Journal of Hydraulic Engineering

Low-head labyrinth weir control structures installed on mild sloping channels or where the channel downstream of the weir is constricting and/or heavily vegetated can experience submergence. Weir submergence occurs when the tailwater surpasses the weir crest elevation, causing an increase in the upstream driving head for a given discharge, relative to a free-discharge condition. The most familiar relationship for predicting submerged weir head-discharge relationships is likely that of James R. Villemonte, which he published in 1947 for sharp-crested linear weirs. For lack of a better alternative, Villemonte’s relation has also been applied to predicting submerged labyrinth weir performance. A new dimensionless submerged head relationship developed in this study is presented for submerged labyrinth weirs. A similar relationship is also presented for linear sharp-crested weirs. The accuracy of the submerged linear weir relationship was equivalent to Villemonte’s and is simpler to solve when working in terms of total upstream head. Relative to Villemonte’s relationship applied to labyrinth weirs, the new submerged labyrinth weir relationship reduced the predictive errors from 23 to 3.5% (maximum) and 8.9 to 0.9% (average), relative to the experimental data.

Sedimentation in the main pool of a deep (maximum depth: $50\mathrm{m}$ ), $227{\mathrm{km}}^2$ hydropower reservoir was modeled using a three-dimensional numerical model of hydrodynamics and sedimentation for different wind, inflow, and outflow conditions. Short-term velocity measurements made in the reservoir were used to validate some aspects of the hydrodynamic model. The effects of thermal stratification on sedimentation patterns were investigated, since the reservoir is periodically strongly stratified. Stratification alters velocity profiles and thus affects sedimentation in the reservoir. Sedimentation of reservoirs is often modeled considering only the deposition of sediments delivered by tributaries. However, the sediments eroding from the shorelines can contribute significantly to sedimentation if the shorelines of the reservoir erode at sufficiently high rates or if sediment delivery via tributary inflow is small. Thus, shoreline erosion rates for a reservoir were quantified based on measured fetch, parameterized beach profile shape, and measured wind vectors, and the eroded sediments treated as a source within the sedimentation modeling scheme. The methodology for the prediction of shoreline erosion was calibrated and validated using digital aerial photos of the reservoir taken in different years and indicated approximately $1\mathrm{m}∕\mathrm{year}$ of shoreline retreat for several locations. This study revealed likely zones of sediment deposition in a thermally stratified reservoir and presented a methodology for integration of shoreline erosion into sedimentation studies that can be used in any reservoir.

Calculations of interfacial diffusion coefficients are often based on tracer flux or penetration into permeable media or sediments. Based on previous investigations, a new empirical relationship for tracer-based interfacial diffusion coefficients is derived. This relationship is a powerful tool for estimating interfacial fluxes over a range of environmentally relevant conditions. Support for this relationship was found in experiments targeting the slip velocity at porous media–boundary layer interfaces. Slip measurements from flume experiments using flat permeable sediment beds and from previous studies using high permeability media were converted to interfacial diffusion coefficients based on the momentum flux needed to drive the observed interstitial flow. Slip-based estimates compared well with the tracer-based predictions over the entire range of flow-permeability conditions. This study presents a relationship for predicting fluxes across the sediment-water interface that is driven by permeability-scale processes. Predicted fluxes are comparable to those documented for other processes driving interfacial transport, such as bed topography and sediment transport.

The present study examines the flow around a self-occurring cluster bed form and the use of general computation fluid dynamics methods for hydraulic and geophysical flow applications. This is accomplished through a comprehensive experimental/numerical investigation. In the laboratory, cluster bed forms are first formed from movable sediment, and laser Doppler velocimeter measurements of two-dimensional fluid velocity are then taken around a formed cluster. A three-dimensional (3D) Reynolds averaged Navier-Stokes simulation of the physical cluster and flow conditions is then conducted using near-wall, shear stress transport (SST) turbulence modeling with the inclusion of hydraulic roughness, $k_s$ ( $\mathsf{R}=\mathrm{31,150}$ , $k_s∕h=0.1$ , $k_s^{+}=274$ , i.e., in the fully rough regime). SST near-wall modeling is advantageous compared to the more widely used wall functions approach for flows with significant roughness and flow separation because the model equations can be integrated down to the wall. Therefore, SST near-wall modeling makes no a priori assumption that the law of the wall is valid throughout the wall region of the flow. Additionally, it has the ability to intrinsically handle boundary roughness through the boundary condition for turbulent specific dissipation at the wall, allowing for wall functions to be bypassed in accounting for roughness effects. The study shows that in the wall region surrounding the cluster, flow is 3D and quite complex, with different scales of embedded flow structures dominating the cluster wake and leading to flow heterogeneities in pressure and bed-shear stress. Results also indicate that near-wall modeling with SST compared favorably with the experimental flow data without tuning of model constants.

