Three-dimensional numerical simulations were performed for different flow rates and various geometrical parameters of step-pools in steep open channels to gain insight into the occurrence of energy loss and its dependence on the flow structure. For a given channel with step-pools, energy loss varied only marginally with increasing flow rate in the nappe and transition flow regimes, while it increased in the skimming regime. Energy loss is positively correlated with the size of the recirculation zone, velocity in the recirculation zone and the vorticity. For the same flow rate, energy loss increased by 31.6% when the horizontal face inclination increased from 2° to 10°, while it decreased by 58.6% when the vertical face inclination increased from 40° to 70°. In a channel with several step-pools, cumulative energy loss is linearly related to the number of step-pools, for nappe and transition flows. However, it is a nonlinear function for skimming flows.
Accurate estimation of head loss introduced via randomly placed roughness elements found in natural or constructed streams (e.g., fish passages) is essential in order to estimate flow variables in mountain streams, understand formation of niches for aquatic life, and model flow structure. Owing to the complexity of the involved processes and the often missing detailed data regarding the roughness elements, the head loss in such streams is mostly approximated using empirical models. In our study, we utilize flume experiments to analyze the effects of the spatial distribution of roughness elements on water surface levels and head loss and, moreover, use the produced data to test three empirical models estimating head loss. The experiments were performed in a 15 m long, 0.9 m wide flume with a slope of 5% under large Froude numbers (2.5–2.8). Flow velocities and water levels were measured with different flow rates at 58 points within a 3.96 m test section of the flume. We could show that different randomly arranged patterns of roughness elements significantly affected head loss (differences up to 33.6%), whereas water jumps occurred when flow depths were in the same size range as the roughness elements. The roughness element position and its size influenced water surface profiles. None of the three tested empirical models were able to well reproduce the differences in head loss due to the different patterns of roughness elements, with overestimated head loss from 12 to 94.7%, R2 from 41 to 73%, NSE from −21.1 to 0.09, and RRMSE from 18.4 to 93%. This generally indicates that these empirical models are conditionally suitable to consider head loss effects of random patterns of roughness elements.
Many methods have been developed for estimating bedload flux under conditions of quasi-steady flow, in which both turbulent velocity fluctuations and changes in bedload flux are assumed to occur over timescales much shorter than variations in flow velocity. Nonetheless, the prediction of bedload transport rate tends to break down when considering timescales over which turbulent fluctuations matter. For example, Escauriaza and Sotiropoulos (2011) conducted numerical modeling in clear water scour conditions and found that bedload transport may occur even when the average bed shear stress is far below the expected threshold value for entrainment, thereby suggesting the importance of highly transient turbulence forces. Sumer et al. (2003) found that a 20% increase in turbulence intensity in the shear layer above the bed caused a 6-fold increase in bedload flux. Videography has shown that bedload motion is temporally variable (Garcia et al., 2007;Venditti et al., 2010), a behavior largely attributed to bursting events associated with turbulent eddies (Nelson et al., 1995).Unsteady flow is characterized not only by changing discharge through time but also by rapid fluctuations in turbulent velocity which, in turn, cause variable amounts of bed material disturbance (e.g., Dey, 2014;Grass, 1971). Lee et al. (2004) observed that gradually-varying unsteady flows induced bedload fluxes as much as 1.6 times greater than those under similar steady flows. Much less is known about bedload flux in very unsteady flows, such as occur in flash floods. The hydrodynamics of flood bores and the consequences for bedload transport have been examined in flume studies (e.g.,
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