The formation of boundary waves in closed conduits with sediment transported

Abstract

There have been a large number of studies on bed waves in rivers. It has been known that bed waves are strongly related to the Froude number. Meanwhile, there are only few studies on waves formed at the boundary between flowing water and erodible beds in closed conduits without free water surfaces. In order to predict the flow resistance of closed conduits such as sediment bypass tunnels and ice-covered rivers, it is important to obtain detailed information on the formation of boundary waves. Seki and Izumi²⁾ have proposed a linear stability analysis to explain the formation of small scale boundary waves in closed conduits. They have also reproduced small scale boundary waves in flume experiments, and compared with their analysis. According to their analysis, the Shields and Euler numbers are the dominant parameters, and the flat bed becomes unstable when the Euler number becomes larger than the critical Euler number, which increases with the Shields number. However, the agreement between the prediction and their observation is not sufficiently good. In this study, we introduce the ratio of the shear velocities between the lower and upper walls as a new parameter, and improve the agreement. In addition, we perform a weakly nonlinear stability analysis to obtain more detailed information on behavior of boundary waves in the vicinity of the critical Euler number. We find that the transition between flat bed and boundary wave regimes in closed conduits is characterized by subcritical bifurcation.