Laboratory experimental results on the turbulent flow characteristics, measured by an acoustic Doppler velocimeter, over loose rough boundaries at the near-threshold of motion are reported. The primary endeavor was to investigate the response of the turbulent flow field, having zero-pressure gradient, to the uniform gravel beds at the near-threshold of motion with reasonably wide range of relative roughness $\epsilon ∕h$ ( $0.02<\epsilon ∕h<0.15$ ; where $\epsilon =\text{Nikuradse}$ ’s equivalent roughness and $h=\text{flow}$ depth). Five uniform gravel sizes, ranging from $4.1\text{to}14.25\mathrm{mm}$ , were used in the experiments. The vertical distributions of time-averaged velocity, turbulence intensities and the Reynolds stress were measured and analyzed. The variation of the mixing-length is considerably linear with the depth within the inner layer, whose thickness is 0.23 times the boundary layer thickness $\delta$ , and the von Kármán constant is obtained as 0.35. The boundary shear stresses were determined by three independent methods, such as using the logarithmic law (the Clauser method), Reynolds stress profiles and bed slope. It is observed that in the inner layer, the logarithmic law of wall for the time-averaged streamwise velocity holds with the von Kármán constant 0.35 and a constant of integration 7.8; whereas in the outer layer, the law of the wake defines the velocity profiles with average value of the Coles’ wake parameter 0.11. Alternatively, velocity profiles based on $1∕n\text{th}$ power law are also put forward, where $n$ is expressed as a function of $\epsilon ∕\delta$ . The equation of the friction factor $f$ is obtained from the depth averaging of the velocity profile; and the collapse of the estimated $f$ and the measured data (experimental and field) is reasonable. The turbulence intensities being non-isotropic can be defined by an exponential law; whereas the Reynolds stress varies almost linearly with the depth. The values of the Shields parameter for the threshold of gravel motion obtained experimentally correspond closely with the curve obtained from the modified model of Dey considering the present logarithmic law of velocity. For all the aforementioned parameters, thorough statistical and error analyses of the experimental data are done to ascertain the adequacy of the proposed equations.

Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.

Algebraic equations relating fluid volume and the free surface elevation in partially wetted quadrilateral computational cells are derived and incorporated into a Godunov-type, finite-volume, shallow-water model. These equations make it straightforward to reconstruct the free surface elevation based on the volume of fluid in a computational cell, the dependent variable tracked by finite volume models for conservation purposes, regardless of whether the cell is fully or partially wetted. Improvements to the variable reconstruction process streamline the computation of mass and momentum fluxes with approximate Riemann solvers, yielding a model that simulates sub-, super-, and transcritical flows over irregular topography with wetting and drying fronts. Furthermore, the model is free from fluid and scalar mass conservation errors and it eliminates nonphysical distributions of scalars by avoiding artificial concentration and/or dilution at wet/dry interfaces. Use of this wetting and drying methodology adds roughly 10% to the execution time of flow simulations.

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.

In this work we incorporate a Gram–Charlier-type joint probability distribution of near-bed two-dimensional instantaneous velocities into a simple mechanistic model to investigate the role of turbulent bursting in sediment entrainment. The results reveal that under typical values of bed-shear stress $(>3\mathrm{Pa})$ , the time fractions of Quadrants 1–4 (Q1–Q4) remain constantly as 16, 34, 19, and 31%, respectively. Entrainment of the fine sediment mixtures is dominated by the lifting mode, whereas entrainment of the coarse ones is dominated by rolling. Sweeps (Q4) are consistently the most significant contributor to entrainment under various types of sediment mixtures. As the standard deviation of grain-size distribution increases, the hiding effect exerted on the finer grains of the mixture is reduced, leading to the elevated correction factors for effective hydrodynamic forces, and thus the reduced threshold velocities for entrainment. The reduced thresholds would, in turn, enhance the fractional contributions of ejections and inward interactions (Q2 and Q3), which are associated with negative longitudinal velocity fluctuations, such that the fractional contribution of outward interactions (Q1) would become less significant.

This study examines low Reynolds number flow over vegetated sloping ground. Instead of using the traditional empirical formula related to resistance or frictional roughness, a new approach is presented by considering the flow inside the vegetation layer as porous media flow governed by Biot’s poroelastic theory as well as inside the soil layer. There is a discrepancy in the velocity distributions of flow over vegetative mantle area and bare area, respectively. Due to the change of the vegetation density, the effects of vegetation porosity and vegetation blockage on surface water flow are discussed.