Alternate bars in and meandering of alluvial rivers

The paper presents a linear perturbation analysis of a horizontal two-dimensional mathematical model for the flow and bed topography in straight alluvial rivers with dominant bed-load. A sediment transport model including effects of transverse bed slope, secondary (helical) flow and secondary flow inertia is employed. The stability and the propagation velocity of an unsteady perturbation is investigated. This stability analysis predicts wave lengths which are in good agreement with the wave lengths of alternate bars in straight laboratory flumes. The analysis predicts rather large propagation velocities of the perturbations. Several investigations have assumed the instability to cause meandering and braiding of rivers. However, in view of the corresponding large propagation velocity of the perturbation and the generally low erodibility of the banks, a non-propagating perturbation offers a more adequate explanation of the initiation of meanders and braids. In order to investigate this hypothesis a linear steady state perturbation analysis is carried out. The results of this analysis are compared with meander lengths measured in small meandering channels (laboratory experiments) and with data from large natural rivers. The agreement is good