式,均可得到完全相同滿足的結果。由此可得知,在考量波動場各流體質點之運動真實性下,對於非旋轉性的重力駐波流場而言,此兩種描述方式所得之解是互通可轉換的。 |
| 英文摘要 | This study reports the transformations between the third-order Eulerian and Lagrangian solutions for the standing gravity waves on the uniform depth. Regarding the motion of a marked fluid particle, the instantaneous velocity, the mass conservation and the free surface must be the same for either Eulerian or Lagrangian methods. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third order asymptotic expressions for the Lagrangian particle trajectories and the period of particle motion can be derived directly in Lagrangian form. It shows that the given Eulerian solutions are capable of being transformed into the completely unknown Lagrangian solutions and the reversible process is also identified. |
本系統中英文摘要資訊取自各篇刊載內容。