Journal of Hydraulic Engineering

A vertical (laterally integrated) two-dimensional numerical model was applied to study the salt water intrusion in the Tanshui River estuarine system, Taiwan. The river system has experienced dramatic changes in the past half century because of human intervention. The construction of two reservoirs and water diversion in the upper reaches of the river system significantly reduces the freshwater inflow. The land subsidence within the Taipei basin and the enlargement of the river constriction at Kuan-Du have lowered the river bed. Both changes have contributed farther to the intrusion of tidal flow and salt water in the upstream direction. The model was reverified with the earliest available hydrographic data measured in 1977. The overall performance of the model is in reasonable agreement with the field data. The model was then used to investigate the change in salt water intrusion as a result of reservoir construction and bathymetric changes in the river system. The model simulation study reveals that significant salinity increases have resulted from the combined changes. It has been speculated by ecological researchers that the long-term increase in salinity might be the driving force altering the aquatic ecosystem structure in the lower reach of the estuary and the Kuan-Du mangrove swamp, particularly the enlargement of the mangrove area and the disappearance of freshwater marshes. However, concrete proof has not been available since no prototype salinity data were available prior to the reservoir construction. This case study offers the first quantitative estimate of the salinity changes due to human interference in this natural system.

Skimming flows in stepped channels are systematically investigated under a wide range of channel slopes (5.7°⩽θ⩽55°). The flow conditions of skimming flows are classified into two flow regimes, and the hydraulic conditions required to form a quasi-uniform flow are determined. An aerated flow depth of a skimming flow is estimated from the assumption that the residual energy at the end of a stepped channel coincides with the energy at the toe of the jump formed immediately downstream of the stepped channel. In a quasi-uniform flow region, the friction factor of skimming flows is represented by the relative step height and the channel slope. The friction factor for the channel slope of θ=19° appears to have a maximum. The residual energy of skimming flows is formulated for both nonuniform and quasi-uniform flow regions. Further, a hydraulic-design chart for a stepped channel is presented.

The well-known Jones formula has long been used to convert a stage hydrograph to a discharge hydrograph under many unsteady flow situations. The logic behind the formula can be explained with the use of the approximate convection–diffusion equation in its development. However, its applicability criterion has not yet been quantified. Assessment of the applicability of the Jones formula is studied herein. In addition, two variations of the Jones formula have been developed: one, incorporating the inertial forces of the one-dimensional momentum equation and the other, incorporating a refined estimate of $\partial y/\partial x\text{,}$ the longitudinal gradient of the water depth, accounting approximately for the parabolic variation of the water surface. The suitability of these three formulas in converting a given hypothetical stage hydrograph to a discharge hydrograph is assessed under varying channel conditions. The study shows, that the Jones formula and its variants developed in this study, indicate a limit of $\left|\right(1/S_0)\partial y/\partial x|<0.5\text{,}$ where, $S_0$ is the bed slope, for their successful application. Further, it is found that the formula developed considering a refined estimate of the longitudinal gradient of the water depth performs better than the other two formulas.

Portable bedload traps (0.3 by 0.2 m opening) were developed for sampling coarse bedload transport in mountain gravel-bed rivers during wadable high flows. The 0.9 m long trailing net can capture about 20 kg of gravel and cobbles. Traps are positioned on ground plates anchored in the streambed to minimize disturbance of the streambed during sampling. This design permits sampling times of up to 1 h, overcoming short-term temporal variability issues. Bedload traps were tested in two streams and appear to collect representative samples of gravel bedload transport. Bedload rating and flow competence curves are well-defined and steeper than those obtained by a Helley–Smith sampler. Rating curves from both samplers differ most at low flow but approach each other near bankfull flow. Critical flow determined from bedload traps is similar using the largest grain and the small transport rate method, suggesting suitability of bedload trap data for incipient motion studies.

