本文以二維波浪數值模式，模擬週期波入射至不同堤面坡度的海堤，探討海堤附近黏性流體的波流場特性。為模擬固體邊界附近的黏性流體運動行為，模式求解二維時變的雷諾平均方程式 (Reynolds Averaged Navier-Stokes eqautions，RANS) 與紊流模式 ( model)。並應用質點等位函數法 (Particle Level Set Method) 捕捉波浪溯升及碎波過程中，複雜的波形演變。此外，本文利用陳 (2011) 及 Huang et al. (2013) 所提出之修正型沉浸邊界法 (Improved Immersed Boundary Method，IIBM)，處理波浪與結構物固體邊界互制之流場演變。此法可於卡氏座標下，模擬不規則固體邊界的流場，並滿足固液交界面中連續方程式與非穿透及無滑移的邊界條件。為了確保數值模式的準確性，本文利用多項前人實驗成果進行模式的驗證，包括波高分佈 (蔡等人，1997) 與水位變化 (Ting and Kirby，1994)，以及堤面波壓分佈 (Sundar and Anand，2010) 等。本研究探討波浪入射不同堤面坡度時 (包括直立堤與 、 斜坡堤)，波浪在溯升及溯降期間的波流場演變、堤面波壓、堤前底床剪應力分佈等特性。模擬結果除展示波浪碎波過程、堤前駐波現象、堤面波壓分佈、堤前底床剪應力外，更探討波浪溯升過程中的回流 (reverse flow) 現象、週期平均流場 (Time-averaged flow field) 中存在的穩環流胞 (steady recirculating cell) 以及水下逆流 (undertow) 現象。

In this study, a two-dimensional Reynolds Averaged Navier-Stokes equations and the turbulence model are developed to simulate the viscous flow field near seawalls. The complex free surface configuration is captured using the Particle Level Set Method. The Improved Immersed Boundary Method (IIBM) is applied to represent the fluid-solid interaction in the vicinity of irregular solid boundary under the Cartesian grid system. To validate the accuracy of numerical model, the results were compared with the experimental data, including the deformation of wave on a steep sloping bed (Tsai et al., 1997), the water surface elevation on a mild sloping bed (Ting et al., 1994), and the wave pressure on the vertical seawall (Sundar et al., 2010). The numerical model is applied to investigate the viscous flow fields induced by periodic waves propagating on three different seawalls, involving vertical wall and steep seawalls with slope of 1:2 and 1:5. The free-surface evolutions, the wave pressure on the seawalls, the bottom shear stress prior to seawalls and the time-averaged flow field are discussed. The results reveal that the reverse flow within the boundary layer is related to the instantaneous wave elevations. An accompanying steady recirculating cells were observed in the time-averaged flow field of standing wave. However, breaking wave leads to an undertow on the seawall surface.

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