Linear stability analysis of fluvial bars considering the time variation of bed slopes with aggradation and degradation

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Bed slope changes due to bed aggradation/degradation caused by an increase/decrease of sediment supply. Though we have performed a linear stability analysis of sand bars incorporating effects of bed aggradation/degradation, the analysis has assumed bed elevation changes without changing its shape, and temporal variation of bed slope has not been taken into account. In order to study bar instability with temporal variation of bed slope, the WKB method is applied with the use of the rate of bed slope changes as a small parameter. The analysis shows that, unstable regions in the instability diagram is expanded to the range of large wavenumbers when bed slope decreases while unstable regions are reduced when bed slope increases.