The flow of water in straight open channels with prismatic complex cross-sections is considered. Lateral distributions of depth-mean velocity and boundary shear stress are derived theoretically for channels of any shape, provided that the boundary geometry can be discretized into linear elements. The analytical model includes the effects of bed-generated turbulence, lateral shear turbulence and secondary flows. Experimental data from the Science and Engineering Research Council (SERC) Flood Channel Facility are used to illustrate the relative importance of these three effects on internal shear stresses. New experimental evidence concerning the spatial distribution of Reynolds stresses τyx and τzx is presented for the particular case of compound or two-stage channels. In such channels the vertical distributions of τzx are shown to be highly nonlinear in the regions of strongest lateral shear and the depth-averaged values of τyx are shown to be significantly different from the depth mean apparent shear stresses. The importance of secondary flows in the lateral shear layer region is therefore established. The influence of both Reynolds stresses and secondary flows on eddy viscosity values is quantified. A numerical study is undertaken of the lateral distributions of local friction factor and dimensionless eddy viscosity. The results of this study are then used in the analytical model to reproduce lateral distributions of depth-mean velocity and boundary shear stress in a two stage channel. The work will be of interest to engineers engaged in flood channel hydraulics and overbank flow in particular.
Koji Shiono - Department of Civil Engineering, University of Bradford, Bradford BD7 1DP, West Yorkshire, UK
Donald W. Knight - School of Civil Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Journal of Fluid Mechanics (1991), 222:617-646 Cambridge University Press
Copyright © 1991 Cambridge University Press
A paper, whose premise is that the accuracy of analytical mathematical models does not accurately take into account the effect of turbulence. This includes effects of bed-generated turbulence, lateral shear turbulence and secondary flows when considering compound channel and varying depth channel flow. Therefore a new analytical model for steady, uniform, non turbulent flow is proposed taking into account the aforementioned aspects, and is compared to previous experimental data collected.
The problem of quantifying the compound or two stage channel was overcome by using depth-mean velocities, which essentially reduces a three dimensional problem to one dimensional, and is therefore applicable to the model including boundary shear stresses etc... Based upon the comparison of results from the analytical and previous experimental data, the model was found to be highly accurate. A couple of assumptions are made in this model, such as the fact that certain constants are calculated from the original experimental data before being fed back into the model. In this way, the analytical model is non necessarily a stand alone model.
The paper provides a useful tool for predicting flow behaviour given all relevant turbulent flow values, for a more accurate prediction model. The work carried out may be of use may be of use to engineers looking into flood channel hydraulic and over-bank flow.