Theory of River Meanders

Abstract

A mathematical model is developed for the calculation of flow field and bed topography in curved channels with an erodible bed. A small perturbation approach is used to linearize the governing equations. The downstream convective acceleration of the secondary flow is shown to give rise to a phase lag between secondary flow and channel centerline curvature, and also to suppress the magnitude of the secondary flow. The model further accounts for the convective transport of primary flow momentum by the secondary flow. This oft-neglected influence of the secondary flow is shown to be an important cause of the redistribution of the primary flow velocity. The governing equations retain the full coupling between the flow field, the bedload transport, and the bed topography. This coupling is shown to increase significantly the lateral bed slope in the upstream part of a channel bend, even beyond the value for fully developed bend flow which is approached in the downstream part of a channel bend. This coupling is also shown to give rise to resonant behavior for certain combinations of input variables; the common origin of the two phenomena is explained. The predicted flow field and bed topography compare very well with both laboratory and field data. Further, assuming the banks to be erodible, the model is used to predict wavelengths of river meanders. The results compare favorably with both laboratory and field data.