Peter M. Steffler

Structure of flow in hydraulic jumps

A high-speed photographic study was made of the hydraulic jump. It was found that the surface roller was made up of several vortices. These vortices are generated in the early part of the jump and travel downstream. As they move downstream, they grow by pairing. At the same time, water spills down the steepened surface to replenish the toe and subsequently is rolled up into new vortices. A Fourier analysis of the time series of the toe position indicates a cyclic mechanism, the frequencies of which appear to scale with the upstream velocity and downstream depth.

LDA study of flow structure in submerged hydraulic jump

This paper presents the results of a Laser Doppler Anemometry (LDA) study of submerged hydraulic jumps in a horizontal rectangular channel of constant width with the submergence factor S varying approximately from 0.20 to 1.70 and inlet Froude number Fx approximately equal to 3.0, 5.5 and 8JX Measurements include surface profiles, mean velocity components of u and v, turbulence shear stress and turbulence intensities Major flow characteristics of submerged hydraulic jumps are discussed and analyzed. The flow in the fully developed region is found to have some degree of similarity. It is also found that a submerged jump is three dimensional in nature.

Depth averaged and moment equations for moderately shallow free surface flow

The classical depth averaged St. Venant equations for shallow free surface flow are extended to treat problems with nonhydroslatic pressure and nonuniform velocity distributions. The equations required to solve for the additional degrees of freedom are derived by a moment weighted residual method from the fundamental Reynolds equations. The new equations are derived in detail in one horizontal dimension and evaluated for the basic problems of uniform flow and small amplitude waves. With further study and application, these new equations may offer a means for obtaining greater detail over a wider range of problems than is presently practical.

A numerical study of submerged hydraulic jumps

A standard two-dimensional k-e turbulence model is used to predict the mean flow and turbulence characteristics of submerged hydraulic jumps. An offset control volume method is developed to facilitate computation of the variable free surface. The numerical predictions are compared with experimental measurements under three conditions with supercritical Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Finally the numerical performance is evaluated and discussed in detail. It is concluded that the model is adequate for predicting the surface profile, mean velocity field and to some extent, the turbulence structure of submerged hydraulic jumps.

Two-dimensional depth-averaged modeling of flow in curved open channels

The application of the depth-averaged De St. Venant equations for open channel numerical models dictate the adoption of hydrostatic pressure distribution. They are thus applicable to cases where vertical details are not significant. The alternative two-dimensional vertically averaged and moment equations model, in which more vertical details are accounted for, is used to analyze problems involved in curved channels of various curvature. The distribution of horizontal velocity components is assumed to be linear, while the vertical velocity and pressure is quadratic. The implicit Petrov-Galerkin finite element scheme is used in these simulations. Computed values for water surface profile, depth-averaged longitudinal and transverse velocities across the channel width and vertical profiles of longitudinal and transverse velocities are compared with experimental data. The comparison shows a good agreement between the simulated results and experimental data. In addition, this study recommends the supplement of the standard conventional De St. Venant model by the proposed model on simulating strongly curved flows. Finally, the use of refined finite element meshes is recommended only when some of the details near the channel edges are sought.

An experimental study of very high velocity circular water jets in air

This paper presents the results of an experimental study on the characteristics of very high velocity water jets in air. Based on a LDA study of the velocity field of jets of diameters of 2,2.5 and 3 mm with nozzle velocities in the range of 85 to 160 m/s, it was found that these very high velocity jets interact vigourously with the surrounding air and diffuse very much like submerged turbulent jets, but at a smaller rate. The velocity profiles at different axial distances were found to be approximately similar. The decay of the maximum axial velocity in terms of the nozzle velocity, with the relative distance from the nozzle was obtained. These jets were found to grow at a rate equal to approximately one-fourth that of submerged turbulent jets.

Two dimensional vertically averaged and moment equations for rapidly varied flows

The classical depth averaged De St. Venant equations, which are used for most of the computational models in open channels, are based on the fundamental assumptions of uniform velocity and hydrostatic pressure distributions. They are thus limited in their applicability to cases where vertical details are not of importance. Alternative two-dimensional vertically averaged and moment equations are developed, by a moment weighted residual method from the fundamental 3D Reynolds equations, to account for problems where more vertical details are significant and essential. The proposed model is applied to rapidly varied flow problems involved in open channel flow. These problems include flow in channel transitions with rapid contraction and/or expansion and flow over a hemispherical hump. Linear distribution shapes are proposed for the horizontal velocity components, while quadratic distribution shapes are considered for vertical velocity and pressure. The implicit Petrov-Galerkin finite element scheme is used in these simulations. A good agreement is attained. In addition, the obtained results show that more details are gained and the flow is better represented by the proposed model compared to the classical De St. Venant model.

Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.

Air Movement Induced by Water Flow with a Hydraulic Jump in Changing Slope Pipes

AbstractThis paper presents experimental and numerical results of air movement in sewer pipes. Both the airflow in a straight pipe and pipes with changing slopes were studied. The result from the straight-pipe model suggests that the air pressure gradient is built up in the pipe even when it is kept at atmospheric pressure at both ends. The combined effects of water drag and the pressure gradient were analyzed. A general method for estimating the airflow rate was proposed. Further, physical and numerical experiments were performed on air movement induced by water flow with a hydraulic jump in pipes with a changing slope. The ratios of air and water flow rates were found to be substantially higher than published values because of different air transportation mechanisms. The rough surface and air/water bubbly flow in the roller of the hydraulic jump can affect the momentum flux of the air phase, and this additional momentum needs to be incorporated in airflow modeling.

Effect of Friction on Spurious Oscillations in Open Channel Modeling with Variable Bathymetry or Roughness

AbstractNumerical 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 practi...