The Hysteresis and Shear Velocity in Unsteady Flows

Abstract

The shear velocity is an important parameter in characterizing the shear at the boundary in open channels and there exist methods to estimate the shear velocity in steady flows, but the application and comparison of these methods to non-uniform unsteady flows is limited. In this study, three artificial triangular-shaped hydrographs were generated where the base flow is non-uniform with fine sand bed and the shear velocity was obtained by the methods, u*SV by using the Saint-Venant equations, u*L by using the procedure given by Clauser Method, u*P by using the parabolic law, u*UN by using the momentum equation assuming the slope of energy grade line is equal to bed slope and u*avg by using the average velocity equation are used in this study. The stream-wise components of velocity time series and the velocity profiles were obtained by means of an acoustic Doppler velocity meter. The variation of the shear velocity and the constant for the parabolic law with time is discussed. It is concluded that the shear velocities found by the parabolic law and the average velocity equation can be used interchangeably. Furthermore a hysteresis intensity parameter is proposed in order to examine the depth variation of hysteretic behavior of depth variation both with point velocity and average velocity. It is revealed that the more the unsteady the hydrograph the more the hysteresis both in terms of point velocity and cross-sectional mean velocity.

Laboratory studies on bedload transport under unsteady flow conditions

“…Bed shear stress definition and measurement methods induce high uncertainty and difficulty in data interpretation. As each method of evaluation of the bed shear stress is uncertain to some extent, a comparison of a few methods may be helpful in interpreting the results as shown in other studies (Bombar, 2016;Qu, 2002).…”

“…Moreover, it should be noted that methods that may be applied under unsteady flow are scarce, mainly due to theoretical assumptions (Mrokowska et al, 2015a). Formulae derived from Saint-Venant model have become popular in unsteady flow experiments (Bombar, 2016;Song and Graf, 1996;Mrokowska et al, 2015b). However, the question about their applicability in evaluating bed shear stress under mobile bed conditions remains unanswered.…”

“…However, our knowledge on how matter, particularly sediment, is transported under unsteady flow conditions is still insufficient. This situation triggered a good deal of experimental, theoretical and computational efforts exploring how it works (Bombar, 2016;De Sutter et al, 2001;Julien et al, 2002;Lee et al, 2004;Mao, 2012;Mrokowska et al, 2016;Phillips and Sutherland, 1990;Wang et al, 2015). Nevertheless, the problem of bedload transport is still open for systematic research.…”

Investigation of the relation between bridge pier scour depth and vertical velocity component

“…The sound waves with high velocity were emitted from the core center of the instrument and the reflected waves were received by the three sensor arms. According to the Doppler principle, the velocity of flow was obtained [29]. The cylindrical sampling volume was 0.25 cm 3 and located 10 cm away from the sensor.…”

A Hydraulic Friction Model for One-Dimensional Unsteady Channel Flows with Experimental Demonstration

“…Hydraulic experiments have been designed to investigate the characteristics of unsteady flows as well as unsteady friction and shear stress [8,9]. For example, Sutter et al reported that the capacity of sediment transport increases when the unsteadiness of flow increases; this can be considered as the result of the effect of flow unsteadiness on shear stress [10].…”