Concentration profiles for fine and coarse sediments suspended by waves over ripples: An analytical study with the 1-DV gradient diffusion model

Field and laboratory measurements of suspended sediments over wave ripples show, for time-averaged concentration profiles in semi-log plots, a contrast between upward convex profiles for fine sand and upward concave profiles for coarse sand. Careful examination of experimental data for coarse sand shows a near-bed upward convex profile beneath the main upward concave profile. Available models fail to predict these two profiles for coarse sediments. The 1-DV gradient diffusion model predicts the main upward concave profile for coarse sediments thanks to a suitable $\beta$(y)-function (where $\beta$ is the inverse of the turbulent Schmidt number and y is the distance from the bed). In order to predict the near-bed upward convex profile, an additional parameter {\alpha} is needed. This parameter could be related to settling velocity ($\alpha$ equal to inverse of dimensionless settling velocity) or to convective sediment entrainment process. The profiles are interpreted by a relation between second derivative of the logarithm of concentration and derivative of the product between sediment diffusivity and $\alpha$.