LINEAR STABILITY ANALYSIS OF FLUVIAL BARS WITH BED AGGRADATION AND DEGRADATION

Abstract

In the existing linear stability analysis of fluvial bars, it is assumed that the river bed is in equilibrium, and the bed slope and flow are uniform in the streamwise direction. Though it is generally said that the bed becomes more unstable under bed aggradation, and becomes more stable under bed degradation, the existing analysis cannot shed further light on their effects. In this paper, linear stability analysis incorporating weakly non-equilibrium processes of bed aggradation/degradaion is performed by the use of the WKBJ method in order to clarify their effects. Bed aggradation or degradation is assumed to be sufficiently slow compared with the bed evolution due to instability, and its non-dimensional speed is used as a small parameter. The analysis explains that river beds become stable and sand bars tend not to be formed under degradation, and that river beds become unstable under aggradation. In addition, alternate bars are more strongly affected by bed aggradation/degradation than multiple bars.