Analysis of secondary current effect in the modeling of shallow flow in open channels

Abstract

The 3D information of a secondary flow evolved in curved or confluent channels, which is usually lost in conventional shallow water models due to the depth-averaging process, can be partially retrieved by incorporating the secondary current velocity profile in the vertical direction. In the present study, the depth-averaged shallow water equations with dispersion stresses were solved by the SU/PG scheme among the various numerical methods of the FEM. In the proposed model, to quantify the strength of the secondary flow, the comprehensive factors such as the deformation of the vertical profile of the streamwise velocity, the roughness coefficient, and the curvature ratio were embedded into the dispersion stress terms. Two sets of experimental data, one with a sharply curved channel by Rozovskii (1961) [40], and the other with a confluent channel by Shumate (1998) [51] were used to validate the proposed model. The computed values of the water surface profile and the depth-averaged velocity across the channel showed good agreement with experimental data, which indicated that secondary velocity profiles were preserved properly. The proposed model was applied to a natural stream with moderate curvature to test the field applicability. The simulation results obtained by the proposed model with dispersion terms matched quite well with the ADCP data, whereas the model without dispersion terms produced excessive velocities at both banks, and the commercial RMA-2 model yielded uniform span-wise velocity distributions at all sections. The analysis of the momentum balance and relative dominance of the secondary current demonstrated that the convection and pressure gradient terms played major roles in achieving equilibrium in momentum equations, and the bottom friction ranked next, followed by the remaining dispersion stresses and viscous term of a similar order. It was also found that the pressure gradient term was the primary factor that triggered velocity redistribution. As the Fr increased, the convective acceleration that formed along the channel curvature was activated as a secondary factor in velocity redistribution, whereas the viscous stress term lost its influence. The bottom friction term had minor exertion on the redistribution mechanism.