Journal of Hydraulic Engineering

Spatial averaging of the Reynolds-averaged Navier–Stokes equations gives the double-averaged Navier–Stokes equations, for which boundary drag appears naturally and explicitly in momentum conservation equations. Increasing use of the double-averaged equations, e.g., for relating flows to three-dimensional bed roughness, for evaluation of profiles of flow stresses and velocities in ecologically significant regions below roughness tops, and for modeling purposes, requires parameterization of boundary drag at subelement scales. Based on seven flows over repeated square-rib roughness and ten flows over repeated fixed simulated sand waves, with measured velocities and bed pressures, expressions for form-drag coefficient $C_D=f$ (elevation below roughness top, relative roughness submergence, roughness steepness) are obtained for each of the two-dimensional roughness types. Using these equations, form drag variation with elevation below roughness tops can be calculated using either the double average of the square of local velocity (preferred based on conceptual considerations, trends in coefficient prediction, and also overall drag prediction) or the squared local double-averaged velocity, the roughness area being normal to the flow in each case. Integration of subelement drag given by these expressions is shown to give form-drag coefficient magnitudes and trends for complete individual elements comparable to those obtained by other authors based on measurements or numerical simulations. The ranges of roughness steepness and relative roughness submergence upon which the present equations have been derived need to be noted in consideration of application of the equations. In addition, effective application of the expressions is limited in regions of strongly negative double-averaged velocity. Further work remains to determine drag parameterization for alternative roughness geometries.

The tidal bore at the estuary of the Qiantang River in China is one of the most spectacular bores in the world. Although it is a famous scenic spot, it may cause disasters due to its destructive power. In this paper, a new numerical model, based on a Godunov-type scheme with the water level–bottom topography formulation combined with the improved wet/dry techniques, is constructed to numerically simulate the tidal bore on the Qiantang River. The simulated results using the model agree well with observed data, which shows that the model can reproduce the formation, evolution, and dissipation of the tidal bore on the Qiantang River.

Protection of banks against erosion is an important but very expensive task in river management. The outer banks in river bends are most vulnerable to erosion and require an enhanced protection. This paper investigates, in an experimental flume, the efficiency of scour reduction and bank protection near the outer banks in open-channel bends by means of a horizontal foundation, called footing, protruding into the flow. First it is experimentally verified that bed mobility has a minor influence on the bed topography, which is mainly shaped by bend effects. Subsequently, the influence of the footing width and vertical elevation on the bed topography is investigated under clear water scour conditions. A maximum scour reduction of more than 40% was obtained with a footing placed at one-third of the maximum scour depth without bank protection and a footing width of about two-thirds of this maximum scour value. But a footing that is too narrow and/or not deep enough is vulnerable to underscour and subsequent bank failure. The experiments convincingly demonstrate the efficiency of this bank protection technique. The optimal footing parameters in the presented experiments should merely be seen as indicative, however, as they are expected to be case dependent.

Understanding the hydraulics of flow in a compound channel with vegetated floodplains is very important for determining the stage-discharge curve and for supporting the management of fluvial processes. In this paper, the flow patterns over different types of vegetation, such as tree, shrub, and grass, are described, based on an experimental study. For vegetation on the floodplain, the authors choose plastic grass, duck feathers, and plastic straws as model grass, shrubs, and trees, respectively. A 3D acoustic Doppler velocimeter was used to measure the local flow velocities for different types of vegetation on the floodplain, and the total discharge and flume slope were measured independently. In the cases of nonvegetated floodplains, all measured streamwise velocity distributions followed the logarithmic distribution, but for vegetated floodplains, they followed an S-shaped profile, exhibiting three zones. For all cases, the fluctuating velocity followed a normal distribution. The influence of different types of vegetation on the distributions of the secondary currents, turbulence intensities, and Reynolds shear stresses were also analyzed.

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a $k-\epsilon$ model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.

A kinematic mixing model has been developed to predict far field effluent distributions for ocean discharges. The model allows for complex outfall configurations and time varying discharge rates to be simulated. The model can use field observations or the output from a proven near field mixing model as input to this far field mixing model. The model uses observed or simulated horizontal currents at one location to advect the effluent plume and a scale-dependent “diffusion velocity” submodel to account for horizontal diffusive processes. To collect data to calibrate and verify the model, long-term continuous dye release experiments were conducted at two New Jersey ocean outfalls. Based upon the results of the dye release experiments, appropriate values for the diffusion velocity were determined for each outfall. Simulations using these diffusion velocities provided reasonable predictions of plume width and of average dye concentration at each transect for each outfall. This work demonstrates that an Eulerian velocity observed at one location in the coastal ocean off New Jersey may be used to predict Lagrangian transport over a distance of several kilometers.

