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題名 | 等水深有限振幅波之Lagrangian解=A Lagrangian Solution for Finite-amplitude Waves in Water of Uniform Depth |
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作者 | 劉勁成; 張憲國; | 書刊名 | 海洋工程學刊 |
卷期 | 2:1 2002.07[民91.07] |
頁次 | 頁33-54 |
分類號 | 443.1 |
關鍵詞 | Lagrangian近似解; 有限振幅波; 攝動法; 漂移速度; Lagrangian solution; Finite-amplitude gravity waves; Perturbation method; Drift velocity; |
語文 | 中文(Chinese) |
中文摘要 | 本文應用Eulerian與Lagrangian座標系統間的轉換關係,推導出在Lagrangian座標下均勻水深上規則前進重力波之控制方程式,並利用攝動展開技巧解析獲得三階解。本文所得Lagrangian近似解的質點運動週波率包含二部份,一部份為含深度b的cosh函數,可表現質點運動的週波率隨深度增加而增加的特性;另一部份為不隨空間中任何一個位置點而改變的常數。本文進一步比較Eulerian及Lagrangian座標的波浪運動週波率的關係,發現本文的Lagrangian近似解的質點運動週波率可轉換至Eulerian座標下固定點觀測波動的週波率。由解析結果可知,Lagrangian系統中奇數階近似解主要進行週波率修正,偶數階近似解主要進行高程修正,且由結果中可知,本文近似解可求得平均靜水位上的波壓。本文的Lagrangian近似解可描述流體質點運動軌跡於波動一週期後,不會封閉而有微量前進的質量傳輸量,且可表現上層質點運動軌跡的位移範圍較下層者大的特性。 |
英文摘要 | A set of governing equations in Lagrangian form converted from ones in the Eulerian form was derived for the propagating gravity waves in water of uniform depth in this paper. The technique of perturbation method was used to obtain the approximations up to third-order for these nonlinear governing equations. The Lagrangian frequency consists of two parts. One part is a function of depth and increases as the water depth increases. The other part is constant for all particles and equivalent with that of Stokes’ wave theory of third-order. The present Lagrangian solution for the particle motion shows that the water particle has a drift displacement of second order, which decreases exponentially with water depth, after a period of time. The pressure of the present solution has zero value at the free surface and this exactly satisfies the dynamic boundary condition. |
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