Non-equilibrium concentration profile formulas of suspended sediment and their preliminary applications

The vertical concentration profiles in non-equilibrium sediment transport processes generally deviate from the equilibrium concentration distribution of suspended sediment. The non-equilibrium concentration profile formulas currently available are those of Han and Brown, respectively. However, the complexity of these formulas limits their use in practical calculations. To improve the usefulness of these formulas, the unknown parameters in Han's formula are reduced from three to two, and the three different forms of Brown's formula are transformed into one. These formulas then are proved to be essentially the same to some extent, and only different in the expression form of the exponent. Han's formula then is improved, based on which the theoretical calculation methods and distribution characteristics of non-equilibrium profiles are presented. Han's and Brown's formulas are verified qualitatively and quantitatively. Finally, these formulas are applied in the investigation of the characteristics of certain physical quantities, such as the recovery factor of sediment concentration, near-bottom sediment flux, and the non-equilibrium Péclet number in the non-equilibrium sediment transport process. These results clearly reveal that the magnitude of these physical quantities decreases in the erosion process and increases in the deposition process. The results also show that the formulas are largely applicable for the non-equilibrium sediment transport conditions.