Journal of Hydraulic Engineering

Results are presented from a laboratory investigation of a continuous discharge gravity current moving down an inclined plane into a linearly stratified fluid; the density of the inflow decreasing linearly with time, initially larger and finally smaller than the bottom ambient density. The inflowing water was observed to follow both underflowing and intrusive flow regimes. Hence, during the time in which the inflow was denser than the water in the stratified reservoir, an underflow was observed to descend down the sloping bottom with a speed that was consistent with that given by the theory for a buoyancy-conserving gravity current on gentle slopes. However, the continuous decrease of the density at the source shortly lead to an unstable density distribution within the initial underflow, which then collapsed into an intrusion that traveled as a horizontal gravity intrusion. Scaling arguments were used to identify both the position and time to the breakup of the underflow. To the end of the experiment, multiple intrusions were established successively at different depths in between the initial underflow and the surface buoyant plume.

A well-tested numerical model based on the Reynolds averaged Navier–Stokes equations with $k\text{-}\epsilon$ turbulence closure is further validated against three groups of experimental data on lock-exchange gravity flows. The model is then applied to study larger-scale turbidity currents with sudden-release and/or sustained inflow mechanisms. At the field-scale, sudden-release turbidity currents are found to be essentially unsteady with depth-averaged flow variables varying with time and distance from the upstream boundary. Turbidity currents with sustained inflows reach a quasi-equilibrium state in the body of the current. The simulation of a turbidity current initiated by sudden-release and then fed by sustained inflow reveals that, initially, two bore heads appear in the current with the second bore head resulting from sustained inflow and eventually catches up with the first one. Model results show that, depending on onset mechanism and slope, if the erosion rate of sediment exceeds the deposition rate, turbidity currents at the field scale can experience self-acceleration, a process predicted earlier by theory but not demonstrated in laboratory experiments.

A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.

Eulerian equations for the vertical flux and momentum of suspended particles in dilute sediment-laden open-channel flow in equilibrium have been derived using the two-fluid approach. Reynolds averaging has been applied in order to allow validation of individual terms with experimental data. Consideration of the various terms of the vertical momentum balance with experimental flume data indicates that the drag force has to be separated into a mean and a turbulent contribution with different timescales, respectively, the (gravitational) particle timescale and the integral turbulence timescale. The resulting formulation further provides a new theoretical closure for the turbulent Schmidt number.

The spreading of solutes or contaminants through water-distribution pipe networks is controlled largely by mixing at pipe junctions where varying flow rates and concentrations can enter the junction. Alternative models of solute mixing within these pipe junctions are presented in this paper. Simple complete-mixing models are discussed along with rigorous computational-fluid-dynamics models based on turbulent Navier–Stokes equations. In addition, a new model that describes the bulk-mixing behavior resulting from different flow rates entering and leaving the junction is developed in this paper. Comparisons with experimental data have confirmed that this bulk-mixing model provides a lower bound to the amount of mixing that can occur within a pipe junction, while the complete-mixing model yields an upper bound. In addition, a simple scaling parameter is used to estimate the actual (intermediate) mixing behavior based on the bounding predictions of the complete-mixing and bulk-mixing models. These simple analytical models can be readily implemented into network-scale models to develop predictions and bounding scenarios of solute transport and water quality in water-distribution systems.

Ratings relating stage and flow discharge have been traditionally established through measurements of discharge and concurrent stage. Inherent in this approach are several difficulties and shortcomings that have resulted in widely recognized problems in developing and applying ratings, such as looped ratings. Purely empirical methods that attempt to improve the agreement between ratings and measurements have met with limited success. This paper suggests a theoretical basis for discharge ratings that reflects the hydraulics of unsteady, nonuniform, subcritical flow. Simplification of the Saint-Venant equations for rating applications results in an approximation of the dynamics of flow that is summarized in the hydraulic performance graph, from which discharge ratings can be developed and updated theoretically. The resulting ratings apply a quasi-steady approximation of the flow, along with semiempirical correction factors developed for the site to estimate the discharge using the same information that is needed for “stage-fall-discharge ratings,” while addressing some of the shortcomings of this type of rating. Comparison of ratings developed using the resulting procedure against laboratory and field observations yields encouraging results.

