Suspended Sediments in Environmental Flows: Interpretation of Concentration Profiles Shapes

In environmental flows, field and laboratory measurements of suspended sediments show two kinds of concentration profiles. For coarse sediments, a near-bed upward convex profile is observed beneath the main upward concave profile. In this study, we consider two 1-DV models, namely, the classical advection–diffusion equation (ADE) based on the gradient diffusion model, and the kinetic model. Both need sediment diffusivity, which is related to the eddy viscosity, and an y-dependent β-function (i.e., the inverse of the turbulent Schmidt number). Our study shows that the kinetic model reverts to the classical ADE with an “apparent” settling velocity or sediment diffusivity. For the numerical resolution of the ADE, simple and accurate tools are provided for both the sediment diffusivity and hindered settling. The results for the concentration profiles show good agreement with the experimental data. An interpretation of the concentration profiles is provided by two “criteria” for shapes. The main for steady open-channel flows shows that the shape of the concentration profiles in the Cartesian coordinate depends on the vertical distribution of the derivative of R (the ratio between the sediment diffusivity and the settling velocity of the sediments): dR/dy > −1 for the upward concave concentration profile while dR/dy < −1 for the near-bed upward convex profile. A generalization is proposed for oscillatory flows over sand ripples, where the time-averaged concentration profiles in the semi-log plots are interpreted by a relation between the second derivative of the logarithm of the concentration and the derivative of the product between the sediment diffusivity and an additional parameter related to the convective sediment entrainment process.