Secondary currents are important mechanisms in open channels, having major contribution in flow field and its corresponding parameters including boundary shear stress and depth-averaged velocity. Compound open channels involve extra plan form vortices in the flow field. Curved open channels generate especial vortices due to the effects of centrifugal force. Precise modeling of secondary currents in curves and meanders is a very important issue in practical applications. Using open source ``OpenFOAM'' software, the flow field in a meandering channel with compound cross section is simulated herein. Reynolds averaged Navier-Stocks equations (RANS) are solved. Applying appropriate boundary conditions over the free-surface, the simpleFoam solver has been used to model the two-phase air-water flow interface, assuming a steady flow condition, and a symmetry boundary condition. The experimental data from FCF belonging to University of Birmingham is selected for verification and validation of the present numerical results. Two turbulent models of Realizable k− varepsilon and SST k− omega are applied. Lateral velocity profiles at the cross sections indicate that at each wave-length of a meander, a vortex forms in the main channel at the apex, directing towards the outer bank near the bed and towards the inner bank near the water free-surface. The secondary current patterns, achieved for curved compound open channels differ from those of the simple channels. This is partly due to the interaction of shear stresses occurring at the interfaces between the main channel and the floodplains. Deviation of paths of the main channel and floodplains, downstream of each apex, results in entering the flow from inner bank to the main channel and exiting the flow from the main channel to the outer bank. These flow patterns shift the flow from inner-to the outer bank, downstream of each apex. Therefore, a helicoidally secondary current pattern forms, growing in size and strength farther downstream of the apex region.

Introduction With the occurrence of flood, the velocity and depth of the flow in the river increases and the flow enters the flood plains. The velocity difference between the deeper section and the shallow area causes the transfer of momentum between these areas and complicates the flow structure. The formation process of secondary flows and its pattern in compound channels have been investigated by researchers such as:Tominaga & Nezu, 1991. The presence of vegetation on flood plains causes complexity in the analysis of hydraulic problems of compound channels. For example, Hamidifar et al. (2012, 2014), using laboratory measurements, showed that the presence of vegetation reduces the flow through the cross section by about 30%. At the same time as the water level rises during the flood, the deck of the bridges will go under water and the current passing under it will be pressurized. In this condition, the flow field is affected by the presence of vegetation, compound channel and pressurized flow. In this research, the laboratory investigation of these complex conditions has been done.MethodologyThe experiments of this research were done with 3 geometric ratios of the compound cross-section, 3 relative depths, 3 vegetation densities, and control experiments in a compound channel with a length of 10 meters and a width of 1.5 meters. The measurement of the flow velocity parameter, the scouring rate of the bridge pier in the conditions of pressurized flow has been done according to the variables mentioned above.Results and Discussion Comparison of depth velocity and logarithmic velocity distribution in the condition without vegetation on the flood plain, the sign shows that in all sections, the distance between the channel bed and the water surface, the difference between the measured velocity values with the logarithmic distribution of the velocity increases. This difference is due to the presence of the bridge deck and the flow retardation. Also, vegetation causes the depth distribution profile of flow velocity to deviate from the curve of logarithmic flow velocity, and the biggest difference will occur in the upstream area between the interface of main channel and flood plain. This phenomenon increases the amount of apparent shear stress between the main channel and the floodplain.With the increase in the density of vegetation, the percentage of floodplain participation in the total discharge is reduced by 20%. The highest participation percentage of floodplain is about 30% in the state without vegetation. In different densities of vegetation with an increase in relative depth from 0.3 to 0.5, the percentage of floodplain participation in the total discharge is less than 10%. With the increase in the density of vegetation, the difference between the percentage of floodplain participation in different cross section widths has decreased.ConclusionsThe findings of recent research to check hydraulic parameters can be summarized as follows:- Increasing the density of vegetation increases the longitudinal velocity in the main channel and decreases it in the floodplain.- Longitudinal velocity and averaged- depth velocity in the main channel in the case without vegetation is lower than the case with vegetation.- Increasing the relative depth increases the percentage of floodplain participation by an average of 5%, and the increase in vegetation density causes a decrease of 17% in the floodplain participation.- With the increase in the vegetation density of the floodplain, the velocity changes in the floodplain decrease compared to the main channel.- Examining the profiles of the depth distribution of the flow shows that due to the presence of the bridge deck and the retardation of the flow, the depth distribution differs greatly from the logarithmic distribution of the velocity . This is despite the fact that in the conditions without the presence of the bridge deck, this amount of difference reaches its minimum.- The presence of the bridge deck and the creation of backwaters reduce the difference in flow velocity in the main channel and floodplain upstream of the bridge, and this in turn reduces the strength of the secondary currents between floodplain and the main channel.- The difference between the global average velocity of the flow and the local velocities increases the slope of the (a-1) and (b-1) lines due to the flow retardation.

