Free–forced interactions in developing meanders and suppression of free bars

Abstract

The coexistence of migrating alternate (free) bars, spontaneously developing in erodible channels as a result of an instability process, with steady point bars, forced by curvature in meandering reaches of rivers, is investigated theoretically.A perturbation expansion is set up in terms of two dimensionless small parameters, ε and ν respectively, describing free and forced perturbations. The effect of mixed interactions at O(ν2ε½) is found to be responsible for the damping and slowing down of free bars as channel curvature increases. The theory allows us to determine the threshold value of channel curvature above which free bars are suppressed as a function of meander wavenumber for given flow and sediment characteristics. The minimum channel sinuosity for free bar suppression is found to be associated with the resonant wavenumber range of Blondeaux & Seminara (1985). Theoretical predictions compare satisfactorily with experimental observations by Kinoshita & Miwa (1974). The theory also suggests that free bars may appear again in a more advanced stage of meander development in accordance with field observations by Kinoshita (1961).