Section: New Results

Simulations of hydraulic jumps with a turbulent Shallow Water model

Participants : Hervé Guillard, Argiris Delis [Technical University of Crete, Greece] , Yih-Chin Tai [National Cheng Kung University, Taiwan] .

We have studied numerically an extension designed for turbulent flows of the shallow water model. The model is able to describe the oscillatory nature of turbulent hydraulic jumps and as such correct the deficiency of the classical shallow water equations. The model equations, originally developed for horizontal flow or flows occurring over small constant slopes, are straightforwardly extended here for modeling flows over non-constant slopes and numerically solved by a second-order well-balanced finite volume scheme. Further, a new set of exact solutions to the extended model equations are derived and several numerical tests are performed to validate the numerical scheme and its ability to predict the oscillatory nature of hydraulic jumps under different conditions. The comparisons with experiments performed at Tainan University are very satisfactory given the simplicity of the model [27].