Application of analytical solutions in trapezoidal compound channel flow

Abstract

The accuracy of predictions using an analytical model for a lateral depth varying open channel flow can be affected by the friction factor and the dimensionless eddy viscosity. In this paper, different approaches to determine these two parameters are discussed by comparing analytical results with experimental data obtained from a symmetrical trapezoidal compound open channel. To reflect different hydraulic characteristics along the wetted perimeter, the trapezoidal cross-section was divided into several sub-sections, and the friction factor in each sub-section was calculated with Manning's formula by adopting local hydraulic parameters. The wetted perimeters of main channel and side slope included the interface between panels to reflect the effects of the lateral momentum exchange. This approach is shown to be effective once the roughness coefficients and hydraulic radius in different sub-regions have been determined. The results show that the friction factor is the major parameter affecting the accuracy of the analytical solution. The effect of dimensionless eddy viscosity on the precision of predictions is much smaller, which means that for practical applications, the dimensionless eddy viscosity can be determined empirically. Inclusion of a term for secondary flows in the model can improve the prediction, especially in the transition from main channel to the floodplain. A reasonable prediction of the lateral distribution of depth mean Reynolds' stress in this region is obtained.

Simultaneous analysis of slope instabilities on a small catchment-scale using coupled surface and subsurface flows

“…In which, νt is eddy viscosity coefficient (m 2 /s), and it can be assumed as follows (Zeng et al, 2010).…”

“…where, U* is the frictional velocity (m/s); λ is dimensionless eddy viscosity, and its standard value for an infinitely wide channel is 0.067 (Zeng et al, 2010); S is the gradient of water surface. As the water depth gradient is much smaller than the slope gradient, it can be assumed that S is equal to the slope gradient (Weill et al, 2009) as shown in Fig.…”