Journal of Hydraulic Engineering

Numerical computations and laboratory experiments are carried out to investigate the three-dimensional structure of large-scale (coherent) vortices induced by bridge abutments on a flat bed. A finite-volume numerical method is developed for solving the unsteady, three-dimensional Reynolds-averaged Navier–Stokes equations, closed with the $k-\omega$ turbulence model, in generalized curvilinear coordinates and applied to study the flow in the vicinity of a typical abutment geometry with a fixed, flat bed. The computed flowfields reveal the presence of multiple, large-scale, unsteady vortices both in the upstream, “quiescent,” region of recirculating fluid and the shear-layer emanating from the edge of the foundation. These computational findings motivated the development of a novel experimental technique for visualizing the footprints of large-scale coherent structures at the free surface. The technique relies on digital photography and employs averaging of instantaneous images over finite-size windows to extract coherent eddies from the chaotic turbulent flow. Application of this technique to several abutment configurations yielded results that support the numerical findings.

The results of a survey aimed at comparing the performances of first-order and total variation diminishing (TVD) second-order upwind flux difference splitting schemes, first-order space-centered schemes, and second-order space-centered schemes with the TVD artificial viscosity term are reported here. The schemes were applied to the following dam-break wave cases: in a dry frictionless horizontal channel; in a dry, rough and sloping channel; and in a nonprismatic channel. Among first-order schemes, the diffusive scheme provides only slightly less accurate results than those obtained by the Roe scheme. For TVD second-order schemes, no significant difference between the upwind scheme and central schemes are reported. In the case of a dam break in a dry frictionless horizontal channel, the second-order schemes were two- to five-fold more accurate than the diffusive scheme and Roe’s scheme. These differences in scheme performances drastically reduce when the results obtained for the rough sloping channel test and for the nonprismatic channel test are analyzed. In particular, the accuracy of the diffusive and Roe’s schemes is similar to second-order schemes when such features of dam break wave, relevant from an engineering viewpoint, like wave peak arrival time and maximum water depths, are considered.

A three-dimensional numerical method, without the hydrostatic assumption, is developed to solve flow problems in hydraulic engineering. This method adopts an unstructured grid technology that is applicable to arbitrarily shaped cells and offers the potential to unify many grid topologies into a single formulation. It solves the three-dimensional turbulent flow equations and utilizes a collocated and cell-centered storage scheme with a finite-volume discretization. In Part I, the technical details of the method are presented, along with its verification and validation by computing a benchmark open channel flow. Meshes of hexahedral, tetrahedral, and prismatic shapes are employed, and results are compared with experimental data and among different meshes. Accuracy estimates and error analyses are also developed and discussed. Our companion paper applies the method to two practical problems: Flow in a hydroturbine draft tube, and flow in the forebay of Rocky Reach Dam for design of a fish passage facility.

A three-dimensional computational method, without the use of hydrostatic assumption, is developed to solve fluid flows for hydraulic applications. Numerical algorithms and verification of the nonhydrostatic model are described in our companion paper. The model employs unstructured grid technology with arbitrarily shaped cells, offering the potential to unify many grid topologies into a single formulation. Herein, the model is applied to two practical steady hydraulic flows to provide further validation of the model and demonstrate its use in practical flows. The flows in a hydroturbine draft tube and in the forebay of Rocky Reach Dam for the fish passage facility design are simulated. Comparisons with experimental data in the former and physical and field measurements in the latter establish the scope of the model.

Numerical or artificial diffusion is the unintentional smoothing of gradients associated with the discretization of the transport equations. In lakes and reservoirs where through-flow is small, the effects of numerical diffusion of mass are cumulative, leading to a progressive weakening of vertical density stratification. This density field misrepresentation precludes accurate, long-term, three-dimensional (3D), hydrodynamic simulations on fixed grids in closed basins with an active thermocline. An ad hoc technique to limit the destratifying effects of numerical diffusion of mass is presented and tested for a 3D, hydrostatic, Z-coordinate numerical model. The technique quantifies the domain-integrated numerical diffusion by assessing the change in the background potential energy $E_b\text{.}$ At each time step, the change in $E_b$ associated with numerical diffusion is calculated, then removed using a sharpening filter applied to each water column. In idealized test cases, the filtering technique is effective in maintaining density stratification over one year while undergoing periodic, large-amplitude forcing by internal waves. Forty-day simulations of Lake Kinneret compared to field measurements demonstrate improved representation of density stratification using the filtering technique.

This technical note presents the results of an experimental study of the erosion of loose cohesionless sand beds by impinging circular water jets with a minimum depth of tailwater. Measurements were made of both the maximum dynamic and static scour depths and the radius of the scour hole. It was found that the dynamic scour depth is about three times that of static scour at the asymptotic state. Dimensional arguments and experimental results are used to show that the main dimensions of the scour hole at the asymptotic state are a function of the densimetric Froude number $F_0^{\prime }=U_0^{\prime }/\sqrt{\mathrm{gD}\Delta \rho /\rho }\text{,}$ where $U_0^{\prime }=\mathrm{velocity}$ of the jet at the original level of the sand bed; $g=\mathrm{acceleration}$ due to gravity; $D=\mathrm{mean}$ diameter of the sand particles; $\rho =\mathrm{density}$ of the eroding fluid; and $\Delta \rho =\mathrm{difference}$ between particle and fluid densities. Useful correlations have been developed to estimate the size of the scour holes. Also included is a comparison between the erosion caused by submerged and unsubmerged impinging circular jets.

This paper describes depositional properties of the fine portion $\left(D<0.075\mathrm{mm}\right)$ of the surficial bed sediments taken from the Upper St. Clair River. The experiments were conducted using the circular flume facility at the Canada Center for Inland Waters in Burlington, Canada. Tests were conducted under the same initial conditions, which involved mechanical mixing following the application of a very high shear stress that resulted in a solids suspension of 200 g/L. Deposition was allowed to occur under five different shear stresses. The deposition rate and the floc size were monitored using a laser based Malvern particle size analyzer. The results were used to estimate the settling velocity as a function of applied shear stress and lapsed time for the selected shear stress.

Application of the finite-volume method in one dimension for open channel flow predictions mandates the direct discretization of integral equations for mass conservation and momentum balance. The integral equations include source terms that account for the forces due to changes in bed elevation and channel width, and an exact expression for these source term integrals is presented for the case of a trapezoidal channel cross section whereby the bed elevation, bottom width, and inverse side slope are defined at cell faces and assumed to vary linearly and uniformly within each cell, consistent with a second-order accurate solution. The expressions may be used in the context of any second-order accurate finite-volume scheme with channel properties defined at cell faces, and it is used here in the context of the Monotone Upwind Scheme for Conservation Laws (MUSCL)-Hancock scheme which has been adopted by many researchers. Using these source term expressions, the MUSCL-Hancock scheme is shown to preserve stationarity, accurately converge to the steady state in a frictionless flow test problem, and perform well in field applications without the need for upwinding procedures previously reported in the literature. For most applications, an approximate, point-wise treatment of the bed slope and nonprismatic source terms can be used instead of the exact expression and, in contrast to reports on other finite-volume-based schemes, will not cause unphysical oscillations in the solution.