本文中擬以Chandrasekera and Cheung(2001) 所提出之水深分佈函數為基礎，重新推導波浪通過擾變地形之緩坡方程式。所推導之緩坡方程式係由Laplace方程式結合邊界條件得知，其型式包含一組耦合之偏微分方程式。模式中的底床邊界條件係以泰勒展開式對底部邊界條件進行微小擾變量的近似展開。本文引用的水深分佈函數，在自由表面仍滿足線性物理的邊界條件，然在底床速度表現上則可表示水平方向與垂直方向上的速度分量，符合實際現象。當微小擾變參數 忽略時，本文之緩坡方程式可退化回Chandrasekera and Cheung(2001)之折繞射模式。藉由所推導之緩坡方程式，配合輻射邊界條件，建立數值模式來求解波浪通過擾變底床地形時之波高分佈、速度剖面及反射率變化情形。計算結果經與試驗值比較，呈現合理之一致性。本文模式並對波浪通過複合式擾變底床地形進行模擬，並且對傳統緩坡方程式、延伸型態緩坡方程式、演進型態緩坡方程式以及Chandrasekera and Cheung(2001)之折繞射模式之數值計算結果進行比較，結果顯示具高精度之優越性。

This thesis presents the methematical formulation, the numerical solution, and the validation of the modified mild-slope equation for undulating bottom. The model involves two decoupled governing equations derived from, respectively, the approximated seabed boundary condition and the Laplace equation, The depth function of Chandrasekera and Cheung (2001) was used to the integration of the modified mild-slope equation. The present approach correctly accounts for the vertical component of the seabed fluid velocity. The present model, which satisfies the approximate bottom boundrty condition, is more accurate in modelling have transformation over undulating bathymetry. The validity of the present model is examined by existing experimental data and compared with the extended mild-slope equation (EMSE, Kirby, 1986) and evolution equation of mild-slope equation(EEMSE, Hsu and Wen,2001). The applicability and accuracy of the proposed model is evaluated and discussed.

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