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In open channel flows, a hydraulic jump is a rapid shift from a supercritical flow to a subcritical flow with a sharp rise in the elevation of the free surface, which is associated with strong energy dissipation, air entrainment, and spray. The present research aims to investigate the air–water flow properties in a hydraulic jump on rough pebbled bed. A range of discharges from 0.06 to 0.1 m3/s, corresponding to inflow Froude numbers Fr1 between 1.7 and 2.84 and Reynolds numbers Re1 from 140,000 to 220,000 were considered. The basic parameters of two-phase flow such as the void fraction and bubble count rate are presented. Close to the jump toe, the mean void fraction on rough bed was larger than on smooth bed, while farther downstream larger magnitudes were observed on smooth bed. No significant difference was observed between rough and smooth beds in terms of the maximum void fraction. In the turbulent shear layer, the bubble count rate was comparatively larger on rough bed than on smooth bed, while the longitudinal distribution decayed for both bed configurations.

In this study, the problem of surface waves induced by water flow in a flow channel was investigated. The mathematical model based on the potential wave theory was established, and a new analytic solution to the corresponding initial and boundary value problem was proposed. To confirm our analytic solution, the mathematical model was applied to simulate experiments conducted in a flow channel in the laboratory. Using our analytic solution, water surface elevations and flow velocities at certain locations in the channel were compared with experimental results. Comparisons between our analytic solution and experimental results confirmed our theory that amplitudes and propagating phases are in very close agreement. Our analytic solution can be used to calculate variations in pressure and velocity along the water depth, which are expensive to calibrate and obtain in experiments. Although our analytic solution was established based on linear theory, it is very practical for applications studying the basic properties of surface elevation, velocity, and pressure of the flow field induced by water current both in space and time.

Hydraulic structures are man-made waterworks interacting with the rainfall run-off to store and convey water, or mitigate the impact of run-off. Current approaches in hydraulic structure design ten...

The Authors developed an interesting discussion on measurements in highly-unsteady transient free-surface flows. Using the dam break wave propagation on a dry bed as an example, they discussed the ...

A positive surge is an unsteady open channel flow motion characterised by a sudden rise in water surface elevation. The literature is focused primarily on rectangular channels. Herein, the free-surface features of positive surges propagating upstream were investigated in an asymmetrical canal. The surge propagation was a three-dimensional unsteady flow motion, resulting in a complicated transient secondary motion compared to positive surge propagating in rectangular canals. The present results may be relevant to surge propagation in man-made trapezoidal canals and natural irregular-shaped channels.

On a stepped spillway, the staircase invert profile generates some intense turbulent dissipation during the spill, associated with a significant reduction of kinetic energy, as well as strong self-aeration. The present study focused on the effects of inclined downward steps on the air-water flow properties, flow resistance, and head losses because these mostly relate to spillway design. Some physical modeling was conducted in a relatively large facility with a 45° stepped chute (1V:1H) operating with Reynolds numbers 2.8×103

The characterization of high-velocity air–water flows is crucial for the design of hydraulic structures including stepped spillways. Recent experimental advances have shown that LIDAR technology ca...

In free-surface flows, the interactions between high-velocity liquid and atmosphere may lead to strong gas-liquid mixing and complex multiphase flow interactions. In this study, the void fraction power spectrum density (PSD) is used to provide an alternative view of the air-water flow composition. The high frequency range of the PSD curve reflects contributions of small chord times, while the low frequency range contains contributions of both small and large chord times. Likewise, the interactions between the smallest bubbles contribute approximately uniformly to the entire frequency range of the spectrum, while any interaction involving large bubbles/drops will be modulated by 1/f2. It is shown that the void fraction spectra are a powerful tool in providing an alternative view of the air-water flow composition.

Although waterway connectivity is a requirement for all freshwater fish, culverts have had negative impacts on freshwater river ecology. Following a recent biological study suggesting that ...

Unimpeded waterway connectivity is a requirement for all freshwater fish. While box culverts are considered the most effective design in terms of upstream fish passage, circular culverts ar...

Waters flowing over rounded weirs experience a rapidly accelerated flow region near the crest. The head-discharge relationship of a half-round crested weir was tested physically under caref...

