  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 $\alpha$.
