Spectral Analysis of Sand Bed Instability

Abstract

In order to clarify the role of sand bed instability mechanism and the significance of linear instability analysis, which has been one of the most interesting subjects of alluvial hydraulics, sand bed instability analysis of a Fourier transformed version was devised by coupling with the stochastic model for bed load motion, and the theoretical prediction for sand wave development was compared with some experiments. In the laboratory, sand wave development from an initially flattened bed was experimentally investigated by using the time variation of wave number spectrum of sand bed. These investigations clarified that an instability mechanism brought about a wave selection process from initially formed bed disturbance due to random motion of bed load particles, and particularly that waves, to satisfy the Airy relation, became dominant through the mechanism of bed instability. The latter fact is a characteristic of sand wave development in open channel, and it has been also certified by experiments without a water surface.