A modified kinetic theory for frictional-collisional bedload transport valid from dense to dilute regime

TL;DR

This paper develops a modified kinetic theory model for sediment transport that accurately captures both dense and dilute granular flow regimes by incorporating effects of inter-particle friction, saltating particles, and drag force nonlinearities.

Contribution

It introduces a new continuum model combining Coulomb friction with kinetic theory, improving predictions across flow regimes and aligning with discrete simulation data.

Findings

Modified kinetic theory reproduces discrete simulations across flow regimes.

Inter-particle friction increases energy dissipation and affects radial distribution.

The model recovers the {} rheology in dense granular flows.

Abstract

Modelling sediment transport is still a challenging problem and is of major importance for the study of particulate geophysical flows. In this work, the modelling of sediment transport in the collisional regime is investigated with a focus on the continuum modelling of the granular flow. For this purpose, a frictional-collisional approach, combining a Coulomb model with the kinetic theory of granular gases, is developed. The methodology is based on a comparison with coupled fluid-discrete simulations, that classical kinetic theory model fails to reproduce. In order to improve the continuum model, the fluctuating energy balance is computed in the discrete simulations and systematically compared with the kinetic theory closure laws. Inter-particle friction is shown to affect the radial distribution function and to increase the energy dissipation, in agreement with previous observations in the literature. Due to saltating particles, whose motion can not be captured by the kinetic theory, departure from the viscosity and diffusivity laws are observed in the dilute part of the granular flow. Finally, the quadratic nature of the drag force is shown to increase the granular fluctuating energy dissipation. Based on these observations, modifications of the kinetic theory closure laws are proposed. The modified model reproduces perfectly the discrete simulations in the entire depth structure of the granular flow. These modifications are shown to impact the rheological properties of the flow and they make it possible to recover the {\mu}(I) rheology in the dense regime.