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In the stilling pool of the spillway and flushing tunnel, there are often problems such as unstable fluctuation range of hydraulic jump and even overtopping the side wall. In order to obtain a good energy dissipation and erosion prevention effect of the stilling pool, the fluid movement during the flood discharge process of the spillway and flushing tunnel was studied through a combination of numerical simulation and physical model testing, which was beneficial for gaining hydraulic dynamics of the flow field and the downstream riverbed erosion conditions . The hydraulic characteristics of water flow under different stilling pool body shape optimization schemes were analyzed, and those schemes were verified by physical experiments. The results show that the flow pattern is more stable under adding a rectangular tailgate at the stilling pool, the water surface fluctuation is reduced. At the same time, the maximum decrease of inlet and outlet velocity in the stilling pool is 7.66 m/s. The pressure distribution is uniform, no negative pressure is generated, and the energy dissipation rate reaches 80.60%. After the addition of the rectangular tailgate, the riverbed scour pit range of the design and verification conditions are reduced by 12.20 m and 13.30 m compared with the original scheme, and it' s maximum scour pit depth are reduced by 0.48 m and 1.00 m compared with the original scheme, respectively. The decrease of the riverbed scour pit range and the maximum scour pit depth shows that the addition of rectangular tailgate has obvious protective effect on the downstream. The research shows that the stilling pool body shape optimization scheme can effectively improve its energy dissipation. The flow field distribution of the optimized stilling pool body shape is uniform, which have great protection on the downstream river bed. The research results can provide reference for diversion and flood discharge and sand flushing projects. [ABSTRACT FROM AUTHOR]

Objective The Dupuit model of well flow is a classical steady-state well flow model for a homogeneous unconfined aquifer in a round island. However, it does not consider the widely existing infiltration recharge from precipitation, and is also inapplicable for stratified heterogeneous aquifer systems. Therefore, it must be modified to address these issues. Methods On the basis of the revised Dupuit well flow model which incorporates infiltration recharge, this study further extended its application to a stratified heterogeneous unconfined aquifer. The Girinskii's potential function was used to construct the differential equations for the radial groundwater flow according to the water balance principle, and the analytical solutions satisfying the boundary conditions are then obtained as formulas of the flow rate, water table and groundwater divide. Taking the bilayer structure as an example, typical groundwater level curves with respect to 30 scenarios of different parameter values were investigated. A special phenomenon was found in which the curves of different hydraulic conductivities intersect at a single point, which could also be proven in theory. This analytical model still adopted the Dupuit assumption and did not consider the "hydraulic jump" phenomenon on the wall of the pumping well. To check the impact of these constraints on the applicability of the analytical formulas, a two-dimensional numerical model for axially symmetric seepage was built for comparison. Results As indicated by the results, the relative error of the groundwater level estimated from the analytical solution is generally less than 4%, except for the zone near the pumping well. On the groundwater divide, where the Dupuit assumption is mostly invalid, the relative errors of the analytical solution to both the distance and height of the divide are smaller than 0.1%. Conclusion The Dupuit assumption does not significantly influence applicability of the analytical model.