A depth-average model using a finite-volume method with boundary-fitted grids has been developed to calculate bed deformation in alluvial channels. The model system consists of an unsteady hydrodynamic module, a sediment transport module and a bed-deformation module. The hydrodynamic module is based on the two-dimensional shallow water equations. The sediment transport module is comprised of semiempirical models of suspended load and nonequilibrium bedload. The bed-deformation module is based on the mass balance for sediment. The secondary flow transport effects are taken into account by adjusting the dimensionless diffusivity coefficient in the depth-average version of the $k-\epsilon$ turbulence model. A quasi-three-dimensional flow approach is used to simulate the effect of secondary flows due to channel curvature on bed-load transport. The effects of bed slope on the rate and direction of bed-load transport are also taken into account. The developed model has been validated by computing the scour hole and the deposition dune produced by a jet discharged into a shallow pool with movable bed. Two further applications of the model are presented in which the bed deformation is calculated in curved alluvial channels under steady- and unsteady-flow conditions. The predictions are compared with data from laboratory measurements. Generally good agreement is obtained.

Experiments of bridge pier scour are carried out under steady and unsteady clear-water scour conditions with uniform and nonuniform sediments. Around the pier nose, the sediment size variation of surface bed materials is investigated, and a regressed formula is obtained for estimating the mixing layer thickness in terms of median sediment size and geometric standard deviation of grain size distribution. A method based on the mixing layer concept is developed for calculating the equilibrium scour depth in nonuniform sediment. Based on the experimental data of scour rate, a model simulating the scour-depth evolution under steady flow in nonuniform sediment is presented. By analyzing experimental data, a scheme is proposed for computing the scour-depth evolution under unsteady flow.

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.

A semianalytical model was developed to predict boundary shear distribution in straight, noncircular ducts and open channels. The model was developed using a simplified streamwise vorticity equation, which involves only secondary Reynolds stress terms. These terms are representative of transverse turbulence anisotropy and nonhomogeneity. Transverse anisotropy is modeled using a universal function. Shear stresses are incorporated into the model by applying the momentum transfer model. An empirical model was employed to calculate the effect of the channel boundary on shear stresses. The final equation was applied to calculate boundary shear distribution in triangular ducts and trapezoidal open channels. The model predictions were well correlated with experimental data.

We analyze the general applicability of a recent explicit expression of the Colebrook–White equation for turbulent flow friction factor calculation. This explicit expression, which is based on the Lambert $W$ function, is characterized by an exponential term which imposes restrictions on its use. These constraints have been expressed in terms of pipe roughness $(\epsilon /D)$ and the Reynolds number R that are required for friction factor calculation. These constraints were determined as $8.0666 \ln \left(R\right)+(\epsilon /D)R<721.97$ and $8.0666 \ln \left(R\right)+(\epsilon /D)R<5731.83\text{,}$ respectively, for machines using single precision and double precision computations. Using the Lambert $W$ function, an explicit equation relating R and $\epsilon /D$ was derived at the limiting case which allowed for a graphical representation of the applicability of the explicit form of the Colebrook–White equation in the R versus $\epsilon /D$ space. Before computing friction factors using the explicit Colebrook–White equation, a quick check must be performed to see if the desired combination of R and $\epsilon /D$ values satisfies the applicable constraint mentioned above.

This study evaluates the use of an acoustic Doppler profiler (ADP) for measurement of velocity profiles over dunes in an estuary. The ADP can be deployed from a moving launch and provides three-dimensional velocity profiles that can be used to describe flow structure and to provide rough estimates of shear stress. Quadratic stress models are recommended for shear stress because they estimate skin friction and form stress whereas the law of the wall only reliably estimates total stress over dunes. The most serious limitation of the ADP is a beam geometry that results in a large sampling diameter close to the bed that does not adequately measure velocity in dune troughs.

Large scale particle image velocimetry (LSPIV) is an extension of quantitative imaging techniques for measurements of water surface velocities using inexpensive standard video equipment. The present Technical Note describes capabilities and limitations of LSPIV for low velocity shallow flows. Measurements in low velocity shallow flume flows were performed to investigate the LSPIV sensitivity to seeding density and time interval between successive images. The results show that the accuracy of the LSPIV technique does not deteriorate as the flow velocity is reduced to as low as 0.015 m/s provided an adequate seeding and suitable time difference between images are selected. The results suggest that LSPIV is well-suited for flow fields with small velocities that are often below the limit of detection of most conventional devices.