Analysis of Flows in Undular and Breaking Hydraulic Jumps by Non-Hydrostatic Quasi Three-Dimensional Model Considering Flow Equations on Boundary Surfaces (Q3D-FEBS)

The analysis of flows in a hydraulic jump is needed for estimating energy dissipation in hydraulic structures and predicting bed scouring in the downstream river channels. A hydraulic jump occurs in various forms and it depends on the upstream Froude number (Fr) and downstream water depth. Broadly speaking, there are two types of hydraulic jumps. One is an undular hydraulic jump which forms the wavy water surface and high-velocity flows appear near the water surface. The other is a breaking hydraulic jump which forms inverse flow zones just below the water surface called surface roller. The surface roller generates a large-scale turbulence and moves high-velocity flows toward the bottom surface. The depth-integral model for the two types of the jumps has been proposed by many researchers. However, it seems so far that no model that has simulated the flows in both types of the jumps. Generally, the undular jump breaks and surface roller develops (i.e. the breaking jump occurs) when the Fr exceeds about 1.7. We think these are the result of a flow separation on the wavy water surface of the undular jump. So, both types of the jumps can be calculated in the framework of the depth-integral model by solving the flow velocity along the water surface and considering the effects of the flow separations.

This paper proposes a new non-hydrostatic quasi three-dimensional model considering flow equations on boundary surfaces (water surface and bottom surface) called Q3D-FEBS. The Q3D-FEBS assumes vertical distributions of horizontal velocities and turbulent kinetic energy as the third order polynomial equations. Flow velocities and turbulent kinetic energy at the boundary surfaces are used for boundary conditions of the polynomial equations. These procedures allow the simulations of the three-dimensional flows considering changes in velocity distributions, pressure distributions and turbulence generation due to the flow separations in the framework of the depth-integral model. The Q3D-FEBS was applied to the previous experiments of the undular jump (Fr = 1.11 and 1.27) and the breaking jump (Fr = 3.1). The results show that Q3D-FEBS can explain measured water surface profiles and velocity distributions of the undular and breaking hydraulic jumps. Besides, the length of the surface roller and longitudinal distributions of turbulent kinetic energy were in good agreement with the previous studies. Moreover, it was showed that Q3D-FEBS can simulate the process of the undular jump breaking and surface roller development due to the increase of Fr.