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Recent developments on the mechanics of sediment suspension
Published in W. Bechteler, Transport of Suspended Solids in Open Channels, 2022
According to Batchelor’s analysis, most of the sediment in suspension resides above the constant-stress layer, when w/κu* < 1. (The constant-stress layer is the layer which lies very close to the bed in which the shear stress is assumed to be constant and equal to the bed shear stress.) Here w = the terminal fall velocity of sediment particles, u* = the shear velocity, and κ = the von Kármán constant ≅ 0.40. A very important implication of this result is: If one particle is put into an open-channel flow for which w/κu* < 1, the particle stays in suspension almost all the time1).
Form Resistance Prediction in Gravel-Bed Rivers
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
The estimation of the friction factor could be complex at gravel-bed rivers, representing spatial changes in channel morphology, flow depth, particle size, and bedforms. The under-prediction of flow resistance results in the under-prediction of flow velocity for gravel-bed rivers and leads to the flood discharge underestimation. To better predict the flow resistance in gravel-bed rivers, the contribution of bedforms should also be determined along with the particle's size of the river bed. Accordingly, this chapter tries to elaborate on the effects of bedforms on flow resistance over gravel-bed rivers and presents an analytical methodology to predict the bedform friction by subtracting the grain friction from the total friction. The methodology has credited the Darcy-Weisbach expression as a well-known flow resistance equation in open channels for the prediction of total friction factor, f. To take flow non-uniformity into the Darcy-Weisbach equation, shear velocity was predicted by the logarithmic velocity distribution. Also, Keulegan's method was presented for the prediction of grain friction factors.
Flood Modeling Using Open-Source Software
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Thomas J. Scanlon, Saeid Eslamian
with the von-Kármán constant κ=0.41 and the shear velocity u* calculated by:u*=τbρ
Experimental investigation and one-dimensional (1D) dynamic modelling of steady flow through a levee breach
Published in Journal of Hydraulic Research, 2022
Ibrahim Adil Ibrahim Al-Hafidh, Ezzat Elalfy, Jasim Imran
By introducing , the interfacial shear force is written in the following form: The non-dimensional Chézy coefficient, , appears in the drag force equations. An individual experiment was run by closing the breach opening and making the water move straight from upstream to downstream for a flow rate of 0.08725 m s. Velocity profiles at different sections along the channel were obtained using an acoustic Doppler velocimeter (ADV). The Chézy coefficient, can be expressed as: where depth-averaged velocity (m s), and shear velocity (m s). The shear velocity was estimated using the law of the wall. An average value of was found for the channel.
Effects of developing ice covers on bridge pier scour
Published in Journal of Hydraulic Research, 2022
Dario A. B. Sirianni, Christopher Valela, Colin D. Rennie, Ioan Nistor, Husham Almansour
To determine the panel surface roughness after the ice cover was constructed, the cover was fastened to the flume floor and a velocity profile test was conducted atop the cover with the panels facing upward, with a water depth of 0.1 m. The roughness of the artificial ice panels was estimated using logarithmic law of the wall, presented in Eq. (3), the semi-log linear region of the velocity profile measured adjacent to the ice cover. where u* is shear velocity, κ is the von Kármán constant (κ = 0.41), and ks is the surface roughness. Figure 6 shows a regression fit to the linear region of the velocity profile where the law of the wall is valid; using the slope and intercept in Eq. (3), the ks of the PVC panels was calculated to be 0.013 m.
A meso-scale gravel tracer model for large gravel-bed rivers
Published in Journal of Applied Water Engineering and Research, 2019
Michael Tritthart, Philipp Gmeiner, Marcel Liedermann, Helmut Habersack
However, in order to utilize x to generate shear velocity fluctuations, two considerations must be made first: (i) appropriate choice of a probability density function of the shear velocity and hence of the bed shear stress; (ii) selection of a suitable standard deviation of the distribution. While a Gaussian probability density function for u* seems to be an obvious choice, there is mounting evidence in the literature that the probability distribution of this property deviates from this distribution. Grass and Ayoub (1982) noted that the distribution is associated with a positive skewness. More recent findings in the literature (Cheng and Law 2003; Oerlue and Schlatter 2011; Mathis et al. 2013) explicitly employed a log-normal distribution to fit the bed shear stress τ to laboratory or DNS results. Detert et al. (2008) determined a positive skewness from pressure measurements, and Celik et al. (2010) also employed a log-normal distribution for momentum components near the bed. Just recently Gmeiner et al. (2016) showed results from a direct bed shear measurement device – deployed both at a rough bed in a laboratory flume and at the Danube River – that indicates a Gaussian distribution of the bed shear stress in the flume and a log-normal distribution in the river (Figure 1). Therefore, we tested both a Gaussian as well as a log-normal probability distribution for the shear velocity in this study.