Abstract
This paper investigates an influence of the modelling of secondary flows to the formation and development of free bars in rivers by comparing the results of the numerical simulation, the linear stability analysis and the experiments. Free bars which are developed by a physical instability phenomenon between turbulent flow and bed surface of rivers are one of fundamental river morphologies. Theoretical studies by the linear stability analysis have successfully shown that two dimensional morphodynamic models for calculating the river bed evolution can explain the formation of free bars. However, three dimensional flow structures, for instance, secondary flows caused by the meandering flows with increasing the bar height, have also important roles in the dynamics of free bars on a nonlinear level. Although quasi-three dimensional flow models can be a powerful tool to include the three dimensionalities of flows on the framework of two dimensional approaches, the applicability of such models to the dynamics of free bars has not been well verified yet. The results of the linear stability analysis suggested that the model of secondary flows which is assumed under the fully developed stage allows developing the bar with unrealistically high mode. This high mode bar tends to develop under the hydraulic conditions in which the effect of transverse slope for the sediment transport direction is relatively weak. Such instability can be physically suppressed by applying a model of secondary flows which includes the effect of development of secondary flows. The results of numerical simulation shows that proposed model which considers the development of the secondary flows can reasonably reproduce the incipient of free bars which is indicated from the linear stability analysis as well as the equilibrium bar waveheight in the experiments.
