Quantifying the forcing effect of channel width variations on free bars: Morphodynamic modeling based on characteristic dissipative Galerkin scheme

Abstract

[1] The forcing effect of channel width variations on free bars is investigated in this study using a two-dimensional depth-averaged morphodynamic model. The novel feature of the model is the incorporation of a characteristic dissipative Galerkin (CDG) upwinding scheme in the bed evolution module. A correction for the secondary flows induced by streamline curvature is also included, allowing for simulations of bar growth and migration in channels with width variations beyond the small-amplitude regimes. The model is tested against a variety of experimental data ranging from purely forced and free bars to coexisting bed forms in the variable-width channel. The CDG scheme effectively dissipates local bed oscillations, thus sustains numerical stabilities. The results show that the global effect of width variations on bar height is invariably suppressive. Such effect increases with the dimensionless amplitude AC and wave number λC of width variations. For small AC, λC has little effects on bar height; for AC beyond small amplitudes, however, the suppressing effect depends on both AC and λC. The suppressing effect on bar length increases also with both AC and λC, but is much weaker than that on bar height. The global effect of width variations on bar celerity can be suppressive or enhancive, depending on the combination of AC and λC. For smaller λC, the effect on bar celerity is enhancive; for larger λC, bar celerity tends to increase at small AC but decreases for AC beyond small amplitudes. We present herein an unprecedented data set verifying the theoretical prediction on celerity enhancement. Full suppression of bar growth above the theoretically predicted threshold AC was not observed, regardless of the adopted amplitude of initial bed perturbation A. The global effects of width variations on free bars can be quantified using a forcing factor FC that integrates the effects of AC and λC. The suppressing effects on bar height and length are both proportional to FC2.16; the global effect on bar celerity is, however, a parabolic function of FC.