A new analytical model for dip modified velocity distribution in fully developed turbulent open channel flow

Abstract

This paper presents a new analytical model to predict the streamwise time-averaged velocity profile affected by the dip phenomenon in open channel flows. The novel approach of the present study is that the Finley wake law has been used instead of Coles’ wake law for the outer layer. To validate the new analytical model, six high quality experiments were conducted in a hydraulically rough bed open channel flow by considering variations of aspect ratio, defined as the ratio of the width of the channel to the depth of flow, from 2 to 4. In these controlled experiments, the time-averaged velocities were measured using a Nortek Vectrino-plus acoustic Doppler velocimeter. In addition, 14 sets of available experimental data, including five field experiments conducted across the globe were also used to test the performance of the proposed model. The proposed model, the Finley-dip-modified-log-wake law (FDMLWL), was used to develop a semiempirical equation to compute the dip position as a function of the dip correction factor and the wake parameter. In addition, using the experimental data and FDMLWL, an empirical equation was developed to compute the dip correction factor for hydraulically smooth open channel flows. The comparison of the FDMLWL model with the experimental data belonging to hydraulically smooth, transition, and rough regimes has consistently indicated better representation of the velocity dip phenomenon. The FDMLWL model has also been compared with other analytical models available in the literature and the superior performance of the proposed model is further observed. Finally, based on the satisfactory validation between experimental data and FDMLWL, it is inferred that the proposed model is better suited for modeling zero velocity gradient at the boundary layer edge, as in open channel flows with dip phenomenon.