Numerical Simulation of NSF PIRE benchmark with a two-phase depth-integrated model.

The analysis of unsteady river flows requires adequate representation of different but mutually interacting processes, for instance the motion of the fluid and the erosion/deposition of solid particles. To this aim, along with models been built upon traditional hydraulics principles (see Cao & Carling, 2002 among many others) and sometimes coupled with additional lag-type differential equations to account for non-equilibrium transport (Armanini & Di Silvio, 1988; Galappatti & Vreugdenhil, 1985; Jain, 1992; Nakagawa & Tsujimoto, 1980; Wu et al., 2004; Xia et al., 2010), the two-phase theory may be regarded as a promising theoretical framework. In fact, Such an approach has been widely applied in chemical engineering, e.g. physics of fluidization (Anderson et al., 1995; Glasser et al., 1996) and in geophysical context, for example to study the propagation of debris flows, avalanches and landslides (Iverson, 1997; Pitman & Le, 2005; Savage & Hutter, 1989). In open channel hydraulics, this theory has been fruitfully applied to predict the sediment concentration profile in uniform flows, incorporating the effect of particle-particle interaction and particle inertia (Greimann & Holly, 2001; Hsu et al., 2004; Jiang et al., 2004). Recently, a depth averaged morphodynamical model based on a two-phase formulation has been proposed for unsteady river flows (Greco et. Al., 2008). While mass and momentum conservation principle, separately imposed for both phases, can be derived in a rather standard way, the expression of the source terms of the conservation equations still offers room for discussion. A novel closure for the above two-phase model is presented in this paper, which is based on both experimental support and theoretical analysis.