A tidal bore is a compressive wave, advancing upstream in an estuary when the flood tidal flow starts. It is observed when a macro-tidal flood flow enters the funnel shaped river mouth with shallow waters. Its upriver propagation impacts the natural system, with sediment scouring and suspension. The tidal bores of the Garonne and Selune Rivers in France were extensively investigated between 2010 and 2016. Instantaneous velocity measurements were conducted continuously at high-frequency (50 to 200 Hz) during each bore event. In the Garonne River, instantaneous sediment concentration data were obtained and the sediment properties were systematically tested. The nature of the observations was comprehensive, regrouping hydrodynamics and turbulence, sedimentology and suspended sediment transport. The key outcomes show that the tidal bore occurrence has a marked effect on the velocity field and suspended sediment processes, including a sudden flow deceleration and flow reversal during the bore passage. The turbulent Reynolds stresses present large instantaneous amplitudes, with rapid fluctuations, during the tidal bore. The sediment flux data imply considerable mass transport rates during the first hour of flood tide. This unique review of field data further shows a number of common features, as well as the uniqueness of each individual event.

Decelerating bores are commonly seen in shorelines, estuaries and rivers in forms of swash run-up, tidal bores, tsunami bores. A decelerating bore propagating upstream can gradually change its shap...

Stepped chutes are built to provide safe flood passage in dams. The steps are associated with strong turbulence generation, which allow air to be entrained from the free surface. The present work a...

A tidal bore is a natural estuarine phenomenon forming a positive surge in a funnel-shaped river mouth during the early flood tide under spring tide conditions and low freshwater levels. The bore p...

Road crossings and culverts are common man-made structures along river courses, ranging from national highways to rural roads and urban networks. Present expertise in culvert hydraulic design is deficient because many empirically-based guidelines are often inadequate for fish passage. This project focused on the development of simple solutions for box culverts, with the aim to maximise slow flow regions suitable for small-bodied fish passage and to minimise the reduction in discharge capacity. Herein a physical study of box culvert was performed under controlled flow conditions, and seven designs were tested. In all the cases, the turbulence of the flowing waters was used to assist with fish migration. One baffle configuration presented promising results: i.e., small corner baffles. The triangular baffle system produced little additional afflux, while creating excellent recirculations both upstream and downstream of each baffle. Another configuration was based upon a rough bed and sidewall, enhancing secondary currents and recirculation in the corner region. This resulted in flow conditions that could be potentially used to enhance small-bodied fish passage, though further experiments involving detailed fish behaviour study are required for quantitative guidelines.

Hydraulic jumps are induced in hydraulic facilities for the purposes of energy dissipation or flow aeration. Presently there is no means for a simple estimate of void fraction distribution and air entrainment flux, without detailed physical modelling. This paper presents a semi-theoretical model to simulate the void fraction and velocity distributions in hydraulic jumps characterized by partially-developed inflow conditions. Relationships were established between the inflow Froude number, jump roller length and key parameters that determine the full expression of void fraction and velocity profiles. The proposed model enables accurate prediction of void fraction, longitudinal velocity, and air flux using the inflow Froude number. The results indicated considerable air flux contribution of free-surface aeration, in addition to the singular air entrainment at the jump toe, for moderate to large Froude numbers. A Froude number between 8 and 9 tended to achieve highest aeration rate with maximum total air flux in the roller.

In open channel flows, the transition from a rapid to fluvial flow motion is called a hydraulic jump. A related flow motion is a compression wave in a channel, such as a tidal bore or surge. A key feature of hydraulic jumps and breaking bores is the rapid spatial and temporal deformations of the free surface of the roller region, in response to the interactions between entrained air bubbles and turbulent structures. The flow structure in the roller remains a great research challenge due to large quantities of entrained air, bubble–turbulence interactions and the coupling between turbulent properties and free-surface deformations. Breaking bores and hydraulic jumps with a marked roller present a number of similar features that are discussed herein. Recent results have shown that the roller is a highly unsteady turbulent region, with both the roller toe and free surface constantly fluctuating with time and space, although the roller shape is quasi-two-dimensional on average. Downstream of the roller toe, air bubbles and vorticity are diffused in the shear zone at different rates. The double diffusive convection process leads to a complex interplay between instantaneous free-surface deformations, velocity fluctuations and interfacial processes including breakup and coalescence.

A tidal bore is a hydrodynamic shock, surging upstream in some shallow-water bays and estuaries during the flood tide under large tidal range. This study investigates experimentally the propagation of tidal bores over a large cylindrical roughness element, representative of damaged bridge pier foundation. In the initially steady flow, the large cylindrical element generated a wake region, with extents comparable to steady flow literature. During the tidal bore propagation, the presence of the element had negligible effect on the free-surface properties, but a significant impact in terms of the instantaneous velocity and Reynolds stresses. This resulted in longer transient recirculation both upstream and downstream of the element and larger maximum velocity recirculation magnitudes, as well as enhanced turbulent stress levels and potential bed erosion around the large element, within two diameters from the element centre. The results showed the potential development of a large scour hole around the cylindrical element.

