Hysteresis and Shear Velocity in Unsteady Flows

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.