Journal of Hydraulic Engineering

A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional hydrostatic flow equations separately in a main river channel and in adjacent floodplains using a two-stage predictor-corrector scheme. The lateral interaction between the main channel and floodplains, due to both advective exchange arising from lateral pressure gradients and turbulent exchange due to lateral shear, is included. The Lagrangian moving grid eliminates numerical diffusion and oscillations commonly experienced in Eulerian models, and can accurately simulate wave propagation and nonlinear steepening until wave breaking. The Lagrangian moving grid is dynamically adaptive, providing variable resolution as the moving fluid parcel’s length changes, either because the cross-sectional flow area or the flow depth changes as the wave moves down a channel of variable cross section. The model also allows flows over dry beds and moving boundaries to be handled efficiently. The model was successfully validated for a flow induced by a simple wave in a prismatic channel, flood waves in laboratory compound channels, and flow in a natural river.

The geometrical development of unlined plunge pools downstream large dams depends on both local geology and type of plunging jet and its diffusion pattern. Experimental investigations in plunge pools with different lateral confinements are presented. They show that the pool geometry influences plunging jet diffusion, air entrainment in the pool, and, as a consequence, impact pressures at the water-rock interface and inside the fissured rock mass. Results include impact pressures definition for variable pool depths, jet velocities, and pool geometries, depending explicitly on the lateral confinement of the jet. The main pool flow features are described focusing on their contribution to energy dissipation. Should the lateral confinement limit the development of macroturbulent rollers around the plunging jet (instead of the pool depth), the mean pressures at impact are considerably reduced, as well as RMS pressures in transitional and deep pools. For shallow pools, RMS pressures increase as a result of enhanced jet development.

Local pier scour experiments were performed in the laboratory to investigate the effect of relative sediment size on pier scour depth using three uniform sediment sizes and three bridge pier designs at different geometric model scales. When the data from a large number of experimental and field investigations are filtered according to a Froude number criterion, the effect of relative sediment size on dimensionless pier scour depth is brought into focus. The choice of sediment size in the laboratory model distorts the value of the ratio of pier width to sediment size in comparison with the prototype which in turn causes larger values of scour depth in the laboratory than in the field. This model distortion due to sediment size is shown to be related to the scaling of the large-scale unsteadiness of the horseshoe vortex by studying the relevant time scales of its coherent structure upstream of a bridge pier using acoustic Doppler velocimeter measurements. Observations of sediment movement, probability distributions of velocity components, and phase-averaging of velocity measured upstream of a bridge pier reveal properties of coherent motions that are discussed in terms of their contribution to the relationship between dimensionless pier scour depth and the ratio of pier width to sediment size over a large range of physical scales.

The three-dimensional turbulent flow field around a spur dike in a plane fixed-bed laboratory open channel was studied experimentally using a microacoustic Doppler velocimeter. Mean and turbulence characteristics in all three spatial directions were evaluated at upstream and downstream cross sections near the dike. Results showed that the primary flow separated in both lateral and vertical directions. Two counter-rotating flow circulations, consisting of the lateral and vertical velocity components, originated at the dike section. Downstream of the dike, the circulation in the flow-separation zone is stronger than the one in the contracted primary flow zone. The maximum bed-shear stresses estimated using Reynolds stresses is about three times as large as the mean bed-shear stress of incoming flow.

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height $\left(k\right)$ to the total depth of flow $\left(d\right)$ equal to 0.10. Three rib separations $\left(p/k\right)$ of 4.5, 9, and 18 were examined. Here, $p$ is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of $d$ - and $k$ -type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for $p/k=4.5$ and 9: on the top of the rib and above the cavity, and an additional location for $p/k=18$ . The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for $y_1<3k$ . In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond $y_1\approx 7k$ . In the outer layer $\left(y_1>3k\right)$ , all higher-order turbulent moments for the $k$ -type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at $p/k=18$ , the flow at $y_1<5k$ tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.

