Journal of Hydraulic Engineering

Using the plane mixing layer analogy, a length scale is proposed to normalize velocity profiles for vegetated open channel flows. The new scaling is an improvement over those based on the logarithmic, velocity-defect, and power laws in collapsing the velocity profiles, which include measurements conducted in this study and also those reported in the literature for a variety of flow and vegetation configurations. An eddy viscosity model is also developed to justify the scaling argument. This study is limited to rigid vegetation submerged in depth-limited flows, in which the flow depth is no greater than twice the vegetation height.

This paper presents a model for quantifying the random errors (i.e., variance) of acoustic Doppler current profiler (ADCP) discharge measurements from moving platforms associated with different sampling times. The model focuses on the random processes in the sampled flow field and has been developed using statistical methods that are currently available for the uncertainty analysis of velocity time series. Analysis of field data that were collected using ADCP from moving platforms from three natural rivers of varying sizes and flow conditions shows that, even though the estimate of the integral time scale of the actual turbulent flow field is larger than the sampling interval, the integral time scale of the sampled flow field is in keeping with the sampling interval. Thus, an equation for computing the variance error in discharge measurements associated with different sampling times, assuming uncorrelated flow fields, is appropriate. The approach is used to help define optimal sampling strategies by choosing the exposure time required for ADCPs to accurately measure flow discharge.

Numerical issues for the friction-dominated steady-state Saint-Venant equations with a shock-capturing upwind finite-element scheme are studied using nonuniform-flow test cases and Fourier analysis. The friction-dominated case is a common phenomenon in open channel flow modeling when the depth becomes small compared with the discretization length. In the nonuniform-flow test cases, abrupt slope changes and abrupt roughness changes are introduced, and in the Fourier analysis, a periodic bed perturbation is used. Nondimensional parameter groups identified are as follows: the upwinding coefficient, the number of elements per wavelength, the average-flow Froude number, and the numerical friction number. The results show that errors in both depth and discharge variables are observed whenever there is any perturbation in the bed topography or bed roughness. These errors increase with increasing Froude number and increasing numerical friction number. A combined friction parameter is introduced for practical application. The combined friction parameter can be used to specify minimum depths or to guide mesh refinement. The analysis framework developed can also be used for other numerical schemes.

This study focuses on the double-averaged (DA) turbulence characteristics and the local flow characterization in the flow zones over and within the flow-gravel-bed interface. The cumulative running averaged (CRA) value of a turbulence quantity for a given interval (in this study, half of the gravel size) of flow measurement is the prerequisite to determine a complete DA value of that quantity. The CRA turbulence quantities within the interfacial sublayer require a longer distance to become spatially independent. A method is proposed to fit the log law for the DA velocity over the bed and a polynomial law within the interfacial sublayer. The form-induced shear stress is 40% of the DA Reynolds shear stress occurring at the virtual bed level. The spatial velocity fluctuations diminish more rapidly than the temporal velocity fluctuations below the virtual bed level. In the inertial subrange of turbulent kinetic energy (TKE), the eddy size decreases significantly near the virtual bed level, and in the dissipation range, it increases slightly. The TKE fluxes directed downward and downstream compose the sweep events that are the prevailing mechanism within the interfacial sublayer. It is also confirmed by the quadrant analysis done for the bursting events. The form-induced energy fluxes below the crest level are comparable with the TKE fluxes. In the TKE budget, the form-induced diffusion rate is significant within the interfacial sublayer. The quantities constituting the TKE budget attain their peaks above the virtual bed level and reduce sharply below it. However, the pressure energy diffusion rate induces suction near the crest. The local flow characterization is done by separating the local velocity profiles into log, S-shaped, and accelerated classes. Unlike the velocity profiles per class, the profiles of turbulence quantities per class are almost indistinguishable within the interfacial sublayer. A comparison of the results of this study with those of previous studies shows more dissimilarities than similarities.

To assess the potential for unraveling failure of flow-through rockfill dams, a systematic study of three aspects of the hydraulic design of these structures was conducted. First, the gradient that is most useful in independently computing the height of the point of first flow emergence was established. The proposed method is based on the idea of the angle of the emergent flow field within the toe of the structure. Secondly, as a result, this study presents a method for independently computing the variation in hydraulic head within the vertical that allows the toe of the structure (i.e., downstream from the vertical associated with first flow emergence) to be isolated. This is based in part on a separate parametric study of 24 numerically simulated flow-through rockfill dams. Thirdly, the gradient that allows for the independent estimation of the default tailwater depth is presented and verified, with the help of laboratory results. The hope is that these three computational tools will facilitate the design and assessment of flow-through rockfill structures, as a particular class of pseudohydraulic structure.

