Case Study: Bed Resistance of Rhine River during 1998 Flood

Detailed field measurements during the 1998 flood of the Rhine River in The Netherlands show that both Manning n and Darcy–Weisbach friction factor f increase with discharge. The changes in bedform roughness height and friction factors are attributed to the increased dune height during floods. There is a near-peak hysteresis in the dune height measurements. At a given discharge, dunes are significantly larger after than before the peak discharge. The trend is most apparent for the Bovenrijn with weaker variations for the Waal. The methods of Engelund and Vanoni–Hwang provide similar estimates of form drag. When combined with van Rijn’s method to estimate grain resistance, both methods tend to overpredict the measured bed friction factor after the peak discharge. These methods perform best when field bedform measurements are available to estimate form drag. The composite effect of primary and secondary dunes should be considered in the analysis of resistance to flow.     

Maximum Velocity and Regularities in Open-Channel Flow

Maximum velocity in a channel section often occurs below the water surface. Its location is linked to the ratio of the mean and maximum velocities, velocity distribution parameter, location of mean velocity, energy and momentum coefficients, and probability density function underpinning a velocity distribution equation derived by applying the probability and entropy concepts. The mean value of the ratio of the mean and maximum velocities at a given channel section is stable and constant, and invariant with time and discharge. Its relationship with the others in turn leads to formation of a network of related constants that represent regularities in open-channel flows and can be used to ease discharge measurements and other tasks in hydraulic engineering. Under the probability concept, the ratio of mean and maximum velocities being constant means that the probability distribution underpinning the velocity distribution and other related variables is resilient, and that the same probability distribution is governing various phenomena observable at a channel section and explains the regularities in open-channel flows.     

Deconvolution Technique to Separate Signal from Noise in Gravel Bedload Velocity Data

A deconvolution procedure is presented to estimate the probability density function of bedload transport velocity from noisy stationary data collected using the bottom tracking feature of acoustic Doppler current profilers (aDcps). The procedure involves the optimization of a computational summation of random variables for the instrument noise (assumed to be Gaussian with zero mean) and the spatially averaged bedload velocity within the insonified area of each acoustic beam (V). The procedure was tested on two aDcp time series, measured in two different gravel-bed rivers (Fraser River and Norrish Creek). Models generated using either a semitheoretical compound Poisson-gamma distribution or an empirical gamma distribution for V were similar and did not differ significantly from the distribution of the original data. Optimized distributions for V were highly positively skewed. The instrument noise was comparable to instrument noise for aDcp water velocity measurements, i.e., an order of magnitude greater than typical bottom tracking noise. The deconvolution procedure presented herein is generally applicable for the difficult measurement problem of determining the actual signal distribution when measurements are contaminated by noise, particularly for the case of positive-valued signal contaminated by Gaussian noise. The procedure produced the first field estimates of spatially averaged bedload velocity distribution.     

Errors in Acoustic Doppler Profiler Velocity Measurements Caused by Flow Disturbance

Acoustic Doppler current profilers (ADCPs) are commonly used to measure streamflow and water velocities in rivers and streams. This paper presents laboratory, field, and numerical model evidence of errors in ADCP measurements caused by flow disturbance. A state-of-the-art three-dimensional computational fluid dynamic model is validated with and used to complement field and laboratory observations of flow disturbance and its effect on measured velocities. Results show that near the instrument, flow velocities measured by the ADCP are neither the undisturbed stream velocity nor the velocity of the flow field around the ADCP. The velocities measured by the ADCP are biased low due to the downward flow near the upstream face of the ADCP and upward recovering flow in the path of downstream transducer, which violate the flow homogeneity assumption used to transform beam velocities into Cartesian velocity components. The magnitude of the bias is dependent on the deployment configuration, the diameter of the instrument, and the approach velocity, and was observed to range from more than 25% at 5?cm from the transducers to less than 1% at about 50?cm from the transducers for the scenarios simulated.     

