Dip-phenomenon and analytical model for velocity profile in open-channel bends

Abstract

The dip-phenomenon whereby the location of the maximum velocity appears below the free surface is related to the advective momentum transport by secondary flow. In open-channel bends, there exist relatively large-scale vorticities termed Prandtl’s secondary flow of the first kind which is remarkably different from Prandtl’s secondary flow of the second kind induced by anisotropy of turbulence in straight channels. Experiments were carried out in a narrow and sharp bend to explore the dip-phenomenon along the bend. It is revealed that at the bend entrance the dip-phenomenon in the outer bank is more pronounced than that in the inner bank, while it is opposite in the rest region. The variation of the dip position reflects the momentum redistribution by the multiple circulation cells developed along the bend. Based on the Reynolds Averaged Navier–Stokes (RANS) equations with a cylindrical coordinate system and the experimental data, a new analytical model for the velocity profile in open-channel bends is proposed. The model verified by the experimental data is able to predict the dip position and velocity profile accurately in both the inner bank and outer bank regions. Two factors are discussed about the effect of the vertical velocity distribution and transverse gradient of secondary flow on the variation of the streamwise velocity profile.