EFFECTS OF THE VARIATION OF DISCHARGE ON THE GROWTH OF FLUVIAL BARS

Abstract

It has been observed that the bank erosion takes place not at the peak of discharge but during the decrease in discharge. We perform linear stability analysis for the formation of alternate bars including the effect of the variation of discharge. We assume that the variation of discharge is sufficiently slower than the variation of bed elevation, and introduce two different time scales: the time for the variation of bed elevation 𝑡 and that for the variation of discharge 𝑇. With the use of the multiple scale expansion method, we obtain the growth rate of perturbation as a function of 𝑇. It is found that the bed is more unstable when the discharge is smaller than the peak in the range of large wavenumbers in particular.