Stelian Ion
Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, Bucharest, Romania

Starting with the pioneering papers of Saint-Venant and Bussinesq the shallow water equations received an increasing interest in both directions of practical applications and theoretical investigations. The enlarging domain of applications has imposed to modellers to weaken the strength of some modeling assumptions concerning the flow variables distribution and the geometrical characteristics of the support surface of the flow. In this context a challenging issue is how the curvature of the surface affects the dynamics of the flow, especially the pressure distribution along the water depth. The model analysed here exhibits an explicit dependence on the curvatures of the surface while the pressure is no more linearly distributed with respect to water depth (hydrostatic distribution).If the curvatures of the surface are set equal to zero then the model coincide with the classical shallow water equations with hydrostatic distribution of the pressure field. In the end of the paper we present a comparative analysis of the solutions of the classical and the new model in the case of a largely used test flow, the flow over a bump.