台灣位於亞熱帶地區且四面環海，因氣象之影響而常有豐沛雨量。當降雨形成地表逕流，受地表之摩擦力與空氣對於流體之阻力影響而形成水波。本研究使用Eulerian方式描述下之質量及運動方程式，配合邊界條件再加上深度積分，推導控制方程式，並且加入 Richard & Gavrilyuk (2012、2013) 因渠底邊界層形成之渦熵(enstrophy)守恆式及波峰處渦熵守恆式，模擬流體於不同型態底床之滾波發生位置與形貌及速度變化。由於流體中之物理量具有高梯度之變化，因此本文以 Non-Oscillatroy-Central(NOC) scheme 之方法模擬當滾波(roll wave)形成及水躍(hydraulic jump)發生時之水面輪廓、速度、壓力、福祿數及滾波處渦熵之變化，並且討論不同渠底粗糙度及傾角變化對於流體所造成之輪廓差異。

Taiwan is an island in the Southwest Pacific Ocean. The location of Taiwan is in the semi-tropical area with mild seasonal differences from northern continent. Because of the unique geographic conditions, the meteorological environment in Taiwan is complex and with abundant rainfall. The rainfall over the land surface forms surface runoff causing roll waves, of which the phenomenon is affected by flow resistance and friction on the ground. This study is based on Eulerian description with boundary conditions and depth-integral to derive governing equations. In addition to the conservation of mass and momentum, the study employs the enstrophy balance as proposed in Richard & Gavrilyuk (2012, 2013), to model the location and profile of roll wave, where the uniform distribution of flow velocity is not valid any longer. Considering the high gradients of physical quantity in the flows, we used the method of non-oscillatory central (NOC) scheme to model the different shapes of flow surface when the roll wave and hydraulic jump occurred. Different fluid shape caused by two kinds of bed roughness and varied inclination were also discussed.

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