Hydrodynamic analysis of fully developed turbidity currents over plane beds based on self-preserving velocity and concentration distributions

Abstract

This paper presents a hydrodynamic analysis for the fully developed turbidity currents over a plane bed stemming from the classical three-equation model (depth-averaged fluid continuity, sediment continuity, and fluid momentum equations). The streamwise velocity and the concentration distributions preserve self-similarity characteristics and are expressed as single functions of vertical distance over the turbidity current layer. Using the experimental data of turbidity and salinity currents, the undetermined coefficients and exponents are approximated. The proposed relationships for velocity and concentration distributions exhibit self-preserving characteristic for turbidity currents. The depth-averaged velocity, momentum, and energy coefficients are thus obtained using the proposed expression for velocity law. Also, from the expressions for velocity and concentration, the turbulent diffusivity and the Reynolds shear stress distributions are deduced with the aid of the diffusion equation of sediment concentration and the Boussinesq hypothesis. The generalized equation of unsteady-nonuniform turbidity current is developed by using the velocity and concentration distributions in the moments of the integral scales over the turbidity current layer. Then, the equation is applied to analyze the gradually-varied turbidity currents considering closure relationships for boundary interaction and shear velocity. The streamwise variations of current depth, velocity, concentration, reduced sediment flux, and Richardson number are presented. Further, the self-accelerating and depositional characteristics of turbidity currents including the transitional feature from erosional to depositional modes are addressed. The effects of the streamwise bed slope are also accounted for in the mathematical derivations. The results obtained from the present model are compared with those from the classical model.