Torricelli’s formula is often used to define the dependence of the leak outflow on the flow conditions inside the pipe and on the leak characteristics. Some tests carried out at the Water Engineering Laboratory of the University of Perugia, Italy, show that differences in the leak head-discharge relationships may arise even when the same leak is machined in pipes with the same inner diameter but different thickness and material. These data can still be explained by Torricelli’s formula if the possible variation of the leak area because of the head is considered. When the pipe material behaves in a linear and elastic fashion, the leak area variation with the head is linear, whereas other formulations are needed when elastoplastic or viscoelastic materials are used. As a consequence, this effect can produce different leak head-discharge relationships, depending on the constitutive law and behavior of the pipe material.

An aggregated model to evaluate tsunami response in semienclosed water bodies is presented in this work. The model is based on one-dimensional shallow water equations and can include long-wave external forcing such as a tsunami. It has been successfully validated against experimental data from a physical model, and its predictions for a case study have been compared with results from the Cornell multigrid coupled tsunami (COMCOT) model. The model can be used as a predictive tool because a calibration using a theoretical value for expansion and contraction losses has been performed and differences with the typical calibration are less than 10%, which is considered acceptable. This allows using the model in the absence of measured data, which is very difficult to obtain in case of a tsunami event. A case study for the Gulf of Cádiz (Spain) has been simulated with the COMCOT model. The aggregated model predicted the response for a harbor more accurately than for estuarine systems with tidal flats. Nevertheless, the aggregated model has been demonstrated as a useful general tool to predict the response of semienclosed tidal basins to a tsunami event, and hybrid models coupling advanced models to simulate ocean tsunami propagation with the model presented here would be useful in developing coastal warning alert systems.

A theory of turbulent shear flow over a sand bed is developed, addressing the instability principle of the fluid-granular bed interface leading to the formation of ripples. The Reynolds-averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation are analyzed using a $1/7$-power law of the time-averaged streamwise velocity and treating the curvilinear streamlines by the Boussinesq approximation. The integration of the RANS equations leads to a governing dynamical equation of flow over a mobile bed. A near-bed flow layer of 3.5 times the ripple height is considered being affected by the ripples. The dynamical equation of the mobile sand bed is based on the Exner’s sediment continuity equation in conjunction with the Meyer-Peter and Müller bed-load transport formula as modified to account for the effect of local bed slope attributable to bed forms. The coupled dynamical equations are then analyzed to estimate the parameters for the instability that results in the formation of ripples on the bed. The nondimensional ripple length (ratio of ripple length to sand size) increases with an increase in Shields parameter. The theoretical results have an agreement with the experimental data.

Imperfections of the ISO 4359 standard related to the application of a boundary layer concept for predicting flow rates through rectangular and U-shaped flumes are described in detail. The primary equation for a flume flow chart results from a system of equations consisting of the energy equation and two continuity equations. The first equation requires a different modification of the stream width and depth when the boundary layer concept is applied to all three equations. Additionally, modification of the stream dimensions should refer to the cross section in the throat, where the critical depth occurs, instead of at the very end of the flume throat, as suggested by the ISO 4359 standard. To improve the accuracy of flow rate computations, the critical depth position in Venturi and Palmer-Bowlus flumes was predicted numerically by solving an ordinary differential equation, which describes the water surface profile of steady and gradually varied flow in open channels of prismatic and nonprismatic cross sections. Computing the stream modification for the position of the critical depth in a flume throat resulted in the reduction of the highest relative error of flow prediction for the Palmer-Bowlus flume for an inside sewer diameter $D=0.762\mathrm{m}$ from 3.3 to 0.8%, for $D=0.381\mathrm{m}$ from 3.7 to 1.2%, for $D=0.203\mathrm{m}$ from 4.3 to 3.2%, and for $D=0.102\mathrm{m}$ from 5.2 to 3.5%. In addition, a simple algebraic equation for calculating the critical depth position in Venturi flumes was developed. Calculation of the stream modification in the cross section of a flume throat in which the critical depth occurs was proved to improve the accuracy of flow rate computations both for Venturi and for Palmer-Bowlus flumes. However, for the latter type of flume, no such simple algebraic equation for the position of critical depth could be developed successfully. In this case, still some improvements of flow rate calculations could be achieved by modifying the stream dimensions as described by ISO 4359 but for the middle of the throat rather than at its end.