An Enhanced Depth-integrated Model for Flows over a Negative Step with Hydraulic Jump

Department of Civil and Environmental Engineering, Graduate School of Engineering, Hiroshima University, Japan

Abstract

Depth-integrated models play an important role of predicting flows for several practical problems. There are many contributions to develop an enhanced depth-integrated model to have the ability of evaluating vertical flow structures. However, it is still challenging for the depth integrated models to calculate flows over a negative step accompanying a hydraulic jump, because the separation zone behind the step and the pattern of the hydraulic jump depend on the several hydraulic conditions such as Froude number, step height and downstream water depth. In this study, assuming gravel bed rivers in which the bed is covered with relatively large roughness, an enhanced depth integrated model is developed to calculate various hydraulic jump patterns generated downstream from the negative step. The present method is based on General Bottom Velocity Computation method employing Dynamic Wall Law with 4th degree polynomial velocity distribution (GBVC4-DWL). The model with the virtual bed slope behind the negative step and the critical slope of wave breaking is validated through the comparisons with the experimental results on flows over a negative step for submerged jet. weak jump and undular jump conditions. Then the essential terms of equations which compose the present method to calculate the flow downstream of the negative step are investigated.