Author(s): Cristiana Di Cristo; Michele Iervolino; Andrea Vacca
Keywords: Morphodynamical models; Boundary conditions; Initial value problems
Abstract: The knowledge of the correct number of boundary conditions which has to be considered to guaranteed the well-posedenes of a morphodynamical model represents a key point for the use of the model itself. The hyperbolic nature, and therefore the characteristic theory, allows to trivially individuate the number of boundary conditions, as far as the three and four equations model are concerned. The present paper aims to individuate the mathematical character of the five-equations two-layer model proposed by Capart and Young (2002), which has been successfully applied to simulate morphodynamical processes as antidune formation and bank erosion. It is found that such a model attains hyperbolic structure only for small values of clear water Froude number. When this parameter exceeds unity, for wide ranges of the ratios between velocities and heights of the two layers the model shows a hybrid character. This feature has strong implications in the field of application of the model, especially as far as the choice of numerical methods and assignment of the boundary conditions are concerned.