前人針對前進波列斜向傳遞於緩坡底床上的波動場，提出許多的解析模式，但尚留有很多改善的空間，例如，前人的解析結果無法完整地呈現底床坡度影響效應，且無法滿足流體質點速度方向與波向線曲面相切之物理特性。本文提出包括波浪折射、淺化與變形之整體波動場的解析，所得結果可適當地展現底床坡度影響效應，並可滿足前人無法符合的波浪折射幾何特性。

　　本文基於線性化處理自由表面邊界條件，且不考慮波浪碎波問題，為呈現底床坡度影響效應，波動場以底床坡度進行攝動展開，並且以波向線座標系統作為參考座標，以滿足流體質點速度方向與波向線曲面相切之物理特性，依此方法，可求得在 Eulerian 系統描述下，展開至二階次之流速勢函數的顯式解。為更明確地描述流體質點的運動特性，Eulerian系統所得結果將線性轉換至 Lagrangian系統，並求得流體質點運動的參數化方程式，藉此參數化方程式，可得前進波列由深水傳遞至淺水，直到碎波發生前的波形整體時空演變現象，並可分析碎波指標、流體質點的運動軌跡、波形起伏間的空間與時間非對稱性，以及波高變化。

　　本文由 Lagrangian 系統所分析的相關波動特性，皆已提出完整的理論解析，並藉由繪製一系列的關係圖，可明確地瞭解這些物理量與深海波浪尖銳度、水深、波浪入射角及底床坡度的關係。為符合波浪折射現象的真實性，改善前人結果無法沿波向線方向進行分析的缺點，因此本文中之波動特性皆沿著波向線方向進行分析。另外，底床坡度對波數、碎波指標、波形的時間非對稱性及波高變化的影響，在攝動展開下會出現在二階次，此乃前人求解至一階次的解析模式所無法展現的特性。

　　本文並未考慮碎波後的波動場，故解析結果僅適用尚未達到碎波臨界的狀況；在大於碎波水深之區域，解析模式於底床坡度<1/2，可有條件地符合學理上的適用範圍。當底床坡度愈大，本文的底床坡度影響項之效應愈強，但攝動級數的收斂性愈差，所得結果愈無法完整地描述底床坡度效應。

　　Although numerous analytical models have been developed to investigate the obliquely incident wave transformation on gentle slope, very few researchers have considered the effect of bottom slope, and the tangential relationship between the direction of a water-particle velocity and the curved surface of a wave ray. In the present study, various aspects of the wave field, including wave deformation, refraction and shoaling has been investigated. Unlike in the previous studies, the effect of bottom slope on the wave propagation has been considered here, and the geometric characteristic of wave refraction is investigated.

　　The present study is based on linearized free surface boundary conditions in absence of wave breaking. In order to describe the effect of bottom slope, the physical quantities related to wave motion are cast in a perturbed series with the bottom slope as the parameter. With the wave-ray coordinate system, the water-particle velocity can be tangential to the curved surface of a wave ray. Accordingly, an explicit expression for the velocity potential is derived as a function of the bottom slope, perturbed to the second order in the Eulerian system. Afterwards, the parametric functions for the water-particle motion are obtained by using a linear transformation between the Eulerian system and the Lagrangian system. By using the parametric functions, the process of successive deformation of a wave profile, the breaking index, the fluid-particle trajectory, the spatial and temporal asymmetry of wave profile, and the variation of wave height have been obtained before the wave breaking occurs.

　　For the Lagrangian system, the wave characteristics, as discussed in the thesis, are derived as explicit solutions, and illustrated with a series of figures under different conditions of the wave steepness in deep water, such as, the water depth, the incident angle and the bottom slope. In order to correspond with the physical characteristic of wave refraction, all the wave characteristics are specially analyzed along the direction of wave rays. However, the bottom slope is observed to affect the wavenumber, the breaking index, the temporal asymmetry of the wave profile and the variation of wave height, which are therefore presented in second-order in terms of the perturbed expansion. The foregoing could not be accurately described using the first-order analytic models.

　　Since the phenomenon of wave breaking is not considered in this study, the present results are applicable for the wave field before the breaking takes place. In the non-breaking region, the theoretical restrictions can be conditionally satisfied for the present analytical model under bottom slope < 1/2. For a steeper bottom slope, the effect of the bottom slope terms can be reinforced, however, it becomes inadequate to expect the full effect of the bottom slope because of the weak nature of convergence of the perturbation series.

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