Non-Fickian transport models for characterising the sediment suspension in unsteady flows

Abstract

Non-Fickian transport of suspended sediment has been observed at field and laboratory scales. Such as turbulent bursting, resulting in complex dynamics for the sediment particles movement. The erosion and deposition of sediment have an impact on the hydraulic engineering and environment. This study makes an attempt to develop the variable-order fractional advection-diffusion equation (VOFADE) and variable-order Hausdorff fractal derivative advection-diffusion equation (VOHADE) models to describe the vertical distribution of suspended sediment in unsteady turbulent flows. From a classical viewpoint, the distribution of the concentration in sediment-laden flows is determined based on Fick?s first law. However, the vertical diffusion of suspended particles exhibits the non-locality/space scale dependency and history memory/time scale dependency properties due to turbulent bursting. Moreover, previous literatures have indicated that turbulence structure changes with the water depth. Hereby, we employ the space-dependent VOFADE and VOHADE models to describe the vertical diffusion of suspended sediment in unsteady flows, and further test its applicability with the experimental data. Numerical simulation results confirm that the VOFADE and VOHADE models give a better agreement with the experimental data and can well characterise the space-dependent anomalous transport. Hence, the models proposed by this study may help to provide a powerful mathematical physical model in the quantification of suspended sediment transport.