For transverse mixing problems in open channels, the effect of secondary currents on a tracer cloud is to disperse and mix the tracer in three dimensions more rapidly than would be the case if transverse turbulent diffusion were acting alone. Transverse mixing of this kind is difficult to simulate using two-dimensional depth-averaged mixing models which typically requires the specification of an equivalent dispersivity combining the effects of vertical shear dispersion and horizontal turbulent diffusion. In this paper, a two-dimensional vertically averaged and moment (VAM) equation technique for describing the transverse mixing mechanics of passive tracer vertical shear dispersion in approximately uniform curved open channel flow is detailed. An analytical expression is generated and compared to previous works in the literature describing the longitudinal development and asymptotic value of transverse dispersivity due to secondary current vertical shear dispersion. This expression is shown to describe the changing value of dispersivity even within the advective zone where traditional two-dimensional models cannot be applied. Distributions of depth-averaged concentration generated from numerical simulations of the VAM equations are compared to other higher fidelity computational results. The practical value of this VAM analysis framework is discussed relative to the potential for implementation in modern river modeling software packages.

Oil released in a deepwater blowout breaks up into droplets. Hence, the time it takes for oil to reach the water surface, its location, and the size of the surface slick at a given time, are all affected by oil droplet sizes. Information on oil surfacing time, its location, and slick size are essential for emergency spill response as well as contingency planning. Despite the importance of the oil droplet size on oil fate in many oil spill problems, our ability to estimate oil droplet sizes has been poor. In this paper, methods are developed for a deepwater oil spill model to estimate the oil droplet size distribution generated due to an accidental release. Models for estimating oil droplet size distribution generated by a deepwater release are developed based on the maximum entropy formalism. The quality of results depends on the constraint equations used. The paper shows results using only the mass balance and specific surface area as constraint equations. The latter case showed markedly improved results. Model results for droplet size distribution are compared with limited experimental data.

Large water waves caused by massive slide impacts are a potential hazard along waterways, coastal areas and Alpine regions. Experimental research has been conducted at the Swiss Laboratory of Hydraulics to assess the risk from landslide-generated impulse waves. Analogously, the Centro Elettrotecnico Sperimentale Italiano performed numerical simulations of initial landslide and consequent impulse wave propagation using two mathematical models based on the conservative shallow-water equations. This paper presents the experimental test results and numerical predictions of impulse waves in a flume for a range of stillwater depths, landslide volumes, and impact velocities at laboratory scale. The comparison between the measured and predicted wave free surface profiles generally produced corresponding wave heights, although the initial wave peak is too steep and arrives too early. Excluding spurious random effects, the relative differences between measured and numerically computed maximum wave heights ranged within $\pm 20\%$ , which can be considered satisfactory from the engineering point of view.

Flood wave propagation is the unifying concept in representing open channel and overland flow. Therefore, understanding flood wave routing theory and solving the governing equations accurately is an important issue in hydrology and hydraulics. In an attempt to contribute to the understanding of this subject, in this study: (1) an analytical solution is derived for diffusion waves with constant wave celerity and hydraulic diffusivity applied to overland flow problems; and (2) an algorithm is developed using the MacCormack explicit finite difference method to solve the kinematic and diffusion wave governing equations for both overland and open channel flow. The MacCormack method is particularly well suited to approximate nonlinear differential equations. The analytical solutions provide the practicing engineer with computational speed in obtaining results for overland flow problems, and a means to check the validity of the numerical models. On the other hand, for larger scale catchment-stream problems, the verified numerical methods provide efficient and accurate algorithms to obtain solutions. Both the analytical approaches and the MacCormack algorithm are used to solve the same synthetic examples. Comparison of results shows that the numerical and analytical solutions are in close agreement. Furthermore, the MacCormack algorithm is applied to a real catchment: a segment of the Duke University West Campus storm water drainage system. In order to check the accuracy of the results obtained by the MacCormack method, the results are compared to predictions of the Environmental Protection Agency storm water management model (SWMM) as calibrated with measured rainfall and surface runoff flow data. The results obtained from SWMM are in good agreement with the results obtained from applying the MacCormack algorithm.

A simple, robust, and general formula for the settling velocity of a particle is presented, taking into account the shape and roundness of the particles. It is based on the two asymptotic behaviors of the drag coefficient for low and high Reynolds numbers, respectively. The three coefficients in the proposed equation were fitted for different shape and roundness using explicit relationships. The proposed relationship yields the best results among the studied formulas for many kind of particles with various sizes, shapes, roundnesses, and densities. This formula could therefore be applied to any particle.

The flow field for a low Froude number nonbuoyant rectangular surface jet is studied using laser induced fluorescence and laser Doppler velocimetry. It is shown that a surface current develops in turbulent, but not in laminar jets. The existence of a self-similar regime is established. The lateral growth rate of the jet below the surface is about 4.8 times its vertical growth rate, while that of the surface current is 8.8 times. The vertical growth rate is about half that of a plane surface jet and less than one third that of a free axisymmetric jet. While the horizontal profiles of the streamwise velocity are similar to those observed in free, submerged, and wall jets, the vertical distributions are distinctly flatter.