Dense granular flow rheology in turbulent bedload transport

Abstract

The local granular rheology is investigated numerically in turbulent bedload transport. Considering spherical particles, steady uniform configurations are simulated using a coupled fluid–discrete-element model. The stress tensor is computed as a function of the depth for a series of simulations varying the Shields number, the specific density and the particle diameter. The results are analysed in the framework of the $\unicode[STIX]{x1D707}(I)$ rheology and exhibit a collapse of both the shear to normal stress ratio and the solid volume fraction over a wide range of inertial numbers. Contrary to expectations, the effect of the interstitial fluid on the granular rheology is shown to be negligible, supporting recent work suggesting the absence of a clear transition between the free-fall and turbulent regimes. In addition, data collapse is observed up to unexpectedly high inertial numbers $I\sim 2$, challenging the existing conceptions and parametrisation of the $\unicode[STIX]{x1D707}(I)$ rheology. Focusing upon bedload transport modelling, the results are pragmatically analysed in the $\unicode[STIX]{x1D707}(I)$ framework in order to propose a granular rheology for bedload transport. The proposed rheology is tested using a 1D volume-averaged two-phase continuous model, and is shown to accurately reproduce the dense granular flow profiles and the sediment transport rate over a wide range of Shields numbers. The present contribution represents a step in the upscaling process from particle-scale simulations towards large-scale applications involving complex flow geometry.