Ill-posedness in modelling 2D river morphodynamics

Abstract

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.