以動量平衡方程式推估潛入點後異重流厚度之變化

Layer Thickness Estimation of Density Current from Plunge Point

林彥廷(Lin Yang-Ting)

指導教授 ： 譚義績

共同指導教授 ： 賴進松(Jihn-Sung Lai)

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.00824

摘要

近年來由於颱風時期進入水庫的入流水源常挾帶大量泥砂，水庫庫區中因為大量泥砂的入流而形成異重流現象。進入水庫中的泥砂無法排除，堆積在庫區之中，造成水庫的庫容嚴重降低。臺灣地區的水庫身兼防洪、蓄水、觀光、發電等多功能，因此無法利用放空庫容的方法排砂，如何利用颱風時期發生之異重流現象，排除大部份入庫泥砂，延長水庫使用年限，是目前各主要水庫面臨之重要問題。
挾帶泥砂的渾水在進入水庫之後，會先在庫區上游堆積形成三角洲，接著在形成潛入條件之後潛入形成異重流。異重流頭部在庫區中前進時會逐漸吸收清水，增加自身的體積。本研究參考[Parker and Toniolo, 2007]使用動量方程式，探討渾水入流後由潛入點至形成異重流過程中之渾水層厚度變化，將其應用於渾水形成異重流後，異重流捲入清水造成異重流厚度變化關係之探討上，並導入坡度變化之壓力修正項及能量損失因子，將理論推展至具有坡度且有能量損失之異重流沿程運移過程。文中以[俞維昇, 1991]及[徐小微, 2002]之異重流實驗量測數據，與石門水庫颱風時期之異重流量測數據，進行理論之驗證與應用，驗證結果顯示本研究推導之理論值與[俞維昇, 1991]之實驗結果比較，當捲水量比γ低於0.5時，能充分描述異重流捲入清水後異重流厚度之變化關係。與[徐小微, 2002]之異重流量測數據相比，證明本研究之理論亦可適用於由底層釋放之異重流及捲水量比偏低之異重流。且由瑪莎、辛樂克及薔蜜三場颱風比較之結果，顯示本研究之理論公式在現場之應用中，以含壓力修正之方式較能符合現場量測之結果，並發現在各斷面中，歷次颱風捲入之清水量差異不大。
本研究之成果顯示以簡單之動量平衡方程式亦可推估異重流厚度之變化，並利用試驗水槽之試驗結果以及颱風時期之石門水庫現場量測異重流數據佐證後，利用本研究之理論公式，推求特定斷面之捲入清水量與異重流厚度之關係式，且將其應用於各斷面之異重流厚度及異重流之平均單寬流量。

關鍵字

動量方程式 ； 潛入點 ； 異重流厚度 ； 捲水量比

並列摘要

In recent years, density current is formed due to reservoir inflow contents large amount of silt during typhoon seasons. The deposits entered reservoirs is difficult to remove, thus heavily reduced the life span of the reservoirs. Reservoirs in Taiwan have multiple objectives, including flood decreasing, water depositing, electricity generating, also are local tourist attractions. Using empty reservoir strategies is not suitable for most of reservoirs in Taiwan. How to take advantage of density current phenomena to discharge silts entering the reservoirs, thus extends life span of the reservoirs, is an important research topic for reservoir management in Taiwan.
As muddy inflow entering the reservoir, depositing delta is formed in the upstream of the reservoir. Then at a point of suitable condition of plunging, the muddy inflow plunge under clear water and density current is formed. As the head of density current flowing across the reservoir, clear water is absorbed into density current, thus the volume of density current is increased. This research is focused on the change of layer thickness of density current from the plunge point to the stable density current behind the head of the current. Referred to [Parker , 2007] using momentum equations estimating layer thickness of muddy inflow from plunge point to the turning point where volume of density current staring to increase. This research uses momentum equation on estimating the increase of layer thickness of density current because of absorbing water into turbidity layer. The effects of slope and energy dissipation on the plunge point are also take into consideration. Experiment results of [俞 , 1991] and [徐 , 2002] is used to verify the estimation of turbidity layer thickness of this research. The turbidity and flow rate measurement data of density current in Shimen Reservoir during typhoon seasons is also used to verify the estimation of this research. The comparison of experiment data from [俞 , 1992] and estimation of this research shows, with the amount of absorbed water is under half the amount of muddy inflow ( denote by γ< 0.5), the experimental data can fit with the estimation in this research. The comparison with experimental data of [徐 , 2002] shows, the estimation of this research is also applicable to the type of density current forced to form by releasing the turbidity water on bed of the experiment tank, and density current layer thickness of low γ value (less than 0.1). With the measurement data in Typhoon Jangmi, Typhoon Sinlaku and Typhoon Matsa compared with theoretical estimation, the result shows the estimation of turbidity layer thickness contenting slope and energy dissipation on plunge point modifications fit the measurement data better. The measurement data also shows that on the same cross-section of Shimen Reservoir, the value of γ is within close range on different typhoon.
This research shows that using simple momentum equations is capable of estimating layer thickness of density current. Also the comparison with theoretical estimation between experimental data and density current measurement data in Shimen Reservoir shows, the theoretical estimation of this research is capable of estimating density current layer thickness and cross-sectional flow rate in every specific cross-sections in reservoirs.

並列關鍵字

momentum equations ； plunge point ； density current layer thickness ； entrainment

參考文獻

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2.Alavian, V., et al. (1992), Density Currents Entering Lakes and Reservoirs, Journal of Hydraulic Engineering, 118(11), 1464-1489.

4.Buehler, J., and C. Siegenthaler (1986), Self-preserving solutions for turbidity currents, Acta Mechanica, 63(1), 217-233.

5.Ellison, T., and J. Turner (1959), Turbulent entrainment in stratified flows, J. Fluid Mech, 6(3), 423–448.

6.Lee, H.-Y., and W.-S. Yu (1997), Experimental Study of Reservoir Turbidity Current, Journal of Hydraulic Engineering, 123(6), 520-528.