Numerical nonlinear analysis of alternate-bar formation under superresonant conditions

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Local geometrical perturbations in alluvial channels can generate a pattern of alternate bars. Each bar is accompanied by a pool at the other side of the channel. This pool can decrease the strength of the bank, which can result in bank failure and bars can hinder navigation. Furthermore, non-migrating alternate bars are considered to be a possible cause of meandering. Previous linear analyses and laboratory experiments showed that these bars arise downstream of perturbations in the relatively narrow and deep channels corresponding to subresonant conditions, but both upstream and downstream of perturbations in the relatively wide and shallow channels corresponding to superresonant conditions. Previous numerical computations reproduced alternate bars under subresonant conditions, but failed to do so under superresonant conditions until the recent 2D depth-averaged computations using Delft3D. This study is an advance on the former modelling work of van der Meer et al. and has the objective to assess to what extent the numerical results agree with linear theory and experimental observations and to investigate the development of bars upstream of a bend under superresonant conditions. The model is validated by reproducing the few available superresonant experiments in a U-curved flume. Downstream of the bend, the numerical model and experimental observations clearly matched. The numerical model, however, was not able to reproduce the development of non-migrating alternate bars upstream of the bend at the experimental conditions. It appeared that the point of resonance was over-predicted by the numerical model. The observed wave lengths and bed-topography spectra complied with the literature. The numerical simulations were unstable for realistic values of the horizontal eddy viscosity (O(10-5 m2/s) for small-scale models). The latter was therefore increased to stabilize the simulations. This increase was the cause of overpredicting the point of resonance by the numerical model. For the bedload transport procedure Delft3D offers two options, the ‘upwind’ procedure and the ‘central’ procedure. The former introduces numerical diffusion, whereas the latter is less stable. The shortening of bars for large width-to-depth ratios, as observed by former numerical simulations, is probably the result of numerical diffusion. The ‘upwind’ procedure causes sediment deposits and scour to be concentrated near the banks, because the higher modes (for example the central mode) within the alternate-bar spectrum were damped. Therefore ‘upwind’ bar peaks are higher and can become inactive, because these bars run dry before they are fully developed and consequently have a smaller wave length. The alternate-bar pattern upstream of the bend under superresonant conditions was found to develop from downstream to upstream, in accordance with linear theory, only if no perturbation was applied at the upstream boundary. A development from upstream to downstream dominated in case of a perturbed upstream boundary. The computed alternate bars migrated invariably downstream, under both superresonant and subresonant conditions. I ascribe this to nonlinear effects, since the bars did migrate upstream under superresonant conditions, in accordance with linear theory, as long as their amplitudes were very small. This study has shown that alternate-bar formation cannot be solely understood from linear equations. It seems therefore recommendable to investigate the contribution of non-linear effects in a more quantitative way. The numerical model can become more accurate by improving the transverse bed slope effect formulation.