Theoretical and numerical analysis of the influence of the bottom friction formulation in free surface flow modelling

Bottom friction modeling is an important step in river flows computation with 1D or 2D solvers. It is usually performed using energy slope based formulations established for uniform flow conditions or a turbulent regime based approach relying on turbulence analysis. However, the use of these formulations is often done for relative roughness far from their validity fields. Furthermore, the theoretical definition of the roughness coefficients, defined by the different authors of both approaches, is no more available for usual numerical flow modeling, considering numerical approximations. The value of this coefficient becomes generally dependent of the flow conditions.
Following the definition of the flow validity field of the main friction formulations proposed in literature, an original formulation has been developed. It combines two explicit turbulent regime based formulations smoothly linked by a polynomial expression, providing a continuous formulation on the wide range of roughness usually encountered in river flows. The formulation is suitable to model, with a unique value of the friction coefficient, river flows with a wide range of hydrodynamic properties (water depth, discharge). The efficiency of this new formulation, fitted on explicit friction formulations and numerically adjusted, is demonstrated through various 1D and 2D practical applications.