References
- Afshar, N. R., Asawa, G. L., & Ranga Raju, K. G. (1994). Air concentration distribution in self-aerated flow. Journal of Hydraulic Research, 32(4), 623–631. doi:https://doi.org/10.1080/00221686.1994.9728359
- Boes, R. M., & Hager, W. H. (2003). Two–phase flow characteristics of stepped spillways. Journal of Hydraulic Engineering, 129(9), 661–670. doi:https://doi.org/10.1061/(ASCE)0733-9429(2003)129:9(661)
- Brocchini, M., & Peregrine, D. H. (2001). The dynamics of strong turbulence at free surfaces. Part 1. Description. Journal of Fluid Mechanics, 449(15), 225–254. doi:https://doi.org/10.1017/S0022112001006012
- Bung, D. B. (2013). Non-intrusive detection of air–water surface roughness in self–aerated chute flows. Journal of Hydraulic Research, 51(3), 322–329. doi:https://doi.org/10.1080/00221686.2013.777373
- Cain, P. (1978). Measurements within Self-aerated Flow on a Large Spillway [PhD thesis]. University of Canterbury, Christchurch, New Zealand. University of Canterbury.
- Castro–Orgaz, O. (2010). Velocity profile and flow resistance models for developing chute flow. Journal of Hydraulic Engineering, 136(7), 447–452. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0000190
- Castro–Orgaz, O., & Hager, W. H. (2010). Downstream curve and turbulent boundary layer development for chute flow. Journal of Hydraulic Research, 48(5), 591–602. doi:https://doi.org/10.1080/00221686.2010.507337
- Chanson, H. (1989). Flow downstream of an aerator-aerator spacing. Journal of Hydraulic Research, 27(4), 519–536. doi:https://doi.org/10.1080/00221688909499127
- Chanson, H. (1993). Self-aerated flows on chutes and spillways. Journal of Hydraulic Engineering, 119(2), 220–243. doi:https://doi.org/10.1061/(ASCE)0733-9429(1993)119:2(220)
- Chanson, H. (1995). Air bubble entrainment in free-surface turbulent flows. Experimental investigations. Report No. CH46/95, Department of civil engineering. The University of Queensland.
- Chanson, H. (1996). Air bubble entrainment in free–surface turbulent shear flows. Academic Press.
- Chanson, H. (2009). Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environmental Fluid Mechanics, 9(2), 125–142. doi:https://doi.org/10.1007/s10652-008-9078-3
- Chanson, H. (2013). Hydraulics of aerated flows: qui pro quo? Journal of Hydraulic Research, 51(3), 223–243. doi:https://doi.org/10.1080/00221686.2013.795917
- Chanson, H., & Toombes, L. (2002). Air–water flows down stepped chutes: turbulence and flow structure observations. International Journal of Multiphase Flow, 28(11), 1737–1761. doi:https://doi.org/10.1016/S0301-9322(02)00089-7
- Chanson, H., & Toombes, L. (2003). Strong interactions between free surface aeration and turbulence in an open channel flow. Experimental Thermal and Fluid Science, 27(5), 525–535. doi:https://doi.org/10.1016/S0894-1777(02)00266-2
- Davies, J. T. (1972). Turbulence Phenomena. Academic Press.
- Dey, S., & Raikar, R. V. (2007). Characteristics of loose rough boundary streams at near-threshold. Journal of Hydraulic Engineering, 133(3), 288–304. doi:https://doi.org/10.1061/(ASCE)0733-9429(2007)133:3(288)
- Ervine, D. A., & Falvey, H. T. (1987). Behaviour of turbulent water jets in the atmosphere and in plunge pools. Proceedings of the Institution of Civil Engineers, 83(2), 295–314. doi:https://doi.org/10.1680/iicep.1987.353
- Falvey, H. T. (1990). Cavitation in chutes and spillways. Engineering. Monograph No. 42, United States Department of the Interior, Bureau of Reclamation.
