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

TL;DR

This study uses an analytical 1-DV gradient diffusion model to accurately predict the distinct concentration profiles of fine and coarse sediments over ripples, addressing previous model limitations.

Contribution

It introduces a new parameter to the model, enabling prediction of near-bed upward convex profiles for coarse sediments, improving understanding of sediment suspension dynamics.

Findings

The model successfully predicts the main upward concave profile for coarse sediments.

An additional parameter is necessary to model near-bed upward convex profiles.

Profiles are explained through a relation involving second derivatives of concentration logarithm.

Abstract

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 $\alpha$.