A mathematical model and numerical method for computation of a turbulent river stream

A mathematical model and a computational method for numerical investigation of turbulent river streams are proposed. The mathematical model is based on the shallow water approach. The model takes into account the influence of bottom friction, wind friction, Coriolis force, and complex geometry of the river bed with inflows and irregular bathymetry. A depth-averaged version of the k-epsilon turbulence model with a specific term for the generation of turbulence by the river bottom friction is used to describe the turbulent structure of the flow.
The numerical method for solving discretized equations is a modification of the SIMPLE algorithm proposed by Patankar. A novel feature of the algorithm is considering the water depth variation in the equations of the model.
The model and the method proposed were applied to computations of a turbulent flow in laboratory open channels and of steady flow in a shallow river with a sharply curved bed.
Computations of the flow in the laboratory channel show a good agreement with the experimental observations and results from references. The results of the calculations of the flow in an S-shaped river flow represent flow patterns observed in studying river flows and show agreement with general concepts.