A breaking bore is a highly unsteady turbulent motion that may affect both riverine and estuarine systems. Like many steady turbulent flows, the turbulent motion is dominated by intense coherent structure and turbulent event activities. A novel analysis of unsteady turbulent events is developed for transient breaking bores in which turbulent bursting events are defined in terms of the instantaneous relative turbulent flux. Using new physical data collected in a large facility under controlled flow conditions, the data analysis is applied to a breaking bore. The unsteady event data show some intense bursting during the flow deceleration associated with the bore passage. The results indicate that a turbulent event analysis may deliver valuable quantitative details into the turbulent bursts beneath bores, with applications relevant to turbulent mixing and sedimentary processes.

Standard box-culvert designs are similar to ancient designs. The acknowledgment of the ecological impact of culverts and road crossings on rivers has led to changes in culvert design guidel...

Hydraulic jumps are characterized by strong flow turbulence, flow aeration, and three-dimensional flow motions. Whereas comprehensive research into hydraulic jumps on smooth bed has improve...

A tidal bore is an unsteady rapidly-varied open channel flow generated by the swift advance of the early flood tide in a funnel-shaped river estuary when the tidal range exceeds 4.5 to 6 m. This contribution presents a detailed field investigation conducted on the tidal bore of the Garonne River (France). The bore was undular and the bore's leading edge was followed by well-defined secondary waves, or whelps. The instantaneous ADV velocity data indicated large and rapid fluctuations of all velocity components during the tidal bore. Large Reynolds shear stresses were observed during and after the tidal bore passage. The investigation characterized some unusual transient turbulence caused by the bore propagation in a large river system, and the results suggested the advection of large-scale eddies in the wake of the bore front. The present study highlighted the need for detailed field measurements with fine temporal resolution, to characterize the highly unsteady rapidly-varied nature of tidal bore ...

In an estuary, a tidal bore is a hydraulic jump in translation generated at the leading edge of the flood tide during the early flood tide under spring macrotidal conditions in a narrow funnelled channel. After formation, the bore is traditionally analysed as a hydraulic jump in translation and its leading edge is characterised by a breaking roller for Fr1 > 1.3–1.5. Herein new unsteady experiments were conducted to investigate in details the upstream propagation of breaking bore roller. The toe perimeter shape fluctuated rapidly with transverse distance and time. A characteristic transverse wave length of the toe perimeter was observed. Both the standard deviation of toe perimeter location and characteristic transverse wave length were comparable to field observations. The celerity of the roller toe fluctuated rapidly with time and space. The instantaneous longitudinal profile of the roller free-surface showed significant temporal and spatial fluctuations. Although the bore propagation may be analysed in an integral form in first approximation, the rapid fluctuations in roller toe perimeter and free-surface profiles indicated a strongly three-dimensional turbulent flow motion.

A tidal bore is a hydraulic jump in translation, propagating upstream as the tide turns to rising and the flood flow advances in a funnel-shaped river mouth under spring tide conditions. This study focused on the unsteady turbulence induced by a breaking tidal bore. Detailed free-surface and velocity measurements were conducted with a high temporal resolution using non-intrusive free-surface measurement probes and acoustic Doppler velocimetry sampled at 200 Hz. The laboratory data were systematically compared with an earlier series of field measurements conducted in the breaking bore of the Selune River (France). Key findings include the agreement, in terms of dimensionless instantaneous free-surface and velocity data, between laboratory and field observations as well as the existence of a transient recirculation region near the bed.

Comparative experiments were conducted between uniform and non-uniform stepped spillway profiles in a large-size laboratory facility. For each stepped configuration, the air concentration distributions matched the advective diffusion equation and the interfacial velocity was well correlated with a power law. A comparison of the air–water flow properties showed small differences in terms of number of entrained air bubbles, chord sizes and turbulence characteristics between the different configurations. For the non-uniform steps, larger flow instabilities and stronger variation in the air–water flow properties were observed. Further some non-intrusive measurements were performed with acoustic displacement metres to characterize the free-surface profiles, free-surface fluctuations and free-surface wave celerity in both non-aerated and aerated flow regions. The experiments highlighted a close agreement between experimental data and theoretical predictions in the non-aerated flows and with conductivity probe d...

Air-water flow experiments were conducted on some flat and pooled stepped spillways with slopes of 8.9° and 26.6° in transition and skimming flows. The study comprised the observations of the flow patterns, characteristic air-water flow properties, and energy dissipation performances. The air-water flow properties showed some differences in terms of interfacial velocity, bubble count rate, and turbulence intensity between the stepped chutes for the two channel slopes. These differences were also reflected in the residual energy data, highlighting a better energy dissipation rate for the pooled stepped spillway with slope of 8.9°. However, the aerated flows on the pooled stepped spillways exhibited some hydrodynamic instabilities, and a safe operation must be tested in physical models. The flat stepped spillway appeared to be the preferable design in terms of energy dissipation and flow stability.

