The article summarizes previous studies on the flow in open channels with rigid vegetation, and constructs a mathematical model for submerged and emerged rigid vegetation. The model involves the forces balance in the control volume in one-dimensional steady uniform flow. For submerged vegetation, the whole flow is divided into four regions： external region, upper vegetated region, transition region and viscous region. According to the Karrnan similarity theory, the article improves the mixing length expression, and then gives an analytical solution to predict the vertical distribution of stream-wise velocity in the external region. For emerged vegetation, the flow is divided into two region： outer region and viscous region. In the two circumstances, the thicknesses of each region are determined respectively. The comparison between the calculated results and our experimental data and other researchers＇ data proves that the proposed model is effective.
By choosing a PVC slice to simulate flexible vegetation, we carried out experiments in an open channel with submerged flexible vegetation. A 3D acoustic Doppler velocimeter （micro ADV） was used to measure local flow velocities and Reynolds stress. The results show that hydraulic characteristics in non-vegetation and vegetation layers are totally different. In a region above the vegetation, Reynolds stress distribution is linear, and the measured velocity profile is a classical logarithmic one. Based on the concept of new-riverbed, the river compression parameter representing the impact of vegetation on river is given, and a new assumption of mixing length expression is made. The formula for time-averaged velocity derived from the expression requires less parameters and simple calculation, and is useful in applications.
The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.
Transverse mixing characteristics of solute in the open channel flow can provide useful information for river environmental management. The lateral mixing coefficient is a crucial parameter for reproducing the transverse mixing either by numerical simulation or by analytical prediction. Since the solute mixing can be greatly affected by the lateral variations in water depth, mixing coefficient should be determined in each sub-section （i.e., the main channel, side slope and flood plain） separately. In this article, the transverse mixing in a symmetric trapezoidal compound channel was studied based on laboratory measurement of longitudinal and transverse velocity components and lateral distribution of solute concentration. The lateral mixing coefficient was estimated by adopting different Schmidt numbers in different sub-sections divided according to the developing trend of the eddy viscosity, and finally a piecewise linear profile of mixing coefficient was adopted to analytically predict the transverse solute concentration. The comparison between the analytically predicted data and the measuring solute concentration proved that this is an effective way to estimate the lateral mixing in the open channel flow with lateral variations in water depth,
This article applies the realizable k - ω model to simulate the buoyant wall jet and gives the results of cling length, centerline trajectory and temperature dilutions at certain sections. The comparison between the numerical results and Sharp＇s experimental data indicates that the model is effective in estimating velocity distribution and temperature dilutions. The velocity profiles at the cental plane and z-plane both show a strong similarity at certain distance from the nozzle, and the distributions of velocity and temperature dilutions also exhibit a similarity along the axial direction at centerline in the near-field. Based on the results, the article gives the corresponding relationships between the distance and the dilutions of velocity and temperature, which is useful in predicting the behavior of the wall buoyant jet.
This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.
This article discusses the transverse distributions of the depth averaged velocity and the Reynolds stress in a steady uniform flow in partially vegetated rectangular channels.The momentum equation is expressed in dimensionless form and solved to obtain the depth averaged velocity.The analytical solution of the velocity in dimensionless form shows that the depth-averaged velocity is determined by gravity and its distribution is mainly determined by the frictions due to water or vegetations.The analytical solution of the Reynolds stress is also obtained.A relationship between the second flow and the inertia is established and it is assumed that the former is proportional to the square of the depth averaged velocity.The Acoustic Doppler Velocimeter（Micro ADV） was used to measure the steady uniform flow with emergent artificial rigid vegetation.Comparisons between the measured data and the computed results show that our method does well in predicting the transverse distributions of the stream-wise velocity and the Reynolds stress in rectangular channels with partially vegetations.
