A Two-Dimensional Two-Phase Depth-Integrated Model for Transients over Mobile Bed

Fast geomorphic transients may involve complex scenarios of sediment transport, occurring near the bottom as bed load (i.e. saltating, sliding and rolling) or as suspended load in the upper portion of the flow. The two sediment transport modalities may even coexist or alternate each-other during the same event, especially whenever the shear stress varies considerably. Modeling these processes is therefore a challenging task, for which the usual representation of the flow as a mixture may result unsatisfactory. In the present paper a new two-phase depth-averaged model is presented, which accounts for variable sediment concentration both in bed and suspended loads. Distinct phase velocities are considered for bed load, while the slip velocity between the two phases is neglected in the suspended load. It is shown that the resulting two-phase model is hyperbolic and the analytical expression of the eigenvalues is provided. The entrainment/deposition of sediment between the bottom and the bed load layer is based on a modified van Rijn transport parameter, while for the suspended sediment a first-order exchange law is considered. A numerical finite-volume method is employed for the simulation of three literature dam-break experiments, which are effectively reproduced in terms of both free surface elevation and bottom deformation, confirming the key role played by the solid concentration variability even for two-phase models.