Journal of Hydraulic Engineering

Several formulas are theoretically and empirically proposed for the alternate bar wavelength. These formulas are tested with laboratory data presented herein and those reported by other workers. It is found that one formula derived in terms of bar stability analysis is invalid for $F\geqq 0.8;$ an alternative empirical formula which is valid for $F\geqq 0.8$ is proposed. A new formula on the bar height is also obtained empirically on the basis of laboratory data. These formulas are applied to an actual river, and are shown to be reasonable in predicting the bar wavelength and bar height. The possible errors of prediction are estimated to be within about $+80\%$ and $-40\%$ for both formulas.

An appropriate oscillatory velocity profile is developed from existing experimental data in an oscillating bed, a wave flume, and a water tunnel. The velocity profile is then used to determine the boundary layer thickness, the shear stress profile, the friction factor, and the eddy viscosity profile. It is found that there are differences between an oscillating bed and an oscillating fluid which contradicts the old belief that they are the same. The thickness of the boundary layer depends upon the flow Reynolds number. The friction factor of the three‐dimensional bed is about 10‐20% higher than that of the two‐dimensional bed. The eddy viscosity profile is expressed explicitly as a function of the friction factor, velocity profile parameters, and the phase profile parameter.

The results of some experiments are reported concerning the boundary shear stress and boundary shear force distributions in a smooth channel of rectangular cross section. An empirically derived equation is presented which gives the percentage of the total shear force carried by the walls as a function of the breadth/depth ratio. Ancillary equations are presented giving the mean wall, bed, and bed center line shear stresses as functions of aspect ratio. A comparison is made between boundary shear stress distributions in open channel and closed conduit flows at comparable aspect ratios. Certain differences are noted in both the distributions and the mean resistance coefficients on account of different secondary flow structure. The results will be useful to those engaged in resistance, sediment, or dispersion studies.

An experimental study motivated by dimensional analysis was carried out to investigate the variation in the transverse mixing coefficient in straight, rectangular, smooth, and rough open channel flows. The findings have led to a number of suggestions relating to the future laboratory simulations of prototype cooling‐water or wastewater dispersion in a river.

The hydrodynamics of recharge mounds that develop on an inclined water table beneath a strip recharge basin are considered. The nonlinear potential (NLP) theory is used to predict the motion of the water table resulting from the recharge operation. The theoretical derivation of the NLP theory uses the saturated flow equations for a homogeneous isotropic medium. Solutions to the NLP theory for recharge to an inclined water table are obtained by using a finite difference method. A few examples of flow patterns showing the motion of the recharged and native water are given. The mathematical model can be utilized to predict the response and movement of recharged water in the design and operation of recharge facilities.

The finite element method based on the classical Galerkin formulation produces very poor results when applied to discontinuous channel flow. A variance of the Galerkin method is proposed that exhibits highly selective damping characteristics. The dissipation affects only the numerically‐generated high‐frequency parasitic waves, while maintaining remarkable accuracy in the approximation to the true solution of the problem. In fact, it is shown that the phase error of the finite element simulation is improved by the introduction of dissipation. The resulting model is second‐order accurate with respect to the time step and produces a clean, sharp jump structure that agrees favorably with the exact solution of some test problems. The method is based on discontinuous weighting functions that produce “upwind” effects but at the same time maintain the accuracy of a central difference scheme. The dissipation level is selected by analytical investigations, so that the numerical error is minimized. No second‐order pseudo viscosity terms are required, which relaxes the interelement continuity conditions and results in a very simple and inexpensive scheme.

In order to clarify the role of sand bed instability mechanism and the significance of linear instability analysis, which has been one of the most interesting subjects of alluvial hydraulics, sand bed instability analysis of a Fourier transformed version was devised by coupling with the stochastic model for bed load motion, and the theoretical prediction for sand wave development was compared with some experiments. In the laboratory, sand wave development from an initially flattened bed was experimentally investigated by using the time variation of wave number spectrum of sand bed. These investigations clarified that an instability mechanism brought about a wave selection process from initially formed bed disturbance due to random motion of bed load particles, and particularly that waves, to satisfy the Airy relation, became dominant through the mechanism of bed instability. The latter fact is a characteristic of sand wave development in open channel, and it has been also certified by experiments without a water surface.

The flow considered herein is a two‐dimensional negatively buoyant flow from a shallow channel over a sloping bottom (mild or steep) into a well‐mixed reservoir. For the analysis, a set of integral equations, in particular the equations of conservation of mass and volume, and the momentum equation, are employed. This study is concerned with the analysis of the plunging phenomenon and is directed towards prediction of the depth at the plunge point in terms of the essential independent parameters governing the problem. These predictions include the inflow densimetric Froude number, ${\mathbf{F}}_D\text{,}$ the initial mixing rate, γ, the bed slope, S, and the total friction coefficient, $f_t\text{.}$ The equations for plunging depth presented in this study agree well with available laboratory and field data.

Salient features of a method to compute turbulent flows in closed and open channels using the $k‐\epsilon$ turbulence model are reviewed. An experimental study to verify the method is described which concludes that the method is capable of predicting the fully‐developed distributions of the time‐averaged velocity component in the longitudinal direction and the shear stress in two‐dimensional, uniform channel flows accurately. The turbulence regime of the flows tested varies from transitional turbulence to fully‐developed turbulence for free‐surface flows and from hydraulically smooth turbulence to transitional turbulence for flows with top cover.

Standard methods for computing backwater at width constrictions of flood plains severely underestimate backwater when the flood plain is wide and heavily vegetated. The energy‐loss term for the approach reach upstream from a constriction depends on the average streamline length in the reach. In standard one‐dimensional step‐backwater procedures, this average streamline length is approximated by the length of the approach reach. Calculation of energy loss in the approach reach can be improved if a more accurate estimate of the average streamline length is used. Potential‐flow streamlines are a reasonable approximation to physical streamlines for convergent flow outside the boundary layer if flood‐plain depth and roughness are fairly uniform. In this paper, potential flow through an eccentric, normal constriction of zero thickness in an infinitely long, straight channel of constant width and unit depth is studied by use of a Schwarz‐Christoffel transformation. The transformation is integrated by a direct approach. Parametric equations for streamlines are obtained and used to compute an average streamline length for a potential‐flow field.

TWO recently developed analytical approaches to a description of the fully developed flow and bed topography in alluvial channel bends are extended to include a description of the development of the flow and bed topography in the initial portion of bends. The approaches have been verified by tests in a laboratory‐channel bend. The results of the study show that the bed topography develops and decays over a much shorter distance than does the velocity profile. The eccentricity of the centers of volume flux appears to oscillate along the channel with a period that is comparable to that predicted by a meander theory. The analyses are limited to the central portion of the channel cross section, where bank effects are negligible.

The basic continuity equation, as it appears in liquid hammer problems, in terms of velocity, and pressure or piezometric head is examined. The term involving the slope of the pipeline is logically removed from the equation to resolve a long-standing troublesome issue in numerical solutions.