Validation of a Three-Dimensional Numerical Code in the Simulation of Pseudo-Natural Meandering Flows

Validation of a three-dimensional finite volume code solving the Navier–Stokes equations with the standard k-ε turbulence model is conducted using a high quality and high spatial resolution data set. The data set was collected from a large-scale meandering channel with a self-formed fixed bed, and comprises detailed bed profiling and laser Doppler anemometer velocity measurements. Comparisons of the computed primary and secondary velocities are made with those observed and it is found that the lateral momentum transfer is generally under predicted. At the apices this results in the predicted position of the primary velocity maximum having a bias towards the channel center, compared to the position where it has been measured. Using a simplified two zone roughness distribution whereby a separate roughness height was prescribed for the channel center and channel sides relative to a single distributed roughness height, generally led to a slightly improved longitudinal velocity distribution; the higher velocities were located nearer to the outside of the bend. Improving both the free surface calculation and scheme for discretization of the convection terms led to no appreciable difference in the computed velocity distributions. A more detailed study involving turbulence measurements and bed form height distribution should discriminate whether using distributed roughness height is a precursor to using an anisotropic turbulence representation for the accurate prediction of three-dimensional river flows.     

End Depth–Discharge Relation at Free Overfall of Trapezoidal Channels

For steady flow near the free overfall (end section) of a horizontal trapezoidal channel, the velocity distribution is nonuniform and the streamlines are curved. An accurate relation between discharge rate and end depth was formulated including these effects. To determine these effects, the streamline pattern in the vertical plane of channel symmetry was determined using measured velocity components and the water surface profile. At the end section, the streamline pattern yielded the streamline curvature, which in turn provided the curvature correction required to predict the true static pressure head profile. The measured static pressure head distribution agreed well with the predicted static pressure head distribution for the end section. The pressure force at the end section was obtained on the basis of the measured static pressure distribution at the end section, and this information yielded a reliable relation between the end depth and the channel discharge rate. Analysis of present and past experimental data indicated that, the pressure head coefficient was the dominant parameter that influences the relationship between discharge rate and end depth in trapezoidal channels. Near the end depth, in the region above the maximum velocity point, the total energy determined from the measured velocity and pressure fields was essentially constant.     

Flood Discharge Prediction using Two-Dimensional Inverse Modeling

A new approach to estimate flood discharges in complex river geometries is presented. Discharges are determined through the combination of nonintrusive measurements of surface velocities and water levels with a Navier–Stokes solver and an inverse optimization algorithm. The numerical model is based on a finite-element solution of the two-dimensional Reynolds-averaged Navier–Stokes equations with a k–ε turbulence model, allowing for computation of the free water surface on adaptive, unstructured grids. The inverse modeling technique uses the Levenberg–Marquardt minimizing algorithm. In order to rule out uncertainties from the numerical model and to strictly quantify the effect of measuring errors, measurements are generated synthetically through forward computations. The methodology is illustrated for the gaging station of the Saltina River at Brig, Switzerland, which involves a complex bed geometry and where laboratory measurements for transcritical flows were available. For perfect measurements the discharge can in principle be estimated to an accuracy of ≈2%, independently of the number of measurements. Measurement errors in the water level have a small influence on the estimated discharge, whereas errors in velocity lead to a major discharge error. This error can be minimized by increasing the number of measurement points and choosing appropriate measurement positions.     

The measurement and prediction of the melt velocities in aturbulent,electromagnetically driven recirculating low melting alloy system

Experimental measurements are reported describing the velocity field in an inductively stirred low melting alloy. The molten metal was held in a cylindrical container, 500 mm high and having an inside diameter of 250 mm; induction stirring was supplied by a three phase coil, which provided a maximum field strength of 350 Gauss (0.035 Wb/m²). The velocities in the melt were measured by a mechanical force reaction probe and were found to range up to about 0.5 m/s. Theoretical prediction of the melt velocities was made by solving Maxwell’s equations, together with the turbulent Navier-Stokes equations, using a digital computer. The experimentally measured and theoretically predicted velocities were found to agree within about 30 pct, thus providing direct experimental proof for the validity of modelling electromagnetically driven flows using this technique.     

