本研究以RANS (Reynolds Averaged Navier-Stokes equations) 方程式建立二維數值模式，結合k −ε 紊流閉合模式，模擬波浪通過斜坡後碎波流場的變化情形，自由液面的追蹤則採用流體體積法 (Volume of Fluid，VOF) 耦合分段線性界面重建法 (Piecewise Linear Interface Construction，PLIC) 液面捕捉方式處理複雜之碎波液面變形。本研究選取Ting 與Kirby (1994) 的溢波型試次實驗資料來校驗模式的適用性與正確性。結果顯示於波浪水位變化與速度分佈的模擬皆呈現良好的一致性，顯示本模式能夠有效地模擬波浪碎波前後，從淺化過程到碎波及能量消散階段的水理變化特性。

The purpose of the present study is to develop a two-dimensional numerical
model based on RANS (Reynolds Averaged Navier-Stokes) equations combined
with a second-order k − ε turbulence closure model. The wave breaking process
such as water waves travel over a sloping bottom is investigated. To track free
surface movements, the VOF (Volume of Fluid) coupled with PLIC (Piecewise Linear Interface Construction) method is employed. To ensure the accuracy of the numerical model, numerical results were compared with Ting and Kirby’s (1994) experiment data for the case of spilling breaker. Good agreement between numerical results and experimental data has been observed for shoaling and breaking cnoidal
waves on a sloping bottom in terms of free surface profiles and mean velocities.

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