A parametrical study on secondary flow in sharp open-channel bends: experiments and theoretical modelling

The dependence of curvature-induced secondary flow on the curvature ratio H/R (H is the average flow depth and R is the centreline radius of curvature), the Froude number Fr, and the dimensionless roughness coefficient Cf was systematically investigated in a series of 25 experiments in a laboratory flume. The investigated H/R values were (±0.005) 0.050, 0.073, 0.112 and 0.151, the Froude numbers were (±0.03) 0.10, 0.23, 0.32, 0.40 and 0.50, and roughness heights of the sediment bed were 0.002 m and 0.067 m.With width-to-depth ratios of 4.9 to 17.1, these experiments are more representative of small and medium-size rivers than the largest rivers on earth. Commonly used parameterizations for secondary flow predict the normalized magnitude to grow linearly with H/R, and to decrease with increasing bed roughness. This behaviour was only observed in mildly curved flows. The normalized magnitude was found to grow less than linearly with H/R in moderately curved flows, and to reach a maximum value in strongly curved flow. This confirms observations by Blanckaert (2009), who called this phenomenon the saturation of the secondary flow. He attributed the less than linear growth to nonlinear interactions between the primary and the secondary flows. For high values of H/R, secondary flow was found to be stronger over the very rough gravel bed than over the smoother sand bed. This is explained by the nonlinear interactions between the primary and secondary flows that are less pronounced over the rougher bed. The experiments did not reveal any dependence of the secondary flow on Fr. Predictions of the magnitude of the secondary flow with the nonlinear model of Blanckaert and de Vriend (2003, 2010) agreed very well with the experimental data over the entire range of investigated experimental conditions. Nonlinear effects are always important when the parameter C H R f −0.25 is larger than an indicative value of 0.1, and negligible when this parameter is smaller than 0.05. These values allow a quantitative and objective distinction between mildly, moderately and sharply curved open-channel flow.