Depth-Averaged Velocity Distribution in Straight Trapezoidal Channels

In trapezoidal channels that are not “wide,” the banks exert form drag on the fluid and thereby control the depth-averaged velocity distribution. As such, commonly used equations for predicting depth-averaged velocities in wide channels are not well suited for predicting depth-averaged velocities in trapezoidal channels. Using data from three previous studies, we developed two models for predicting depth-averaged velocity distributions in straight trapezoidal channels. The data used to develop the models had a range of discharges (8.05–4,248?L/s), velocities (0.16–1.03?m/s), bottom widths (0.305–3.62?m), flow depths (0.0518–0.805?m), and bank slopes (1.0–3.0, horizontal/vertical). The first model requires measured velocity data for calibrating the model coefficients, whereas the second model uses prescribed coefficients. The first model yielded velocity distributions with coefficients of determination (r2) from 0.84 to 0.90 and we recommend its use when possible because it yields predictions that are more accurate. The second model also yielded good results (r2 = 0.86 and 94% of the predicted velocities were within 20% of the observed values).     

Calibration Method of Current Meters

This paper presents a rapid method for propeller current meter calibration, enabling calibration of current meters in their actual working conditions using simpler equipment than what is currently used in traditional calibrations, and exploiting the uniform velocity profile present through submerged outflows (e.g., flow nozzles and orifices). Experiments were performed to confirm the fundamental hypothesis of uniform horizontal and vertical velocity distribution downstream of a submerged jet. Two experimental velocities were adopted to determine the calibration curve: one based on the discharge and the outflow area; the other derived from Torricelli’s formula, which relies on the head difference between two reservoir levels. Because a current meter measures local velocity, the influence on the measurements’ reliability as a function of current meter position in the submerged outflow jet was investigated. An uncertainty analysis was also performed, and a comparison of the results with the preexisting calibration lines obtained by towing tank is presented.     

Investigation of Two Elemental Error Sources in Boat-Mounted Acoustic Doppler Current Profiler Measurements by Large Eddy Simulations

Measurements of water discharge and flow velocities in riverine and tidal environments are commonly made with acoustic Doppler current profilers (ADCPs) mounted on a moving boat. This paper presents results of high-resolution Large Eddy simulations (LES) conducted to investigate two elemental error sources in ADCP measurements from a moving boat. One of these errors is due to the flow disturbance induced by the boat-mounted ADCP. The other error is due to the lack of flow homogeneity in horizontal layers assumed by the ADCP algorithm to compute orthogonal velocities from the measured radial velocities along the acoustic beams. The first error is investigated by comparing LES results for an undisturbed flow field with LES results for a flow field disturbed by a boat-mounted ADCP. The second error is investigated by comparing the velocities beneath the ADCP simulated by LES with virtual ADCP velocities, which are obtained by applying the ADCP algorithm to LES velocities data mined along the path of the acoustic beams of the virtual profiler. The distribution of the Reynolds stresses beneath the ADCP estimated with the ADCP algorithm from the virtual ADCP velocity data are also compared with those obtained from the LES solutions for both the undisturbed and ADCP-disturbed flows. Results show that the boat significantly disturbs the flow field and that the disturbed flow field is qualitatively different from the flow fields observed around an isolated ADCP (no boat).     

Experimental Approach to the Hydraulics of Vertical Slot Fishways

The performance of two particular designs of vertical slot fishways for two different slopes was studied in a wide range of discharges. Water depths were measured in almost the whole surface of pools. A linear relation between dimensionless discharge and depth of flow, and the same flow patterns for each design were found. With an acoustic Doppler velocimeter, three-dimensional velocities were measured at several levels in the entire pool to detect the structure of the flow and quantify velocity distribution. Two different regions in flow patterns were found: a direct flow region characterized by maximum velocities; and a recirculation region, defined by low velocities and horizontal eddies. For a given slope, the velocity at any point of the pool (particularly at the slot) may be considered independent of the discharge and constant with the depth. Some suggestions on kinetic turbulent energy are also made.     