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Ｔｈｅ ｈｙｄｒａｕｌｉｃ ｊｕｍｐ ｉｎ ｒｅｃｔａｎｇｕｌａｒ， ｈｏｒｉｚｏｎｔａｌ ａｎｄ ａｂｒｕｐｔ ｅｎｌａｒｇｅｍｅｎｔｓ ｃｈａｎｎｅｌｓ ｗａｓ ａｎａｌｙｚｅｄ． Ｂａｓｅｄ ｏｎ ｔｈｅ ｉｎｖｅｓｔｉｇａｔｉｏｎ ｏｆ ｈｙｄｒａｕｌｉｃ ｊｕｍｐｓ ｆｏｒｍａｔｉｏｎ ｍｅｃｈａｎｉｓｍ ｔｈｒｏｕｇｈ ｂｏｔｈ ｅｘｐｅｒｉｍｅｎｔａｌ ａｎｄ ａｎａｌｙｔｉｃａｌ ｍｅｔｈｏｄｓ ｉｎ ａｂｒｕｐｔ ｅｎｌａｒｇｅｍｅｎｔｓ ｃｈａｎｎｅｌｓ， ｔｈｉｓ ｐａｐｅｒ ｆｏｕｎｄ ｏｕｔ ｔｈａｔ ｔｈｅ ｃｈａｎｎｅｌ ｓｉｄｅ ｗａｌｌ ａｖｅｒａｇｅ ｄｅｐｔｈ ｏｆ ｔｈｅ ｒｅ⁃ｃｉｒｃｕｌａｔｉｏｎ ｚｏｎｅ ａｔ ｔｈｅ ｓｕｄｄｅｎ ｅｎｌａｒｇｅｍｅｎｔ ｃｈａｎｎｅｌ ｃｒｏｓｓ ｓｅｃｔｉｏｎ ｗａｓ ｒｅｌａｔｅｄ ｔｏ ｔｈｅ ｉｎｆｌｏｗ ｅｎｅｒｇｙ ｈｅａｄ ａｎｄ ｔｈｅ ｒａｔｉｏ ｏｆ ｕｐｓｔｒｅａｍ ａｎｄ ｄｏｗｎｓｔｒｅａｍ ｃｈａｎｎｅｌ ｗｉｄｔｈｓ， ａｓ ｗｅｌｌ ａｓ ａｓｓｕｍｅｄ ｔｈａｔ ｔｈｅ ａｖｅｒａｇｅ ｄｅｐｔｈ ｅｑｕａｌｅｄ ｔｈｅ ｐｒｏｄｕｃｔ ｏｆ ｔｈｅ ｉｎｆｌｏｗ ｅｎｅｒｇｙ ｈｅａｄ ｔｉｍｅｓ ｔｈｅ ｃｏｒｒｅｃｔｉｏｎ ｃｏｅｆｆｉｃｉｅｎｔ， ｗｈｉｃｈ ｗａｓ ｐｒｅｓｅｎｔｅｄ ｉｎ ｔｅｒｍｓ ｏｆ ｔｈｅ ｉｎｆｌｏｗ Ｆｒｏｕｄｅ ｎｕｍｂｅｒ ａｎｄ ｔｈｅ ｒａｔｉｏ ｏｆ ｕｐｓｔｒｅａｍ ａｎｄ ｄｏｗｎｓｔｒｅａｍ ｃｈａｎｎｅｌ ｗｉｄｔｈｓ ａｃｃｏｒｄｉｎｇ ｔｏ ｓｏｍｅ ｏｂｓｅｒｖａｔｉｏｎ ｄａｔａ ｐｒｅｓｅｎｔｅｄ． Ｔｈｅｎ ｔｈｅ ｓｅｑｕｅｎｔ ｄｅｐｔｈｓ ｆｏｒｍｕｌａ ｗａｓ ａｃｑｕｉｒｅｄ ｂｙ ｐｌｕｇｇｉｎｇ ｔｈｅ ａｖｅｒａｇｅ ｗａｔｅｒ ｄｅｐｔｈ ｉｎｔｏ ｔｈｅ ｅｑｕａｔｉｏｎ ｆｏｒ ｔｈｅ ｓｅｑｕｅｎｔ ｄｅｐｔｈｓ ｒａｔｉｏ． Ａｎｄ ｉｔ ｃｏｕｌｄ ｂｅ ｆｏｕｎｄ ｔｈａｔ ｔｈｅ ｓｅｑｕｅｎｔ ｄｅｐｔｈｓ ｃａｌｃｕｌａｔｅｄ ｂｙ ｔｈｅ ｆｏｒｍｕｌａ ｗｅｒｅ ｉｎ ｇｏｏｄ ａｇｒｅｅｍｅｎｔ ｗｉｔｈ ｔｈｅ ｏｔｈｅｒ ｏｂｓｅｒｖａｔｉｏｎ ｄａｔａ ｐｒｅｓｅｎｔｅｄ， ｗｉｔｈ ｈｉｇｈｅｒ ｃａｌｃｕｌａｔｉｏｎ ａｃｃｕｒａｃｙ ｔｈａｎ ｔｈｅ ｐｒｅｓｅｎｔｅｄ ｆｏｒｍｕｌａ． [ABSTRACT FROM AUTHOR]