J N Kaguchwa, J K Kwanza, P W Gathia


Despite substantial research on various aspects of velocity distributions in curved meander rivers,  no systematic effort has yet been made to establish the relationship between the dominant meander wavelength, discharge and the velocity distributions. In this research the secondary current theory is used in investigating the wavelength of a meander when it just emerges in a river channel. Rate of meander growth and downstream migration velocity is also investigated. To achieve this, a small-perturbation stability analysis is developed for investigation of the role of the secondary current accompanying channel curvature in the initiation and early development of meanders in open channels.Equations of the transverse velocity profile are analyzed. Since the magnitude of the vertical velocity is negligible compared to the transverse velocity in secondary currents, this study concentrates on thetransverse velocity which is the radial component of the secondary current. This formulation leads to a linear differential equation which is solved for its orthogonal components which give the rates of meander growth and downstream migration. It is found that the amplitude of the meanders tends to increase and that the meanders migrate downstream. The obtained dominant discharge is important to engineers in predicting stable slope upstream of grade control-control structures and forecasting flooding in river channels. Engineers also use dominant discharge in predicting channel migration and hence they are able to evaluate and determine bridge and other highway facility locations and sizes and ascertain the need for countermeasures considering the potential impacts of channel meander migration over the life of a bridge or highway river crossing. The mathematical description  meander formation will be essential to geomorphologists since it contributes to theory development and provides solutions of practical problems associated with stream channelization.


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