Measurement of Fluctuating Pressures on Coarse Bed Material

Bed protections are usually characterized by low-mobility transport conditions and nonequilibrium turbulence profiles. As the present knowledge of the influence of turbulence on stability of cover layer units is minimal, an in-depth investigation was undertaken regarding the influence of turbulence on the stability of rough granular beds. Detailed measurements of (fluctuating) pressures on a bed element are used to evaluate certain concepts that are often used in modeling the entrainment of bed material from hydraulically rough beds. Three pressure transducers are placed in a cube that is part of a rough granular bed under open-channel flow, and velocities are measured using laser Doppler velocimetry. The measurements show that the magnitude of the fluctuating pressure at a certain point of the cube is a function of the exposure relative to the stones upstream of the cube. A quadrant analysis reveals that the drag force is not only directly dependent on the horizontal near-bed velocity, but on the vertical velocity as well. Further, the effect of small-scale eddies shedding from the stone during large-scale increases of longitudinal velocity is shown. The fact that large-scale velocity fluctuations create a large part of the pressure (or force) variance indicates that downstream of a roughness transition these fluctuations have to be taken into account in order to evaluate the stability of the bed.     

Case Study: Particle Velocimetry in a Model of Lake Ogallala

In a case study of Lake Ogallala, a reservoir in central Nebraska, large scale particle tracking velocimetry (LSPTV) is used to measure surface velocities in a physical model of the lake. Knowledge of flow patterns in the lake is essential for predicting the transport of dissolved oxygen (DO). A preliminary comparison with acoustic Doppler velocimetery (ADV) measurements shows that both LSPTV and large scale particle image velocimetry (LSPIV) accurately measure surface velocities. In the present study, LSPTV works better near flow boundaries and in regions with high velocity gradients since smaller sampling areas are possible, and unlike LSPIV measurements, LSPTV measurements are unbiased. Discharges measured at eight different transects using LSPTV were within 6% of the discharge measured with an orifice, the worst correlation occurring where the bathymetry was slightly nonuniform (making application of the 1/7-power law suspect). In the prototype, DO content periodically drops to unacceptable levels throughout most of the Keystone Basin (a subbasin of Lake Ogallala). Predicted flow patterns suggest that low DO problems are exacerbated in regions with low velocities since oxygen consumed by macrophytes during nighttime hours is not quickly replenished.     

Time-Averaged Mixing Behavior of Circular Jet in Counterflow: Velocity and Concentration Measurements

The time-averaged mixing behavior of a circular jet issuing into a counterflow is investigated in the laboratory at a number of jet-to-current velocity ratios between 3 and 15. The velocity field is obtained from laser Doppler anemometry measurements and the mean concentration field of the jet is measured by laser-induced fluorescence. A similarity analysis is performed on the radial profiles of mean velocity at successive streamwise stations. This is achieved by expressing the mean velocities as jet excess velocities over the ambient counterflow. The agreement of data to the similarity profiles suggested by previous studies is discussed. A similarity analysis is also attempted for the radial distributions of mean concentration. Data are presented on the axial growth of the momentum width and the concentration width of the jet in a counterflow.     

Measurement of physical characteristics of bubbles in gas-liquid plumes: Part II. Local properties of turbulent air-water plumes in vertically injected jets

The structural development of air-water bubble plumes during upward injection into a ladle-shaped vessel has been measured under different conditions of air flow rate, orifice diameter, and bath depth. The measured radial profiles of gas fraction at different axial positions in the plume were found to exhibit good similarity, and the distribution of the phases in the plume was correlated to the modified Froude number. Different regions of flow behavior in the plume were identified by changes in bubble frequency, bubble velocity, and bubble pierced length which occur as bubbles rise in the plume. Measurement of bubble velocity indicates that close to the nozzle the motion of the gas phase is strongly affected by the injection velocity; at injection velocities below 41 m/s, the velocity of the bubbles along the centerline exhibits an increase with height, while above, the tendency reverses. High-speed film observations suggest that this effect is related to the nature of gas discharge,i.e., whether the gas discharge produces single bubbles or short jets. In this region of developing flow, measurement of bubble frequency and pierced length indicates that break-up of the discharging bubbles occurs until a nearly constant bubble-size distribution is established in a region of fully developed flow. In this largest zone of the plume the bubbles influence the flow only through buoyancy, and the spectra of bubble pierced length and diameter can be fitted to a log-normal distribution. Close to the bath surface, a third zone of bubble motion behavior is characterized by a faster decrease in bubble velocity as liquid flows radially outward from the plume.     