Global positioning system (GPS) data are used to measure boat velocity during acoustic Doppler current profiler (ADCP) discharge measurements, particularly when bottom tracking (BT) is biased by moving bed. A Kalman filter is developed to improve the velocity reference used by the ADCP under such conditions. Kalman filtering is a recursive statistical technique that estimates the current state of a process, given various inputs and their variance. In the case of data obtained by ADCP, the availability of two independent velocity measurements and a position measurement makes this method particularly attractive. The new Kalman filter combines raw inputs for GPS position (GGA) and Doppler velocity (VTG) with BT data in real time to produce best estimates of velocity. The technique is evaluated and calibrated using various accuracies of GPS data collected simultaneously along with unbiased BT data at two different sites. On the Gatineau River, real-time kinematic and wide area augmentation system corrections were used for this study. On the Saint Mary’s River, nondifferential GPS was collected. To examine the conditions under which such a system would be required, synthetic data for a moving bed contamination of BT were created. In all moving bed conditions evaluated, the Kalman filter estimates of reference velocity were superior to raw inputs.

This paper is devoted to nonlinear observer and controller design for water level control of open-channel flow in irrigation canals or dam-river systems. A finite-dimensional model, previously developed by orthogonal collocation methods, based on Saint Venant equations and used for control design, is now further used for online flow rate and water infiltration estimation. This is done by a so-called state observer. In particular, the estimates obtained in this way can successfully be used in a controller previously proposed, resulting in a water level control law using only two level measurements along the canal (instead of the four measurements previously needed). The study is restricted to the case of a rectangular wetted section and subcritical flow. The results have been validated by simulations, on an implicit finite difference simulator based on a Preissmann scheme for various scenarios.

The main flow features of three-dimensional plunge pool scour are explored in this experimental research for steady flow conditions. These include the maximum depth of the scour hole, its streamwise geometry, and the maximum width, the maximum height of the ridge, its shape in plan view, and its profile. Expressions for all these parameters are presented in terms of the basic scour variables, including the approach flow densimetric Froude number, the jet impact angle, the jet diameter, and the tailwater elevation above the originally horizontal sediment bed. This research is based on a previous work relating to two-dimensional plunge pool scour. Differences between the two phenomena are outlined, and the results are discussed in terms of engineering applications. The results of the two works allow for the prediction of the most salient features of plunge pool scour for both the dynamic and the static scour holes.

The Big Bay Dam embankment failure occurred on March 12, 2004, releasing $17,500,000{\mathrm{m}}^3$ $(14,200\text{acre}\text{-}\mathrm{ft})$ of water. In all, 104 structures were documented as being damaged or destroyed as a result of this failure. No human lives were lost. This paper documents data gathered and analyses performed on the hydraulics of the failure. High water levels from the failure were marked and measured. A HEC-RAS unsteady flow model was developed. Using observed breach geometry, HEC-RAS provided results that agreed with the measured high water marks from $-0.02\text{to}-0.90\mathrm{m}$ and $0.01\text{to}0.62\mathrm{m}$ with associated modeled flow depths ranging from $9.3\text{to}5.7\mathrm{m}$ (from $30\text{to}19\mathrm{ft}$ ). A peak breach flow of $4,160{\mathrm{m}}^3∕\mathrm{s}$ $(147,000{\mathrm{ft}}^3∕\mathrm{s})$ was predicted at the embankment. Breach peak flow prediction equations were found to substantially underpredict the peak flow indicated by HEC-RAS for this failure. HEC-RAS modeling utilizing predicted breach geometry and formation time also underpredicted the peak flow, but by a lesser amount. The National Resources Conservation Service models WinTR-20 and TR 66 were also assessed. WinTR-20 results compared reasonably well with the high water marks for this failure. TR-66 results did not compare well.

The uniform flow of natural debris mixture is generally modeled assuming a uniform solid concentration and the absence of lateral walls. The resulting flow discharges are, however, higher than those observed and, in the case of erodible boundaries, the equilibrium between the moving and nonmoving mixtures cannot be simulated. Such a model also cannot simulate the effect of lateral rigid boundaries that generate lateral velocity and concentration gradients. This paper describes a numerical model to determine the concentration and velocity distribution in the two directions transverse to the flow. The model is applied to a uniform laminar flow of a mixture with a shear-thickening Herschel–Bulkley constitutive behavior, with rheological parameters expressed in terms of the local solid concentration, and allows the simulation of different conditions in the presence of both erodible and rigid boundaries.

Experiments were conducted over uniform gravel bed materials to obtain 143 friction factor values under bed-load equilibrium flow conditions in an attempt to add to the scarce data available on slopes between 1 and 9% for Shields numbers between 0.08 and 0.29. Analyses showed that when only flows over flat beds are considered, a distinction must be made between flows with and without bed load. More particularly, fitting flow resistance equations indicated that the roughness parameter increases by a factor of 2.5 from clear water flow to intense bed-load transport. Between these two states, the flow resistance can be approximated by a constant for a given slope.

