Journal of Hydraulic Engineering

Existing bed-load transport formulas may overestimate the transport rate in mountain rivers by two orders of magnitude or more. Recently published field data sets provide an opportunity to take a fresh look at the bed-load transport relationship and it is hypothesized that the overestimate is due to a failure to account for the effect of a coarse surface layer of bed material inhibiting the release of fine subsurface material. Bed-load transport is determined as $g_s=a\rho (q-q_c)$ where $q$ =water discharge per unit width; $q_c$ =critical value for initiation of bed material movement; $\rho$ =water density; and $a$ =coefficient. The $g_s∕q$ relationship is typically piecewise linear, characterized by two transport phases with, respectively, low and high rates of change. Twenty-one flume and 25 field data sets were used to quantify the relationship for Phase 2. The flume data confirm the dependence of $a$ on $S^{1.5}$ , where $S$ =channel slope, in agreement with earlier studies. The field data additionally show that $a$ varies inversely with the degree of bed armoring, given by the ratio of surface to subsurface bed material size. The finding is consistent with the hypothesis and suggests the need to account for the bed material supply limitation in the bed-load transport formula. However, the available data are not entirely sufficient to rule out an alternative dependency, or codependency, on flow resistance. The critical conditions for initiation of Phase 2 transport are also quantified as a function of bed material size and channel slope. The resulting set of equations allows a more accurate estimation of Phase 2 bed-load transport rates. However, the equations are empirical and should be restricted for use within the range of conditions used in their development, to determine mean rather than instantaneous transport rates and to determine bulk transport rates, not transport by size fraction.

This paper presents the application of hydrostatic and nonhydrostatic three-dimensional hydrodynamic models to a stratified lake. Focus was given to the multiscale response of the internal wave field to strong wind gusts exceeding $20\mathrm{m}{\mathrm{s}}^{-1}$ . Simulations were performed using different horizontal grid resolutions with uniform grid sizes varying from $100\times 100$ to $10\times 10\mathrm{m}$ . Results of the hydrostatic models were used to investigate the large-scale features of the internal wave motion. With the intent of investigating the high-frequency waves, observed results of these simulations were used as initial conditions for nonhydrostatic simulations using smaller grids. Wavelength of the high frequency waves decreased with grid resolution. However, none of the uniform grids were sufficiently fine to capture the waves of the highest frequency. Simulations performed using a nonuniform grid produced internal waves of similar frequency of the waves observed in the field. The simulations showed that these waves were shear unstable modes and that their vertical and horizontal length scales were in close agreement with results from linear stability analysis.

Theoretical predictions of wall shear stresses in unsteady turbulent flows in pipes are developed for all flow conditions from fully smooth to fully rough and for Reynolds numbers from ${10}^3$ to ${10}^8$ . A weighting function approach is used, based on a two-region viscosity distribution in the pipe cross section that is consistent with the Colebrook–White expression for steady-state wall friction. The basic model is developed in an analytical form and the resulting weighting function is then approximated as a sum of exponentials using a modified form of an approximation due to Trikha. A straightforward method is presented for the determination of appropriate values of coefficients for any particular Reynolds number and pipe roughness ratio. The end result is a method that can be used relatively easily by analysts seeking to model unsteady flows in pipes and ducts.

Extensive studies on the temporal evolution of scour were recently conducted at Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie VAW, ETH Zürich, Switzerland, along with a computational model for the scour depth estimation. The VAW scour data are revisited in the present study to present a further refinement. Additional experiments conducted on the scour entrainment at piers, at rectangular and sloping abutments, as well as at singular and multiple spur dikes are reported. A general criterion is proposed to determine the densimetric particle Froude number for scour entrainment. A new relationship for the temporal scour evolution at bridge foundation elements is then developed based on the similitude of Froude by relating the scour depth to the difference between the actual and the entrainment densimetric particle Froude numbers. The new relationship is validated by the complete VAW scour data set, and verified by the available literature data. The combination of sediment characteristics, approach flow velocity, and obstruction geometry leading to an end scour are identified and a relationship is proposed for determining the corresponding time scale. The limitations of the present work are outlined.

The scour process downstream of block ramps is an important research topic of value to engineering practice. The object of the present experimental study is to examine the scour mechanism in order to predict the main geometrical parameters of the scour hole downstream of block ramps. The investigations have been conducted using two physical models located in the hydraulic laboratory of the Department of Civil Engineering in Pisa, Italy. Sediments with different values of the nonuniformity parameter were used as channel bed material. Moreover, different ramp slopes, ranging from 1/4 to 1/12, were tested. Equations and graphs demonstrate that the results can be interpreted by means of simple relationships in the case in which a ridge is present downstream of the scour hole.