Introduction: Bridges are one of the most important structures built on rivers and are considered as a structure connecting the two parts of the road. One of the most important reasons for the destruction of bridges is the scouring of its piers. New bridge design challenges, due to climate change and human intervention, as well as uncertainties associated with maximum events, may not adequately lead to accurate hydraulically design of bridges and may therefore as a result, in some floods, the bridge deck submerged. Under these conditions, the flow can be converted to a pressurized. This pressurized flow passes at high velocity in the region of bridge piers. As a result, it can increase the erosion potential of bed materials near bridge piers. Up to now, many studies have been performed to determine the relationship between estimating the rate of scouring of bridge piers in laboratory conditions with clear water and living bed, Such as: CSU equation. Under pressurized flow condition, researchers such as Umbrel et al., Richardson and Davis, Zehi, and Karankina et al. Have developed relationships to determine the amount of scouring of bridge piers in simple channels. Due to the difference in flow velocity in the main channel and floodplains in the compound open channels, the important changes occur in the kinetic structure of the flow near the connection line between the main channel and floodplains. These changes also cause vortices as a result of excess energy loss in the flow. In addition, the presence of vegetation on floodplains complicates the hydraulic analysis of the flow in such sections. Up to now, many studies have been performed to explain the hydraulic conditions of the flow in compound channels with and without vegetation, including Shiono knight (1991), Rameshwaran and Shiono (2007), Zarati et al. (2008), Yu-qi Shan et al. (2016), Tanino et al. (2008). and Sonnenwald et al. (2019). In previous studies, the amount of scouring of bridge piers in the conditions of pressurized flow under the deck in compound channels with vegetation has not been investigated. The aim of this study was to investigate the effects of vegetation density, pressurized flow under the bridge deck with different geometric and hydraulic conditions on the scour depth of bridge piers in a compound channel. Methodology: Experiments of this research was performed in a laboratory channel with a width of 1. 5 meters and a length of 10 meters. The experiments in this study were performed with 3 geometric ratios of cross section ( =B/b), 3 relative depths (Dr) and 3 vegetation densities ( ). It should be noted that the experiments are designed in such a way that in all of relative depths, the bridge deck is submerged and the flow pressurized. The maximum depth of scouring under the flow pressurized passing under the bridge can be expressed as a simple and dimensionless equation (1): y U B f h ((1 ( ) max, , , a     Z f, , , , , T f    = Dr T b a U h h h =     c b a Considering the control volume from the upstream of the bridge deck to the downstream of it, the momentum equation can be written to calculate the apparent shear stress as follows: ( ) ( ) QU QU L)SF SF2( LSAg F F + − + + + − −     mc2 mc1 mc1 mc2 mc2 mc2 4 3 0 mc backwater mc2p mc1p + (2) 0 ASF 2 = v Results and Discussion: A: Depth averaged velocity: In vegetation densities used in this study, the average velocity on floodplains with vegetation is relatively constant in most cases. This shows that except in the interface of the main channel and floodplains, the flow distribution on floodplains can be considered two-dimensional. As the vegetation density increases, the depth averaged velocity difference between the main channel and the floodplain increases between 50%-80%. B: Shear stress: Due to the presence of vegetation, the reduction of the average flow velocity on the floodplain occurred as a result of shear stress has also decreased. The transverse changes of shear stress downstream of the bridge, due to the behavior of the pressurized flow passing in the deck, have more fluctuations and are on average about 25% more than the average values upstream of the bridge. C: Local friction factor: The Darcy– Weisbach friction factor in the floodplain area increases significantly due to the presence of vegetation elements. The pattern of variability of Darcy– Weisbach friction factor on the floodplain also causes a sinusoidal pattern due to the reduction of flow velocity and the presence of skin friction on the surface of the rods. D: Apparent shear stress: Due to the resistance due to increasing vegetation density, the amount of apparent shear stress at higher densities increases. On the other hand, with increasing relative depth and decreasing of secondary current, the amount of apparent shear stress decreases. E: Equation for predicting maximum scour depth: Based on determining the effective parameters in the amount of scour rate and using the data of this study, the following equation is presented to estimate the amount of scour of the bridge pier under pressurizes flow conditions. . 16 012. 0 (298 ). 19 (078 )Dr. 0 )T(494. 13 (406 ). 0 (509 ) Zmax − = +  + − +  +  (3) Conclusion:-Increasing the density of vegetation increases the longitudinal velocity in the main canal and decreases it in the floodplain. -Bridge pier scouring develops faster in pressurized flow than in free surface flow.-With the exception of the height of the dune in the pressurized flow, the depth of scour hole on a small laboratory scale is less than 50% of the depth of the upstream of the bridge deck.-The position of the maximum scouring depth quickly reaches its equilibrium position near the downstream edge of the bridge deck.

