ABSTRACT
Natural rivers which have compound cross section are more complicated due to the interaction between main channel and flood plains. It is important for engineers to predict the lateral velocity distribution and boundary shear stress in order to accurate estimation of sediment transport rate. In this paper, a depth averaged form of streamwise Reynolds-averaged Navier-Stokes equation (RANSE) known as Shiono and Knight Model (SKM) (Eq. 1) is used to estimate lateral distribution of velocity. () ρ g H S 0 − ρ 8 ¯ f U d 2 1 + 1 s 2 + ∂ ∂ y { ρ λ H 2 ( f 8 ) 1 / 2 U d ∂ U d ∂ y } = ∂ H ( ρ U V ) d ∂ y https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315623207/4fbc492d-6678-4a12-aaf6-5c2b8ea38e5f/content/eq469.tif"/>
Where ρ = fluid density; g = gravitational acceleration; H = depth; S0 = river bed slope; f = Darcy-Weisbach friction factor; Ud = depth-averaged streamwise velocity; s = channel side slope (1:s, vertical: horizontal); λ = dimensionless eddy viscosity; and y = lateral coordinate the longitudinal river slope.
Many researchers tried to presented numerical and analytical solution for solving RANSE. Shiono and Knight (1991) by considering secondary flow term (Γ), proposed an analytical solution for estimation of lateral velocity distribution. The goal of this study is to solve this equation by finite difference method in gravel bed rivers and then computed distribution of the bed shear stress for prediction of bed load transport rate with various proposed formulas; such as Meyer-Peter and Muller, vanRijn, as well as Engelund and Fredsoe. An OTT velocity meter and a Helley-Smith sampler used to measure flow velocity and bed load data, respectively. The observed data were used to calibrate the main parameter of this model i.e. friction factor (f). As illustrated in Figure 1, the numerical solution can predict lateral velocity distribution accurately. Also the result showed Meyer-Peter and Muller formulae agrees well with the measured data. Lateral distribution of velocity. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315623207/4fbc492d-6678-4a12-aaf6-5c2b8ea38e5f/content/fig63_1.tif"/>