Using a variable parameter Muskingum method, a procedure for discharge hydrograph routing in prismatic channels considering downstream effects is presented. The method involves a two step process: (1) a given routing reach is divided into a number of subreaches with each subreach having a representative unique stage–discharge relationship established by using a gradually varied flow profile estimation technique; and (2) the routing of a given inflow hydrograph through these subreaches successively using the variable parameter Muskingum method with parameter variation achieved using the established stage–discharge relationships pertinent to the subreaches and the assumptions of the routing method. The ability of this procedure to route floods accounting for downstream effects is demonstrated by routing a given hypothetical inflow hydrograph in three rectangular channels each with a reach length of $40\mathrm{km}$ , and for two different scenarios of downstream boundary conditions, one resulting in an M1 profile and another in an M2 profile with the control at the end of the $40\mathrm{km}$ reach. The M1 profile is formed due to the prescribed boundary condition at the outlet of the reach that the flow depth at that section is equal to twice the normal depth in the channel reach. The M2 profile is formed due to a free fall located at the outlet of the reach. The routing results obtained using this procedure are compared with the corresponding Saint-Venant solutions arrived at using the U.S. National Weather Service’s DAMBRK model, which is used as a benchmark. The performance of this discharge routing procedure compares well with the corresponding DAMBRK model solutions subject to the criterion $\mid (1∕S_0)\partial y∕\partial x\mid <1$ being satisfied.

Technical note discusses a detailed approach to dimensional analysis for the bridge pier scour phenomenon and the introduction of flow intensity. It demonstrates the dependence of critical upstream velocity on the rest of the parameters describing the process and its implications on dimensional analysis. Assuming that the viscous effects are negligible in the local scour phenomenon, it is concluded that the flow intensity of the approaching undisturbed flow is not an adequate parameter to describe the process in usual laboratory conditions. A new proposal is established.

The results of an experimental investigation of riprap stability at wing-wall abutments are reported. The aim of the experiments was the determination of the size of riprap stones necessary to resist shear failure by the flow. The results, which were obtained under a wide range of mobile-bed conditions, are compared with predictions of riprap stone size given by existing equations. Two existing methods, with the addition of suitable factors of safety, are shown to give stable stone size for riprap layers at wing-wall abutments under mobile-bed conditions. It is noted that consideration needs also to be given to filter protection, edge effects, and the effects of bed-form undermining in the design of such riprap layers.

Despite advances in computing technology and derivation of explicit approximation formulas, the experimentally verified and widely applicable Colebrook–White friction factor formula is often rejected in favor of the limited and less accurate Hazen–Williams equation. The general reluctance of practicing engineers to embrace the Colebrook–White formula may be due to the relatively large available database for Hazen–Williams $C$ coefficient values versus a relatively small database of the equivalent sand roughness $k_s$ values required by the Colebrook–White equation. Until now, converting $C$ to $k_s$ required knowledge of both the Reynolds number and pipe diameter originally used to determine $C$ . The current effort derives implicit equations relating $C$ to $k_s$ that do not require additional information and compare well with published data. The exact solution is approximated with a single explicit equation, accurate to within 4% error.

Transient tests can be reliably used for the diagnosis of pressurized pipe systems. As a matter of fact, the pressure signals acquired during these tests can reveal the presence of anomalies, e.g., leaks, since any irregularity in the pipe gives rise to reflected waves which in turn create discontinuities in the observed signal at the measurement section. In order to make the most of the interpretation of the pressure signals, as well as to improve the effectiveness of the location of leaks, wavelet analysis—a powerful tool within the realm of harmonic analysis—can be used. It aids in the diagnosis of pressure pipe systems by better exposing pressure signal discontinuities and precisely determining the arrival time of the pressure waves reflected by leaks, thus locating the leak itself. Since many wavelet transforms are available and the choice is driven by the specific application, both continuous and discrete wavelet transforms are considered in the paper, comparing different mother wavelets. Then the reliability of the technique with respect to the noise effects is tested on numerically simulated and experimental pressure signals. Specifically, it is shown that the wavelet analysis of numerical signals, with and without superimposed white noise, facilitates testing the ability of this tool to recognize small step variation—corresponding to small leaks—using low cost transducers.