  A minimal Lagragian two-phase model to study turbulent bedload transport
focusing on the granular phase is presented, and validated with experiments.
The model intends to describe bedload transport of massive particles in fully
rough flows at relatively low Shields numbers, for which no suspension occurs.
A discrete element method for the granular phase is coupled with a one
dimensional volume-averaged two-phase momentum equation for the fluid phase.
The coupling between the discrete granular phase and the continuous fluid phase
is discussed, and a consistent averaging formulation adapted to bedload
transport is introduced. An original simple discrete random walk model is
proposed to account for the fluid velocity fluctuations. The model is compared
with experiments considering both classical sediment transport rate as a
function of the Shields number, and depth profiles of solid velocity, volume
fraction, and transport rate density, from existing bedload transport
experiments in inclined flume. The results successfully reproduce the classical
3/2 power law, and more importantly describe well the depth profiles of the
granular phase, showing that the model is able to reproduce the particle scale
mechanisms. From a sensitivity analysis, it is shown that the fluctuation model
allows to reproduce a realistic critical Shields number, and that the influence
of the granular parameters on the macroscopic results are weak. Nevertheless,
the analysis of the corresponding depth profiles reveals an evolution of the
depth structure of the granular phase with varying restitution and friction
coefficients, which denotes the non-trivial underlying physical mechanisms.
