本研究目的為透過實驗量測水躍現象中紊流強度的變化，以及躍趾處因表面 roller 所產生之渦度擬能 (Enstrophy) 隨下游距離增加的變化。實驗方面本研究利用小尺度流槽進行上游福祿數介於 1.92 至 3.05 的水躍實驗，並分別在流槽的側視以及仰視方向使用高速攝影機進行拍攝，分析方面透過粒子影像測速法(Digital particle image velocimetry, DPIV)來獲取速度場資料。在側視的水躍量測中，發現低福祿數下的紊流強度分布與前人的量測結果趨勢不同，卻與福祿數較高的穩定水躍相似 (Lin et al.[25])，其紊流強度較高的區域分布在近躍趾底床附近，並往下游方向消散，故福祿數並非決定水躍中紊流強度分布之唯一條件，並且受實驗條件所影響。另外在仰視方向觀測的水躍中，在接近水面邊壁兩側有較快的速度分布，並且發現了與波狀水躍相似的特徵。本研究以實驗的角度來假設水躍中渦度擬能之計算方式，而分析出來的結果與 Richard and Gavrilyuk [37] 的模擬結果尺度相同，其在躍趾產生較大的渦度擬能，並隨著下游距離增加而逐漸消散，可以很好的來表示時間平均的水躍紊流場中，roller 隨空間消散的現象。最後本研究利用剪力淺水波方程式 (Richard and Gavrilyuk [37])進行一維的水躍模擬，過程中發現了許多問題並進行探討，而模擬的過程中發現渦度擬能的不穩定會導致躍趾產生來回振盪的現象。

This study is devoted to investigation on the hydraulic jumps in inclined channel, where the evolution of the turbulence intensity behind the hydraulic jump and the variation of enstrophy produced by the roller at the jump toe through hydraulic jump are examined by laboratory experiments. A small-scale rectangular open channel flume is utilized to carry out hydraulic jump experiments with upstream Froude number ranging from 1.92to3.05. The instantaneous velocity field are recorded by a high-speed camera and analyzed by the technique of the digital particle image velocimetry (DPIV). The high-speed camera recorded the velocity fields both in the side view and the bottom view of the flume, where the side view is at the 1/4 of the channel width and the bottom view consists of 4 levels (depths) above the bottom. In the side view measurement, the turbulence intensity of the hydraulic jump at low Froude number is different from the one in the previous study (Lin et al., 2012) due to the different channel orientation in experiment (inclined versus horizontal). In the bottom view measurement of the upper most slice, higher speeds are detected near the both side walls, similar characteristics to the undular jump (bore) in the weak jump. In the present study, we hypothesize the calculation method of enstrophy in the hydraulic jump from an experimental point of view. The analyzed result shows that the roller enstrophy is generated around the toe which dissipating in the down stream part of the flow. It is noted that the results are of the same scale and with a similar trend as given in Richard and Gavrilyuk (2013). Finally, a one dimensional simulation tool with shock-capturing property is implemented based on the shear shallow water equation (Richard and Gavrilyuk, 2012; 2013). Through numerical investigation, the instability of toe oscillation as well as the evolution of the enstrophy are thoroughly examined.

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