重力水波下之粒子運動軌跡及質量傳輸之研究

Particle Trajectories and Mass Transports of Progressive Gravity Waves

陳莉妏(Li-Wen Chen)

指導教授 ： 丁肇隆

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.03420

摘要

本文利用粒子影像測速儀(P.I.V.)量測系統並搭配影像接圖技巧，研究單一頻率深水波至中間性水深波，其水粒子運動軌跡型態於空間上之演化特性，並探討當波浪之非線性增加時，其與質量傳輸速度間之關係及對動能、位能間之影響。研究包含速度向量場、粒子運動軌跡型態、平均質量傳輸速度及平均動、位能等四項分析，其中利用粒子軌跡重建演算法作為分析本實驗速度場之用，其結果較Voronoï演算法之計算結果符合實際流場情形，速度向量場之一致性也較Voronoï演算法佳。從實驗結果可知，在質量傳輸速度方面，發現靠近自由液面以及底床處有一向前之質量傳輸速度，介於其間之流場，則有一向後之質量傳輸速度。整體而言，平均質量傳輸速率會隨著非線性量增加而愈大。然而平均動能與位能之量測結果其大小均很接近，且會隨著波高愈高其值愈大，彼此間之差距並不隨著非線性度增加而增加。

關鍵字

粒子影像測速儀 ； 粒子運動軌跡 ； 質量傳輸速度 ； 漂移速度 ； 動能 ； 位能 ； 粒子軌跡重建演算法 ； Vorono&iuml ； 演算法

並列摘要

Using the PIV system and image-connection technique. The properties of monochromatic frequency wave for the cases varying from deep water to intermediate water depths were studied. The effects of wave nonlinearity on the mean drift velocity, kinetic energy and potential energy were investigated. Wave velocity field and particle trajectory were calculated based on the analysis of the particle motion on recorded images. This study using reconstruction and temporal filtering analyzed flow field, the result was better than Voronoï construction’s. It was found that positive mean drift velocities exist near the free surface and the bottom of the flume and negative drift velocity occurs in between. In general, a negative drift velocity was found in most cases and the magnitude of the drift velocity increases with wave nonlinearity. The measured kinetic energy and potential energy was also found to be nearly the same.

並列關鍵字

PIV measurement system ； particle trajectory ； mass transport ； drift velocity ； kinetic energy ； potential energy ； Trajectory reconstruction and temporal filtering ； Vorono&iuml ； construction

參考文獻

1.Adrian, C. (2006) “The trajectories of particles in Stokes waves,” Invent. math. 166, pp. 523-535.

2.Adrian C. and Gabriele V. (2008)“Particle Trajectories in Linear Water Waves,” J. math. fluid mech.10,pp. 1-18.

4.H. Capart, D. L. Young, Y. Zech (2002) ”Voronoï imaging methods for the measurement of granular flows,” Experiments in Fluids, Vol. 32, pp. 121-135.

5.Hogan, S. J. (1984) “Particle trajectories in nonlinear capillary waves,” J. Fluid Mech., Vol. 143, pp.243-252.

6.Hogan, S. J. (1985) “Particle trajectories in nonlinear gravity-capillary waves,” J. Fluid Mech., Vol. 151,pp. 105-119.