Secondary flow in mildly sinuous channel

Most analytical models of the flow and bed topography in sinuous channels include the assumption that the secondary flow is locally adapted to channel curvature. Recently, Kitanidis and Kennedy (1984) and Ikeda and Nishimura (1986) have, however, established the existence of a phase lag between the two, induced by inertia, i.e., downstream convective acceleration of the secondary flow. The analysis of Ikeda and Nishimura (1986), nevertheless, includes an unverified assumption. Herein a more rigorous derivation of the effect is obtained with a minimum of assumptions. The predicted lag appears to be sufficiently small to warrant neglect in natural channels. The theory predicts much higher values in many experimental channels, in agreement with data. The reason for this is that a scaled dimensionless meander wave number r, found to be order-one in natural channels, is found to be an order of magnitude higher in many laboratory meandering flumes.