On the physical origin of enhanced turbulent-dispersion of 'heavy particles' in suspended-load

In the state-of-the-art for suspended-load modeling it is commonly assumed that the concentration profile results from a balance between a settling flux, in which the settling velocity is considered as equal to its value for a single settling particle in quiescent water, and an upward turbulent flux modeled using a Fickian gradient diffusion approximation. While this model provides a general framework, comparison with experiments reveals that the concentration diffusivity is not equal to the eddy viscosity and a turbulent Schmidt number needs to be introduced. Based on Coleman (1970,1981) data, van Rijn (1984) proposed an empirical model which suggests that the Schmidt number is a decreasing function of W_s/u_*. This result is intriguing as it suggests that the turbulent dispersion of sediment concentration is enhanced when the particle’s settling velocity increases relative to the bed friction velocity. Van Rijn suggested that this is due to centrifugal forces that tends to throw inertial particles out of the turbulent vortices leading to an enhanced particle dispersion compared to momentum. In the present contribution, we use high-resolution experimental data and turbulence resolving two-phase flow simulations that directly resolve the turbulent momentum and particle fluxes and the flow turbulence to investigate the different terms appearing on the mass balance mentioned above.  Both the experimental and the numerical results show that the actual turbulent Schmidt number based on the resolved sediment flux is higher than unity meaning that turbulent dispersion efficiency of « heavy particles » is reduced. This contradicts van Rijn’s prediction model of the Schmidt number. One plausible explanation is that the settling velocity of particles is reduced in highly turbulent flows. Using the experimental and numerical results, the actual settling velocity in the turbulent flow is retrieved from the mass balance at steady state. It is found that it is significantly retarded compared with the value in quiescent water (10 to 40%). This result is in good agreement with the one obtained in recent experiments performed in a turbulent grid at KIT (Germany) using the same particles (Akutina et al., 2020). The authors found a settling retardation of 16% for the same turbulent intensities as in the present experiments. The results presented herein completely change the paradigm for turbulent suspension load modeling and open new perspectives on the development of new, physical process-based, parametrizations required for large-scale models. This, of course, will require to extend the proposed methodology to a wider range of flow and sediment conditions.