Abstract
Linear stability analysis of fluvial sand bars with bank erosion is performed with the use of shallow water equations in two-dimensional flow, Exner equation and a process-based bank erosion model. An initially straight channel with erodible bed and constant width is assumed. The bank is also assumed to be erodible and composed of fine-grained sediment. The conditions allowed for alternate sand bars to grow are investigated considering the variation of aspect ratio, the magnitude of the transverse bank slopes, and the case of a channel with non-erodible banks. It is found that there exists a stable region in the range of small aspect ratios and small wavenumbers for the case of bar instability with bank erosion. The results also suggest that aside from the aspect ratio, the bank slope is one of the parameters that influence bed instability for the case of channels with erodible banks. This reveals that bank erosion has a stabilizing effect on the formation of alternate bars by increasing sediment supply, leading to an increase in bar wavelength.