- Felder, S., & Chanson, H. (2016). Air–water flow characteristics in high–velocity free–surface flows with 50% void fraction. International Journal of Multiphase Flow, 85, 186–195. doi:https://doi.org/10.1016/j.ijmultiphaseflow.2016.06.004
- Felder, S., & Chanson, H. (2017). Scale effects in microscopic air–water flow properties in high–velocity free–surface flows. Experimental Thermal and Fluid Science, 83, 19–36. doi:https://doi.org/10.1016/j.expthermflusci.2016.12.009
- Hager, W. H. (1991). Uniform aerated chute flow. Journal of Hydraulic Engineering, 117(6), 528–533. doi:https://doi.org/10.1061/(ASCE)0733-9429(1991)117:4(528)
- Heller, V. (2011). Scale effects in physical hydraulic engineering models. Journal of Hydraulic Research, 49(3), 293–306. doi:https://doi.org/10.1080/00221686.2011.578914
- Isachenko, N. B. (1965). Effect of relative roughness of spillway surface on degrees of free–surface aeration. Izv. VNIIG, 78, 350–357. (in Russian).
- Killen, J. M. (1968). The surface characteristics of self-aerated flow in steep channels [Ph.D. thesis]. University of Minnesota, Minneapolis, USA. University of Minnesota.
- Kironoto, B. A., & Graf, W. H. (1994). Turbulence characteristics in rough uniform open channel flow. Water Maritime and Energy-ICE, 106(4), 333–344. doi:https://doi.org/10.1680/iwtme.1994.27234
- Kramer, K. (2004). Development of aerated chute flow. Mitteilungen 183, Laboratory of Hydraulics, Hydrology and Glaciology. ETH Zürich.
- Matos, J. (2000, March 22–24). Hydraulic design of stepped spillways over RCC dams. International Workshop on Hydraulics of Stepped Spillways, Balkema (pp. 187–194).
- Matos, J., & Meireles, I. (2014, June 25–27). Hydraulics of stepped weirs and dam spillways: engineering challenges, labyrinths of research. 5th IAHR International Symposium on Hydraulic Structures, Brisbane, Australia.
- Michels, V., & Lovely, M. (1953, September 1–4). Some prototype observations of air entrained flow. Proceeding of Minnesota International Hydraulic Convention, ASCE, 430–414.
- Montes, J. S. (1998). Hydraulics of open channel flow. ASCE Press.
- Nezu, I. (1977). Turbulent Structure in Open-Channel Flows [PhD thesis]. Kyoto University, Kyoto, Japan. Kyoto University.
- Nezu, I., & Rodi, W. (1986). Open-channel flow measurements with a laser doppler anemometer. Journal of Hydraulic Engineering, 112(5), 335–355. doi:https://doi.org/10.1061/(ASCE)0733-9429(1986)112:5(335)
- Pope, S. B. (2000). Turbulent Flows. Cambridge University Press.
- Rao, N. S. L., & Kobus, H. E. (1971). Characteristics of self–aeration free–surface flows. Water Waste / Current Research and Practice, 10, Eric Schmidt Verlag, Germany.
- Rein, M. (1998). Turbulent open-channel flows: drop-generation and self-aeration. Journal of Hydraulic Engineering, 124(1), 98–102. doi:https://doi.org/10.1061/(ASCE)0733-9429(1998)124:1(98)
- Ruff, J. F., & Ward, J. P. (2002). Hydraulic design of stepped spillways. Report No. 99FC800156, U.S. Bureau of Reclamation Denver, Colorado.
- Straub, L. G., & Anderson, A. G. (1958). Experiments on self-aerated flow in open channels. Journal of Hydraulic Division, 84(HY7), 1–35. doi:https://doi.org/10.1061/JYCEAJ.0000261
- Straub, L. G., & Lamb, O. P. (1956). Studies of air entrainment in open–channel flows. Transition, ASCE, 121(1), 30–44. doi:https://doi.org/10.1061/TACEAT.0007393
- Toombes, L., & Chanson, H. (2007). Surface waves and roughness in self-aerated supercritical flow. Environmental Fluid Mechanics, 7(3), 259–270. doi:https://doi.org/10.1007/s10652-007-9022-y
- Valero, D. (2018). On the fluid mechanics of self-aeration in open channel flows [PhD Thesis]. Liège University, Liège, Belgium. Liège University.