Two-Phase Analysis of Vertical Sediment-Laden Jets

In this study, we investigated a vertical dilute sediment-laden jet both experimentally and theoretically. First, an instantaneous whole-field velocimetry tool, particle image velocimetry, was applied to measure the sediment and fluid mean and fluctuating velocities of a downward sediment-laden jet at the same time. Subsequently, an analysis was performed based on two-phase conservation equations for both downward and upward jets. The analysis shows that the mean sediment velocity can be taken as the sum of fluid velocity and the settling velocity in both cases. For the downward jets, the decay rate of the centerline sediment concentration increases with the sediment settling velocity while decreases with the initial discharge velocity. The zone of flow establishment for the sediment velocity is found to be longer than that of the fluid. For the upward jets, the maximum rise of the sediment particles and their deposition distribution on the ground were derived theoretically. The predicted results compare well to the experimental data in the literature.     

Flow Patterns in Compound Channels with Vegetated Floodplains

Understanding the hydraulics of flow in a compound channel with vegetated floodplains is very important for determining the stage-discharge curve and for supporting the management of fluvial processes. In this paper, the flow patterns over different types of vegetation, such as tree, shrub, and grass, are described, based on an experimental study. For vegetation on the floodplain, the authors choose plastic grass, duck feathers, and plastic straws as model grass, shrubs, and trees, respectively. A 3D acoustic Doppler velocimeter was used to measure the local flow velocities for different types of vegetation on the floodplain, and the total discharge and flume slope were measured independently. In the cases of nonvegetated floodplains, all measured streamwise velocity distributions followed the logarithmic distribution, but for vegetated floodplains, they followed an S-shaped profile, exhibiting three zones. For all cases, the fluctuating velocity followed a normal distribution. The influence of different types of vegetation on the distributions of the secondary currents, turbulence intensities, and Reynolds shear stresses were also analyzed.     

A stochastic model of leukocyte rolling

Selectin-mediated leukocyte rolling under flow is an important process in leukocyte recruitment during inflammation. The rolling motion of individual cells has been observed to fluctuate randomly both in vivo and in vitro. This paper presents a stochastic model of the micromechanics of cell rolling and provides an analytical method of treating experimental data. For a homogeneous cell population, the velocity distribution is obtained in an analytical form, which is in good agreement with experimentally determined velocity histograms obtained previously. For a heterogeneous cell population, the model provides a simple, analytical method of separating the contributions of temporal fluctuations and population heterogeneity to the variance of measured rolling velocities. The model also links the mean and variance of rolling velocities to the molecular events underlying the observed cellular motion, allowing characterization of the distribution and release rate of the clusters of molecular bonds that tether the cell to substratum. Applying the model to the analysis of data obtained for neutrophils rolling on an E-selectin-coated surface at a wall shear stress of 1.2 dyn/cm2 yields estimations of the average distance between bond clusters (approximately micron) and the average time duration of a bond cluster resisting the applied fluid force (approximately 0.5 s).     

Ultrasonic velocity change with creep damage in copper

We studied the ultrasonic velocity change caused by the accumulative creep damage in polycrystalline pure copper after high-temperature tensile loading. The propagation velocities of bulk waves, longitudinal and shear waves polarized parallel and perpendicular to the stress direction, showed a strong sensitivity to intergranular creep controlled by grain-boundary cavitation and subsequent microcracking. The velocities decreased slowly with creep time up to approximately 60 pct of the lifetime, when the steady creep shifted to the tertiary creep. Beyond this point, they decreased at ever increasing rates until eventual failure. The total velocity changes amounted to several percent of the original velocities. The creep damage also caused velocity anisotropy in the shear waves. Evolution in the anisotropy revealed that formation of cavity arrays, cavity coalescence, and microcracking, which occurred preferentially on boundaries lying normal to the stress axis, were restricted to the last 20 pct of the lifetime. Metallography and measurements of porosity support the ultrasonic observations.