水躍是河道水流由超臨界流轉換成亞臨界流的過程，以往水躍研究拘限於清水水躍。台灣地區在颱風豪雨期間河道中的水流往往挾帶大量泥砂而形成渾水水流，有些地方會形成渾水水躍，因此本研究將探討渾水之水躍特性。
本研究主要分為三部份，首先簡要整理前人對清水水躍之研究成果，然後以冪定理流變模式及賓漢流體模式表示渾水之流變特性，進行理論推導矩形渠道上渾水水躍共軛水深比之關係式，並分別探討共軛水深比受渾水含砂濃度、水躍前的水流福祿數及渠床坡度的影響。最後進行矩形渠道上渾水水躍共軛水深比之敏感度分析，探討關係式中水躍前的水流福祿數、渠床坡度、運動黏滯係數、流動指數及比重量等五個參數對水躍共軛水深比之影響。
分析結果顯示，不論以冪定理流變模式或賓漢流體模式表示渾水水躍理論特性，其結果均顯示渾水含砂濃度越大，渾水水躍之共軛水深比越小；而在固定渾水濃度的情形下渾水水躍之共軛水深比會隨水躍前的水流福祿數的增加而增加，也會隨坡度的增加而增加。而敏感度分析結果顯示，水躍前的水流福祿數對水躍共軛水深比的影響較大。

Hydraulic jump is a natural phenomenon in which the supercritical flow is rapidly transformed into a subcritical flow in a channel. In the past, most of study focused on hydraulic jump of pure water. The heavy rainfall brought by typhoon in Taiwan often results in hyperconcentrated flows in channels, and some of hyperconcentrated flows are even to form hydraulic jumps. Due to the lack of knowledge on the hydraulic jump of hyperconcentrated flow, the present study is aimed to investigate the characteristics of hydraulic jumps for flows entrained with sediment.
This study involves three parts. Firstly, we briefly summarized the previous study on hydraulic jump of clear water are. Secondly, using the power-law and Bingham fluid model to describe the rheological properties of hyperconcentrated flows, we derived a theoretical relation of sequent-flow-depth ratio for a hydraulic jump of a hyperconcentrated flow, and discussed the effects of the Froude numbers、bottom slopes、kinematic viscosity、fluid index and specific weight on the sequent-flow-depth ratio. Finally, we conducted the sensitivity analysis for the sequent-flow-depth ratio.
No matter using the power-law model or the Bingham fluid model, the sequent-flow-depth ratio for hyperconcentrated flow decreases with the increase of sediment concentration in the flow. For the case of the same sediment concentration, the sequent-flow-depth ratio increases with the increase of the Froude number or the bottom slope. And the results of sensitivity analysis show that the influence of Froude number on sequent-flow-depth ratio is larger than other parameters.

1. Belanger, J. B. (1828), “Essai sur la solution numeric de quelques problem relatifs an movement permanent des causcourantes” (in French) (“Essay on the numerical solution of some problems relative to the steady flow of water.”) Carilian-Goeury, Paris.
2. Berezin et al. (2001), “Hydraulic jump on shallow layers of non-Newtonian fluids.” Journal of Non-Newtonian Fluid Mechanics, Vol.101, p.139-148.
3. Bidone, G. (1819), “Observations sur le hauteur du ressaut hydraulique en 1818.” Report (in French) (“Observations on the height of the hydraulic jump in 1818”) Royal Academy of Science of Turin, Italy.
4. Chow, V. T. (1959). Open channel hydraulics. McGraw-Hill Book Company, New York.
5. Demetriou, J. D. (2005), “Unique length and profile equations for hydraulic jump in sloping channels.” 17th Canadian Hydrotechnical Conference, p.891-898, Canada.
6. Demetriou, J. D. (2006), “Tractive force along repelled hydraulic jump within inclined channel.” XXX Convegno di Idraulica et Construzioni IDRA, Italy.
7. Ead, S. A., Rajaratnam, N. (2002), “Hydraulic jump on corrugated beds.” Journal of Hydraulic Engineering, Vol. 128, No. 7, p.656-663.
8. Elevatorski, E. A. (1959). Hydraulic Energy Dissipators. McGraw-Hill Book Company, New York.
9. French, R. H. (1986). Open channel hydraulics. McGraw-Hill Book Company, New York.
10. Henderson, F. M. (1966). Open channel flow. Macmillan, New York.
11. Hughes, W. C., and Ernest Flack, J. (1984), “Hydraulic jump properties over a rough bed.” Journal of Hydraulic Engineering, Vol. 110, No. 12, p.1755-1771.
12. Jan, C. D. and Chang, C. J. (2009), “Hydraulic jump in an inclined rectangular chute contraction.” Journal of Hydraulic Engineering, Vol. 135, No. 11, p.949-958.
13. Ng, C. O. and Mei, C. C. (1994), “Roll waves on a shallow layer of mud modeled as a power-law fluid.” Journal of Fluid Mechanics, Vol. 263, p.151-183.
14. Ohtsu, I. and Yasuda, Y. (1991), “Hydraulic jump in sloping channels.” Journal of Hydraulic Engineering, Vol. 117, No. 7, p.905-921.
15. Press, M. J. (1961), “The hydraulic jump.” Engineering honours thesis presented to the University of Western Australia, Nedlands, Australia.
16. Rajaratnam, N. (1968), “Hydraulic jumps on rough beds.” Tans. Engineering Institute, Canada, 11(A-2), p.1-8.
17. Rajaratnam, N. and Subramanya, K. (1968), “Profile of the hydraulic jump” Journal of Hydraulic Division, Proc. ASCE, Paper, No. 5931, p.663-673.
18. Shu and Zhou (2006), “Characteristics of a hydraulic jump in Bingham fluid.” Journal of Hydraulic Research, Vol.0, No.0, p.1-6.
19. Silvester, R. (1964), “Hydraulic jump in all shapes of horizontal channels.” Journal of Hydraulic Division, ASCE, Vol. 90, No. 1, p.23-55.
20. Subramanya, K. (1997). Flow in open channels. McGraw-Hill Book Company New York.
21. Tevzadze and Kukhalashvili (1991), “Calculation of conjugate depths of a hydraulic jump.” Translated from Gidrotekhnicheskoe Stroitel’stvo, No.12, p.45-47.
22. Wan, Z. (1982), “Bed material movement in hyperconcentrated flow.” Series Paper 31. Inst. Hydrodynamics and Hydraulic Engineering, Technical University of Denmark.
23. Wu, S. and Rajaratnam, N. (1995), “Free jump, submerged jump and wall jets.” Journal of Hydraulic Research, Vol. 33, No. 2, p.197-212.
24. 王志賢 (2007)，「泥砂顆粒組成對黏姓土石流體流變參數影響之研究」，國立成功大學水利及海洋工程研究所博士論文。
25. 余昌益 (1996)，「高含砂水流流變參數之實驗研究」，國立成功大學水利及海洋工程研究所碩士論文。
26. 陳弘殷 (1998)，「阿公店水庫淤泥之流變特性」，國立成功大學水利及海洋工程研究所碩士論文。
27. 張家榮 (2008)，「斜坡矩形束縮渠道斜震波及水躍研究」，國立成功大學水利及海洋工程研究所博士論文。
28. 詹錢登、張家榮 (2005) “斜坡矩形束縮渠道上的水躍特性” 中國土木水利工程學刊，Vol. 17(2)，第227-233頁，台灣。
29. 錢寧、萬兆惠 (1983)，「泥砂運動力學」，科學出版社，北京。
30. 謝平成 (1997)，「明渠水力學」，曉園出版社，台北。