WEAKLY NONLINEAR ANALYSIS OF MULTIMODAL FLUVIAL BARS

Abstract

Fluvial bars are large-scale topography with a planimetric scale of the order of channel width, which appears on riverbeds when the aspect ratio is sufficiently large. In order to describe the formation of such multimodal fluvial bars, a weakly nonlinear analysis is performed in this paper with the use of the amplitude expansion method. In the analysis, the fundamental perturbations with four different harmonic modes are imposed on an initially flat riverbed. The equilibrium bar profiles obtained by the present multimodal analysis are comparable to those obtained from the uni-modal analysis and the numerical analysis when the aspect ratio is small. An irregularity in the time variation of bar amplitude that has not appeared in the uni-modal bar analysis, is promoted with increasing aspect ratio.