Approximation zones of the Saint-Venant equations f flood routing with overbank flow

Abstract. The classification of river waves as gravity, diffusion or kinematic waves, corresponds to different forms of the momentum equation in the Saint-Venant system. This paper aims to define approximation zones of the Saint-Venant equations for flood routing in natural channels with overbank flow in the flooded area. Using linear perturbation theory, the different terms in the Saint-equations were analysed as a function of the balance between friction and inertia. Then, using non-dimensionalised variables, flood waves were expressed as a function of three parameters: the Froude number of the steady uniform flow, a dimensionless wave, number of the unsteady component of the motion and the ratio between the flooded area zone width and the main channel width. Finally, different theoretical cases, corresponding to different flooded area zone widths were analysed and compared. Results show that, when the width of the flooded area increases, the domain of application of the diffusive wave and the inematic wave models is restricted.

Keywords: Saint-Venant equations; river waves; overbank flow