Most previous laboratory studies of local scour at bridge abutments were performed in rectangular channels in which the distributions of flow velocity and bed shear stress were considered uniform in the transverse direction. In reality however, bridge abutments are usually located in the floodplain zone of rivers where velocity and shear stress distributions are directly affected by the lateral momentum transfer. The influence of channel geometry and lateral momentum transfer in compound flow field on scouring phenomenon, however, has not been fully investigated and understood as yet. This paper presents the results of an experimental study performed to investigate the impact of both sediment size and lateral momentum transfer on local scour at abutments terminating in the floodplain of a compound channel. It is shown that, by accounting for lateral momentum transfer at small floodplain/main channel depth ratios (ya/H<0.3), estimates of maximum local scour depth are increased by up to 30%. In relation to the sediment size, earlier studies of scouring around circular bridge piers proposed a limit for the relative size of sediment (pier diameter/median size of bed material) beyond which the sediment size has no effect on the equilibrium sconr depth (Ettema, 1980; Chiew, 1984). The results of the current laboratory studies, however, indicated that the limit established for circular bridge piers might not be appropriate for the abutment case installed in the floodplain zones; further studies are required to draw a more general conclusion regarding the effects of relative grain size in the abutment case.

Natural channels always form meanders along their path, and it is important to consider the effect of this meander on the flow characteristics pattern. When a flood occurs, the water level crosses the main section of the river and enters its floodplains. In this case, the river crossing becomes a compound cross-section. In this study, using the Flow3D software (powerful software in the field of computational fluid dynamics), the vortex rotational power and transverse flow in the meandering compound channel under the influence of relative depth and Sinusoidal Change were investigated. For this purpose, six channels with different sinuosity and three relative depths were used. The results of the numerical simulation showed that the maximum rotational power of vortices increased with an average of about 195% by increasing the sinusoidal rate from 1 to 1. 209. The maximum rotational strength of the vortices and the transverse flow rate occurred at a 45-degree angle to the central arc and a sinusoidal value of 1. 209. In the main cross-section of the meandering compound channel, for all sinusoidal values, by decreasing the relative depth, the vortex and transverse rotation strengths increased and the rate of change in transverse current power relative to relative depth changes decreased with increasing sinusoidal rate.

Generally, natural open channels have sections in which by increasing the water level, the crosssectional area will be increased considerably. These sections have consisted of relatively wide floodplains. In compound channels with asymmetric cross-sections, the hydraulic behavior of the flow would be complicated. Rating curves estimation in compound channels is one of the most critical issues of river engineering. In the current study, a new approach based on the concept of the crosssectional isovel contours is introduced for the estimation of rating curves in compound channels. To extract the exponent values of the governing parameters, minimization approach is used to the difference between the observed and estimated data. In this method, in order to set up the rating curves in various cross-sections, it is only requisite to have the flow information at a reference water level. The results show that the proposed method has a good accuracy for predicting rating curves in asymmetric compound channels even in compound channels with different floodplain levels.

In this paper twelve different empirical resistance coefficients expressed in terms of Manning's roughness are used apiece in seventeen known compositing methods. The data obtained from ten different cross-sections of the Sefidrood River, Iran, are used for the evaluation of the empirical formulas. The present case-study is selected from a reach with gravel bed topology. Then no remarkable bed form exists. Comparison of the calculated discharges and resistance coefficients with measurements shows that the Keulegan formula used simultaneously with the Brownlie formula in different compositing methods results in highly over estimated discharges, while the Meyer-Peter & Muller, Marion, Chien-Mai formulas in conjunction with the total force approach match best with the measurements. Also comparison of the calculated discharges from empirical formulas in individual sections reveals that Chien-Mai and Subramanya formulas have the least discrepancies from measurements.

Due to large differences in hydraulic characteristics of main channel and floodplains, unsteady flow mechanisms in compound open channels is very complex. In these types of channel sections, the main channel velocity is considerably higher than that of floodplains and this leads to high momentum transfers from main channel to floodplains. Available unsteady mathematical models for compound channels have such limitations that need to be modified. In this paper, to take this interaction effect into account in the flood routing computations, the combined depth-averaged Shiono and Knight model (1991) with Saint-Venant equations in diffusion form, have been solved numerically using the finite difference method. For evaluating the accuracy of this model, the results have been compared with two benchmark unsteady mathematical models for the homogeneous and heterogeneous compound channels. The finite element DAMBRK and RFMFEM models selected in this paper are based on full dynamic and diffusion wave solutions, respectively. The results showed that in comparison to the selected models, the present proposed model have considerably shorter execution time, i.e. about 10% that of DAMBRK model. Furthermore, compared to the experimental data of Treske (1988) in a straight compound open channel, the results showed that the computed peak outflow discharge differs from the observed one by a factor of 3.5%. Generally, the most important features of the proposed model are the small execution time and good performance in both homo and heterogeneous compound channels.