水躍是在明渠中經常觀察到的現象，當流體在上游處高速的超臨界流進入到較低速度的亞臨界流區域時，就會形成水躍。Chandrashekar et al. (2019)提到使用淺水波方程式進行模擬會因忽略垂直剪應力而失去流體中該有的波動細節，並透過改良之淺水波方程式，有效模擬出流體中平均深度之波動現象。故本研究利用粒子影像測速法量測水躍後內部之波動及觀察紊流消散之現象，並比對兩者之相關性。由於水躍流場常夾帶著大量氣泡，有礙於量測之精確度，故本次研究選取低福祿數水躍來進行量測。並針對兩組弱水躍(Fr=2.24、2.43)及一組震盪水躍(Fr=2.86)以及兩種不同位置的雷射切面、兩種影像處理之實驗條件，在穩定水循環系統下進行實驗。由於在PIV分析中，任意的限制速度場範圍，僅能剔除過大之異常值，並不適用在流場中速度較小之區域。本研究嘗利用水躍紊流場之特性，訂定速度場方向及大小之限制，使量測之實驗值有更好的精確度。透過震盪水躍的實驗中發現，在水躍後上層之紊流強度，隨著距離的變化強度呈現出波浪型的遞減，這與使用速度場限制時的數據損失率之高低相當吻合，可推測該波形位置可能與水躍內部流場之渦流有關。另外，也與Chandrashekar et al. (2019)紊流波動之模擬與實驗分析有相同的趨勢。本研究主要為修正粒子影像測速法中之速度場限制獲取更可靠且準確的數據，並量測水躍後之內部流場結構，以供研究參考。

Hydraulic jumps often take place in rivers, channels or spillways, when flow in super-critical stage goes into sub-critical state. Conventionally, the hydraulic jumps are described by shallow water equations. However, as elaborated in Chandrashekar et al. (2019), the shallow water equations are depth-averaged ones and neglect many details concerning the velocity distribution in normal direction as well as the fluctuation and the associated variation of the stress. The first improvement can be found in Richard and Gavrilyuk (2012), where the fluctuation is considered as roller vorticity in a rather elegant manner in the depth-averaged equation system. In the present study, the instantaneous velocity field is measured by the employment of particle image velocimetry (PIV) technique, so that the turbulence density and its decay can be described. We focus on the characteristics of the turbulent flow field behind the hydraulic jump, especially on the phenomenon of turbulence dissipation, and compare the correlation between the fluctuation and turbulence intensity. In the PIV analysis, we investigated the parameters for determining the velocity for improving the accuracy, and found that it is rather challenging when the velocity variation is very large. Both the experimental measurement and the simulation in Chandrashekar et al. (2019) are in consistency and revealed the wavy decline after the toe of the jump.

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