Abstract
Linear stability analysis of sand fluvial bars with bank erosion is performed with the use of the shallow-water equations. We assume that the average total channel width is constant, and the bank erosion takes place due to increases in the bed shear stress in the vicinity of banks. We obtain analytical solution by the use of asymptotic expansions around the state of no bank erosion (the bank erosion coefficient γequals 0) in order to clarify the effect of bank erosion on the instability of sand bars with different lateral wavenumbers. We obtain instability diagram for γ evaluated from field and experimental data, and found that bank erosion stabilizes the bed in the ranges of small wavenumbers, and of large wavenumbers and aspect ratios.
