Abstract:
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 smallperturbation
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 the
transverse 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.