- Valero, D., & Bung, D. B. (2016). Development of the interfacial air layer in the non-aerated region of high–velocity spillway flows. Instabilities growth, entrapped air and the influence on the self–aeration onset. International Journal of Multiphase Flow, 84, 66–74. doi:https://doi.org/10.1016/j.ijmultiphaseflow.2016.04.012
- Valero, D., & Bung, D. B. (2018). Reformulating self-aeration in hydraulic structures: turbulent growth of free surface perturbations leading to air entrainment. International Journal of Multiphase Flow, 100, 127–142. doi:https://doi.org/10.1016/j.ijmultiphaseflow.2017.12.011
- Wei, W. R., & Deng, J. (2019, September 1–6). Observations of free surface deformation and air entrainment process in supercritical open channel flows. Proceeding of 38th IAHR Congress, Panama city, Panama.
- Wei, W. R., Deng, J., & Zhang, F. X. (2016). Development of self-aeration process for supercritical chute flows. International Journal of Multiphase Flow, 79(1), 172–180. doi:https://doi.org/10.1016/j.ijmultiphaseflow.2015.11.003
- Wei, W. R., Deng, J., Zhang, F. X., & Tian, Z. (2015). A numerical model for air concentration distribution in self-aerated open channel flows. Journal of hydrodynamics, 27(3), 394–402. doi:https://doi.org/10.1016/S1001-6058(15)60497-8
- Wei, W. R., Xu, W. L., Deng, J., Tian, Z., & Guo, Y. K. (2020). Free surface air entrainment and single-bubble movement in supercritical open-channel flow. Journal of Hydraulic Engineering, 146(7), 04020050. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0001769
- Wei, W. R., Xu, W. L., Deng, J., Tian, Z., & Zhang, F. X. (2017). Free-surface air entrainment in open-channel flows. Science China Technological Sciences, 60(6), 893–901. doi:https://doi.org/10.1007/s11431-016-0220-1
- White, F. M. (2006). Viscous Fluid Flow. McGraw-Hill.
- Wilhelms, S. C. (1997). Self-aerated spillway flow [PhD thesis]. the University of Minnesota, Minneapolis, USA. University of Minnesota.
- Wilhelms, S. C., & Gulliver, J. S. (2005). Bubbles and waves description of self-aerated spillway flow. Journal of Hydraulic Research, 3(6), 522–531. doi:https://doi.org/10.1080/00221680509500150
- Wood, I. R. (1983). Uniform region of self-aerated flow. Journal of Hydraulic Engineering, 109(3), 447–461. doi:https://doi.org/10.1061/(ASCE)0733-9429(1983)109:3(447)
- Wood, I. R. (1984, September 3–6). Air entrainment in high speed flows. Symposium on Scale Effects in Modelling Hydraulic Structures, Esslingen, Germany.
- Wood, I. R. (1985, August 19–23). Air water flows. Proceeding of 21th IAHR Congress (pp. 18–29).
- Wood, I. R. (1991). Air entrainment in free-surface flows. Hydraulic Structures design Manual, IAHR-AIRH Monograph 4. Balkema.
- Wood, I. R. (1995). Discussion of “Air concentration distribution in self-aerated flow.”. Journal of Hydraulic Research, 33(4), 582–585. doi:https://doi.org/10.1080/00221689509498663
- Wood, I. R., Ackers, P., & Loveless, J. (1983). General method for critical point on spillways. Journal of Hydraulic Engineering, 109(2), 308–312. doi:https://doi.org/10.1061/(ASCE)0733-9429(1983)109:2(308)
- Wu, C. G. (2003). Hydraulics (3rd Edition). Higher Education Press. (in Chinese).
- Xi, R. Z. (1988, November 15–18). Characteristics of self-aerated flow on steep chutes. International Symposium on Hydraulics for High Dams, IAHR, Beijing, China.
- Zhang, G., & Chanson, H. (2017). Self-aeration in the rapidly-and gradually-varying flow regions of steep smooth and stepped spillways. Environmental Fluid Mechanics, 17(1), 27–46. doi:https://doi.org/10.1007/s10652-015-9442-z
- Zhong, Q., Chen, Q., Wang, H., Li, D., & Wang, X. (2016). Statistical analysis of turbulent super-streamwise vortices based on observations of streaky structures near the free surface in the smooth open channel flow. Water Resources Research, 52(5), 3563–3578. doi:https://doi.org/10.1002/2015WR017728