Numerical study on two dimensional distribution of streamwise velocity in open channel turbulent flows with secondary current effect

For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.