A real-time estimation of water distribution system state variables such as nodal pressures and chlorine concentrations can lead to savings in time and money and provide better customer service. While a good knowledge of nodal demands is prerequisite for pressure and water quality prediction, little effort has been placed in real-time demand estimation. This study presents a real-time demand estimation method using field measurement provided by supervisory control and data acquisition systems. For real-time demand estimation, a recursive state estimator based on weighted least-squares scheme and Kalman filter are applied. Furthermore, based on estimated demands, real-time nodal pressures and chlorine concentrations are predicted. The uncertainties in demand estimates and predicted state variables are quantified in terms of confidence limits. The approximate methods such as first-order second-moment analysis and Latin hypercube sampling are used for uncertainty quantification and verified by Monte Carlo simulation. Application to a real network with synthetically generated data gives good demand estimations and reliable predictions of nodal pressure and chlorine concentration. Alternative measurement data sets are compared to assess the value of measurement types for demand estimation. With the defined measurement error magnitudes, pipe flow data are significantly more important than pressure head measurements in estimating demands with a high degree of confidence.

The nonlinear Muskingum and diffusion wave methods for flood routing are deduced from a conservative modified-advection equation as an approximation of the one-dimensional Saint-Venant equations. The modified-advection equation has the kinematic wave speed and attenuation parameter as functions of discharge, which can be derived for the particular averaged geometry for the cross section and hydraulic properties of the reach. The nonlinear Muskingum and diffusion wave methods also include any uniformly distributed time-dependent lateral inflow along the river and are valid for any Froude number. The methods are discussed in relation to corresponding methods derived recently for Muskingum routing and for diffusion wave routing. Numerical experiments on a synthetic river including extensive flood plains show that the proposed nonlinear Muskingum method is highly accurate compared with a full solution of the Saint-Venant equations. The deterioration of accuracy with decreasing bed gradient is highlighted for cases with and without lateral inflow.

This note focuses on the temporal and spatial evolution of local scour below low-head spillways. Steady-flow experiments were carried out in a 1-m wide and 20-m long rectangular straight channel. The jet was generated by an ogee-crest spillway followed by a positive-step stilling basin. Nearly uniform sandy beds were generally tested, but additional tests were also performed with a special bed of lead spheres. To circumvent the combination of local and general scour phenomena, tailwater depths were set such that tailwater flow intensities were below the threshold of sediment motion. As a consequence, for each run a submerged hydraulic jump formed. Tests were of long durations (of order of days) mainly to achieve conditions of quasi-equilibrium. Based on the data collected, literature approaches are discussed. Then, empirical models are proposed to estimate: (1) the maximum scour depth at the quasi-equilibrium stage and its horizontal distance from edge of stilling basin; (2) the time variation of scour depth; and (3) the axial scour profiles. The proposed equations agree well with experimental data. Findings also highlight that affinity rather than similarity may be the typical property of low-angle eroding jets.

Traditional methods of measuring the profile of a scour hole or bed form have poor temporal resolution and may require the temporary cessation of the flow in order to be executed. These are undesirable characteristics since many hydraulic flows have unsteady water-sediment interfaces that can display considerable differences between their “dynamic” (flow on) and “static” (flow off) states. The present technical note discusses the application of planar laser sheet illumination to the erosion of a cohesionless granular bed due to a planar turbulent wall jet. The measurements allow for the quantitative study of the evolution of the bed in its earliest stages. In some cases an ephemeral bed form is observed to form prior to the development of the main bed form. Additionally, the measurements illustrate the oscillatory nature of the bed form under certain conditions. The experiments therefore demonstrate the great potential of this experimental technique for gaining previously inaccessible information on scour processes.

An experimental study was conducted to investigate the flow field in a rectangular basin with a line inlet and a circular outlet. The basin has a length about four times of the water depth and the outlet level was varied in the study. The flow field in the basin can be characterized into three zones: the wall jet zone with an induced recirculation eddy, the outlet zone in the vicinity of the outlet, and the transition zone in between the two zones. The spreading of the wall jet was found to significantly exceed that of a classical wall jet. In the transition zone, the wall jet separated from the basin bed due to the adverse pressure gradient created by the jet impingement on the outlet wall. Upstream of the outlet, a special three-dimensional balloon-like flow pattern was observed. Within a distance of three times of the outlet diameter, potential flow theory predicts well the measured velocity.