Steady, 2D Darcian seepage in a homogeneous isotropic porous medium under an impervious structure is studied by the methods of complex analysis. The geometry of the structure is studied focusing on the travel time of a marked (neutral tracer) particle from the upper pool to the tailwater. In the Verigin problem, the angle of inclination of a sheetpile resulting in minimal time along the bounding streamline is $\pi ∕2$ . If the maximum of the minimum of the travel time is searched between all streamlines originated in the upper pool, then the optimal angles are found to be $0.404\pi$ and $0.596\pi$ . The minimization of the total volume of fluid that arrives from the upper pool to the tailwater during a prescribed time span is also considered. For arbitrary geometry, structure optimization with respect to travel time is carried out explicitly for the bounding streamline with a constraint on the wetted perimeter of a depressed structure. The minimal-time shape is found to be the Voshinin semicircular structure, which is mathematically generated by a line vortex.

An exact solution for transient Forchheimer flow to a well does not currently exist. However, this paper presents a set of approximate solutions, which can be used as a framework for verifying future numerical models that incorporate Forchheimer flow to wells. These include: a large time approximation derived using the method of matched asymptotic expansion; a Laplace transform approximation of the well-bore response, designed to work well when there is significant well-bore storage and flow is very turbulent; and a simple heuristic function for when flow is very turbulent and the well radius can be assumed infinitesimally small. All the approximations are compared to equivalent finite-difference solutions.

This technical note examines vegetation effects on hydraulic resistance in small streams and suggests simple quantitative relationships for predicting and quantifying these effects using the plant characteristics with the greatest explanatory power. In particular, we examine the effects of aquatic plant biomass, stature, and architecture on hydraulic performance of five New Zealand streams representing a wide range of channel dimensions, flows, aquatic plant species, and assemblages. Comparisons among the vegetation parameters indicated that ratios of the site-averaged canopy height to the mean flow depth and of the site-averaged plant length to the mean flow depth were the best roughness descriptors. Effects of individual plant species and their characteristic patch patterns were not significant. The data from all sites collapsed around single lines, suggesting that general physical parameters of vegetation should be the primary determinants of hydraulic resistance in streams studied, not species-specific parameters, as often assumed.

A laboratory characterization of cohesive sediment has been carried out in which data obtained from standard sedimentation and rheological measurements were combined in a determination of the critical solid concentration for the detection of elasticity in a weakly cohesive suspension. The corresponding storage modulus and shear stress are very critical in any in situ rheometry of sediments, especially in the study of mud-water surface erosion in a flume. Sedimentation results showed that particle size distribution rather than surface treatment controlled the rheological behavior of the suspension while the critical solid concentration for the appearance of three-dimensional space-filling network, showing some measurable elasticity in the suspension, occurred in the region of 0.015. This parallel between the consolidation behavior and shear rheology development for the flocculating system has been established. This technique could be an adjunct to the laboratory characterization of cohesive sediments for the estimation of critical shear stress for surface erosion, especially in a typical flume experiment under water wave pressure.

This paper presents a method to predict depth-averaged velocity and bed shear stress for overbank flows in straight rectangular two-stage channels. An analytical solution to the depth-integrated Navier–Stokes equation is presented that includes the effects of bed friction, lateral turbulence, and secondary flows. The Shiono and Knight method accounts for bed shear, lateral shear, and secondary flow effects via three coefficients, $f$ , $\lambda$ , and $\Gamma$ , respectively. A novel boundary condition at the internal wall between the main channel and the adjoined floodplain is proposed and discussed along with other conventional boundary conditions. The analytical solution using the novel boundary condition gives good prediction of both lateral velocity distribution and bed shear stress when compared with experimental data for different aspect ratios.

When using finite-volume methods and the conservative form of the Saint Venant equations in one-dimensional flow computations, it is important to establish the correct balance between the discretized flux vector and the geometric source terms. Over the last few years various improvements to numerical schemes have been presented to achieve this correct balance, focusing on the capability to simulate water at rest on irregular geometries (C-property). In this paper it is shown that common schemes can lead to energy-violating solutions in the case of steady flow. We present developments based on the Roe TVD finite-volume scheme for one-dimensional Saint Venant equations, which results in a method that not only satisfies the C-property, but also preserves the correct steady flow when stationary boundary conditions are used. We also present a totally irregular channel test case for the verification of the method.

A two-dimensional depth-averaged model was used for the simulation of scour and deposition in sand-bed meandering channels with fixed banks. The model employs unstructured meshes based on triangular elements and incorporates the effects of curvature-induced helical flow and transverse bed slope in the direction of bed-load sediment transport. The model was tested using experimental data from a well-known laboratory curved channel and a full scale meandering river. The numerical results agreed well with observed data, demonstrating that the model can reproduce the main features of bed profiles along meandering rivers, such as the formation of point bars and pools.

