碎波波高與底床坡度相關性之非線性解析及印證

Nonlinear Analysis and Verification of the Relation between Breaker Height and Bottom Slope

曾文哲(Wen-Jer Tseng) ； 陳陽益(Yang-Yih Chen) ； 許弘莒(Hung-Chu Hsu) ； 程嘉彥(Chia-Yan Cheng) ； 李孟學(Meng-Syue Li)

《海洋工程學刊》 11卷2期 (2011/12) Pp. 101-118

https://doi.org/10.6266/JCOE.2011.1102.02

摘要

本文主旨係於二度空間裡，針對前進在平緩坡度α底床上的週期性規則表面重力波，產生連續時空變形至碎波（breaker） 時，探討其碎波波高、碎波水深與底床坡度之相關性。在聯合代表波浪本質的波浪尖銳度ε，作為兩攝動參數展開下，本文引用已被印証之所得至ε^2階的Eulerian系統與被轉換至對應的Lagrangian系統的非線性流場解析解。然後，由波峯處水粒子之水平速度分量u恰等於波速c之碎波條件的引入，來描述波動由深至淺至碎波的時空連續演化，及進而理論解析推導出碎波波高、碎波水深與底床坡度之相關性並與前人之試驗結果比較印證之。

關鍵字

碎波 ； Eulerian系統 ； Lagrangian系統 ； 流速函數

並列摘要

The major purpose of this study is focused on the characteristics of the breaker caused by wave breaking. Two-dimensional surface regular gravity water waves propagating on a gentle sloping bottom are considered and the consecutively temporal-spatial evolution of wave traveling form deep water to shallow water is also investigated. Under nonlinearized conditions, the analytical solution for velocity potential function is derived to perturbation's ε^2 order for the gentle sloping bottom and wave steepness in the Eulerian system. The wave profile and the characteristic of breaking wave are also found by using the transformation in the Lagrangian system. Furthermore, the relation between the breaker height, breaker depth and bottom slope is discussed and verified with the previous experiments.

並列關鍵字

breaking wave ； eulerian system ； Lagrangian system ； velocity potential function