Ill-posedness in modelling 2D river morphodynamics

The set of equations used in modelling river  morphodynamics needs to be (at least) wellposed  to be representative of the real natural  phenomenon. As we deal with a time dependent  process the solution needs to be wave-like to be  well-posed. In other words, the solution must  have a domain of dependence and of influence.  Otherwise, the future river state influences the  present solution, which is physically unrealistic.  Based on an analysis of the system of  equations to model one-dimensional river  morphodynamics with unisize sediment and a  Chezy-based friction term, Cordier (2011)  concluded that the system is always well-posed.  Stecca (2014) extended the analysis to a mixture  of sediment with 2 size fractions and concluded  that under degradational conditions the system  may become ill-posed. This result supported the  first analysis that found ill-posedness in mixedsize  sediment morphodynamics conducted by  RIbberink (1987) assuming a simpler model.  Here we extend these analyses by adding the  effects of flow curvature which creates an  intrinsically 3D flow referred to as secondary or  spiral flow (Van Bendegom, 1947). In this study  the flow is assumed bi-dimensional which implies  that the secondary flow needs to be  parameterized.