Origination of Cellular Secondary Cells in Wide Open-Channel Turbulent Unsteady Flows over Spanwise-Oriented Alternate Rough and Smooth Bed Strips

This study presents an analysis of the formation of large-scale turbulent induced cellular secondary flows commonly occurring in straight wide open channel uniform flows with rectangular cross-sections. The study aimed to investigate the plausible scenario of the formation of cellular structures of the secondary currents (SC) occurring in open channels with spanwise-oriented alternate rough and smooth bed strips. Starting with the continuity equation and the Reynolds averaged Navier–Stokes equation, the governing equations for secondary flow velocities are obtained with linear stability analysis of the convective terms. Unlike previous studies, the governing equation results as the balancing between two opposite effects, the generation of SC (consists of normal stresses) and suppression of SC due to viscous force and the Reynolds shear force. Using the spectral collocation method the semi-analytical solutions are derived assuming a sinuous instability along transverse direction due to spanwise-oriented alternate rough and smooth bed strips. The obtained solutions are validated with experimental observations for the stationary state and a good agreement was obtained. Time analysis results show that though the formation of cellular cells originates due to lateral variation in bed conditions, the centers of circulations are generated near the free surface which gradually shifts with time towards the middle of the flow depth. Apart from these, the effects of SC on the settling velocity vector are analyzed. Results demonstrate how the streamlines of the settling velocity vector are distorted due to the formation and generation of cellular secondary flow cells. This study also provides a clear idea of how the retention zones are formed with the existence of secondary flow circulations.