It is experimentally demonstrated that fitting the log law to the mean velocity profile in turbulent open-channel flow to determine the friction velocity, roughness length, and zero-plane displacement, can lead to relatively high standard errors in these parameters. It is also demonstrated that this approach, where the log law alone is used to estimate these parameters, may yield values of these parameters that are significantly different from those obtained when the friction velocity is determined independently of the log law. Although the statistical estimation of the three log law parameters from mean velocity data alone is frequently necessary, this procedure can lead to inaccurate and imprecise estimates of these quantities.

This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse’s experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows.

The original derivation of the Einstein bed-load formula involves several oversimplified assumptions concerning step length of a particle, exchange time, and probability of being lifted into motion. A modified version of the Einstein formula that relaxes these assumptions and incorporates a nonuniform sediment model is proposed and tested with both field and laboratory data. The modified formula shows promise as being more reliable than the original version in estimating bed-load transport rates.

The additional resistance to erosion due to flows down steep slopes that can be achieved by placing rock instead of dumping randomly has been quantified during a large-scale flume investigation. Testing was undertaken for slopes of 0.2, 0.3, and 0.4 with two layers of armor overlying a filter, consistent with conventional rock protection designs. Two sizes of sandstone with mean diameters of 76 and $109\mathrm{mm}$ and basalt with a mean diameter of $94\mathrm{mm}$ were tested. Placing rock to achieve maximum bulk density (mass per unit in situ volume) increased failure flow (flow at exposure of the filter) by 30% of that achieved with the same type of randomly dumped material but the total armor mass per unit surface area increased by 35%. A damage approach to steep erosion protection that is similar to that used for coastal breakwater design is presented. An improved method of partition between the aerated flow over as well as flow through both random and placed rock has also been quantified. Better characterization of aerated surface flow descriptions for random and placed crushed rock is presented. A non-Darcy coefficient of $3.3\pm 1.1$ best characterized the interflow component through random and placed rock.

Scour control downstream of a hydraulic structure is an important topic in river engineering. A block ramp is a structure that can be built with a low-environmental impact stilling basin realized by means of a sill that controls the scour hole. The scour that occurs downstream of block ramps is analyzed and the effect of rock sills on scour geometry is evaluated. Experiments have been carried out with ramp slopes varying between 1V:4H to 1V:12H. Three different sill types were tested for a total of 300 experiments among which about 140 tests involved rock sills. Useful equations for the design of the stilling basin are proposed.

The analytical solution of the differential-form momentum equation for the outflow distribution along a continuous multiple-port diffuser is derived. The solution is verified by comparison with available experimental data. The outflow patterns along the diffuser are determined by the range of two dimensionless parameters, which measure the effects of wall friction and port momentum, respectively. A concept of flow uniformity of lateral discharge is explored, and an analytical formula for the evaluation of uniformity is derived. A simple formula is also proposed which may be useful in the design of the multiple-port diffuser.

This research work focuses on the analysis of hydraulic transients in polyvinyl chloride (PVC) pipes, which are characterized by a viscoelastic rheological behavior. Transient pressure data were collected in a pipe rig consisting of a set of PVC pipes. The creep function of the PVC pipes was determined by using an inverse transient model based on collected transient pressure data and compared with that obtained by carrying out mechanical tensile tests of PVC pipe specimens. The numerical results obtained from the transient solver have shown that the attenuation, dispersion, and shape of transient pressures were well described. The incorporation of the viscoelastic mechanical behavior in the hydraulic transient model has provided an excellent fitting between numerical results and observed data. Calibrated creep function based on inverse analysis fit the one determined by mechanical tests well, which emphasized the importance of pipe-wall viscoelasticity in hydraulic transients in PVC pipes.

A pressurized water system may be subjected to high pressure surges because of the expulsion of a trapped air pocket through an orifice at the downstream end of the pipe. Results are presented of laboratory experiments, in which pressure histories were recorded for different upstream heads, air pocket volumes, and orifice sizes. The resulting pressure oscillation pattern was divided into two distinct stages: a first phase of low-frequency pressure oscillation during the air release, followed by a sudden pressure increase with water hammer characteristics when the water column reaches the orifice. The experimental results show that the duration of the first phase decreases substantially with increasing upstream head and orifice size, and increases with air pocket volume. A simple relationship was deduced, which agrees well with experimental data. The maximum pressure peaks, always observed in the water hammer phase, increased with upstream head and orifice size, whereas the volume of the air pocket appeared to be a less significant factor in the range investigated. A simple predictive equation was deduced based on Allievi–Joukowski results.