Towards Improved Constitutive Laws for Two-Phase Flow Sediment Transport Models: Application to Sheet-Flow Under Unidirectional Flow Forcing.

The open source two-phase sediment transport model sedFoam (Cheng and Hsu, 2014) is used to test different constitutive laws for the modeling of interparticle stresses under sheet-flow conditions. The numerical model is first validated on Sumer et al. (1996) data for three different Shields numbers using both the kinetic theory of granular flows as proposed by Hsu et al. (2004) and the mu(I) dense granular rheology as proposed by Revil-Baudard and Chauchat (2013). Beyond these validation tests we use the numerical model to investigate the validity of the closure laws for the interparticle stresses and the turbulent models for a range of particle diameter. Our goal is to provide a better parametrisation of the two-phase model for a wide range of particle inertia. In fact, it has been observed that kinetic theory is not relevant for small sands for which collisions are almost inefficient and the mu(I) rheology has to be tested for coarse sands for which a gaseous collisional regime can be significant. From this analysis an hybrid constitutive law mixing both approaches will be proposed to cover the full range of particles inertia (fine to coarse sand). The proposed constitutive law will then be used for applications to coastal engineering problems like sand transport under asymetric waves. This problem is one of the key issues for improving beach morphodynamic models.