Modelling suspended sediment in environmental turbulent fluids

Modelling sediment transport in environmental turbulent fluids is a challenge. This article develops a model of the longitudinal transport of suspended sediment in environmental fluid flows such as floods and tsunamis. The model is systematically derived from a three-dimensional turbulence model based on the Smagorinski large eddy closure. Embedding the physical dynamics into a family of problems and analysing the linear dynamics of the system, the centre manifold theory indicates the existence of a slow manifold parameterised by macroscale variables. Computer algebra then constructs the slow manifold in terms of fluid depth, depth-averaged longitudinal velocities, and suspended sediment concentration. The model includes the effects of sediment erosion, advection and dispersion and the interactions between the sediment and turbulent fluid flow. Vertical distributions of the velocity and concentration in steady flow agree with established experimental data. For a pilot study, numerical simulations of the suspended sediment under long waves show that the developed model predicts physically reasonable sediment flow interaction.