Equation for streamwise variation of secondary flow in sinuous channels

Abstract

The secondary flow in a bend takes the helical motion by which the water in the upper part of the river is driven outward and the water near the bottom is driven inward. This phenomenon is commonly explained as the result of the interplay between the centrifugal force, the pressure gradient due to the decline of the water surface, and the bottom friction. The behavior of secondary flow in alternating bends is more complicated than that in a bend. In this study, a theoretical equation was derived based on Odgaard (1986) and Chang (1988) to reveal the stream-wise variation of the secondary flow in sinuous channels. The derived equation describes the transverse component of the secondary flow as a function of stream-wise and vertical coordinates. To validate the proposed equation, hydraulic experiments were conducted in laboratory meandering channels having different sinuosity. Comparison of experimental results with the proposed equation and an existing equation revealed that the new equation was in good agreement with the experimental data, whereas the existing equation overestimated. Sensitivity analysis of the new equation with respect to hydraulic parameters showed that the size of helical motion of secondary flow tended to increase as the sinuosity, the roughness, and the aspect ratio (ratio of width to depth) became larger. Also, the behavior of the secondary flow along the channel was sensitive to variations of the roughness and the aspect ratio.