In turbulent free-surface flows, the deformation of the surface leads to air bubble entrainment and droplet projections when the turbulent shear stress is greater than the surface tension stress that resists to the interfacial breakup. These complex processes at the water–air interface have been the focus of extensive experimental, numerical and theoretical studies over last two decades and this paper reviews the key advancements. It is highlighted that the recent progress in metrology enables the detailed measurements of a range of air–water flow properties under controlled flow conditions, representing the sine qua non requirement for the development of improved physical understanding and for validating phenomenological and numerical models. The author believes that the future research into aerated flow hydraulics should focus on field measurements of high quality, development of new measurement approaches and data analyses tools, computational fluid dynamics modelling of aerated flows, and the mechanic...

Air–water flows on stepped spillways were investigated experimentally in the last decades with a focus on steep slope chutes equipped with flat horizontal steps. Detailed air–water flow properties were recorded herein with three stepped geometries down a slope of θ = 8.9° with: flat horizontal steps, pooled steps, and a combination of flat and pooled steps. The data included the distributions of basic air–water flow properties, as well as the energy dissipation and flow resistance data deduced from the air–water flow measurements. The results on the flat slope showed that the pooled stepped design enabled a greater rate of energy dissipation, but the pooled stepped geometries were affected by some flow instabilities and unsteady flow processes for a range of flow rates.

Negative surges can be caused by a sudden change in flow resulting from a decrease in water depth. In the present study, some physical experiments were conducted in a rectangular channel to characterize the unsteady free-surface profile and longitudinal velocity beneath a negative surge propagating upstream. The physical observations showed that, during the first initial instants, the celerity of the surge leading edge increased rapidly with time, while later the negative surge propagated upstream in a more gradual manner with a celerity decreasing slowly with increasing distance. The velocity data highlighted some relatively large turbulent fluctuations beneath the negative surge. The physical results were used to test the analytical solution of the Saint-Venant equations and some numerical models. The findings suggested that the negative surge propagation appeared relatively little affected by the boundary friction within the investigated flow conditions. DOI: 10.1061/(ASCE)HY.1943-7900.0000674. © 2013 American Society of Civil Engineers. CE Database subject headings: Storm surges; Open channel flow; Unsteady flow; Numerical models; Velocity. Author keywords: Negative surges; Unsteady open channel flow; Physical modeling; Numerical modeling; Water depth; Velocity; Negative waves.

In urbanized areas, flood flows constitute a hazard to populations and infrastructure, as illustrated during major floods in 2011. During the 2011 Brisbane River flood, some turbulent velocity data were collected using acoustic Doppler velocimetry in an inundated street. The field deployment showed some unusual features of flood flow in the urban environment. That is, the water elevations and velocities fluctuated with distinctive periods between 50 and 100 s linked with some local topographic effects. The instantaneous velocity data were analyzed using a triple decomposition. The velocity fluctuations included a large energy component in the slow fluctuation range, whereas the turbulent motion components were much smaller. The suspended sediment data showed some significant longitudinal flux. Altogether, the results highlighted that the triple decomposition approach originally developed for periodic flows is well-suited to complicated flows in an inundated urban environment.

The writers thank the discussers for their interest in the original paper, and the comments offered. During the inspection of the discussers’ assertions, it was found that most of them were unsupported by hydraulic analysis. Detailed replies to each comment are given, with bullet points used to differentiate between specific items to be presented.

In skimming flow on a stepped spillway, the upstream flow motion is nonaerated and a turbulent boundary layer develops until the outer edge of the boundary layer interacts with the free surface; that is, at the inception point of air entrainment. Herein, new experiments were performed in the developing flow region on a large 1 V∶1 H stepped spillway model with step height h=0.10 m. The flow properties in the developing flow region were carefully documented. In the developing boundary layer, the velocity distributions followed a 1/4.5th power law at the step edges. Detailed velocity and pressure measurements showed some rapid flow redistribution between step edges and above step cavities. The application of the momentum integral equation indicated an average friction factor of 0.18, which is close to the observed air-water-flow friction factor of 0.23, suggesting that the spatially averaged dimensionless shear stress was comparable in the developing flow and fully aerated flow regions.

On a stepped spillway, the steps act as macroroughness elements, contributing to enhanced energy dissipation and significant aeration. In a skimming flow, the upstream flow motion is nonaerated, and the free surface appears smooth and glossy up to the inception point of free-surface aeration. In this developing flow region, a turbulent boundary layer grows until the outer edge of the boundary layer interacts with the free surface and air entrainment takes place. The flow properties in the developing flow region were documented carefully in a large stepped spillway model (1V:1H; h=0.10 m). The upstream flow was controlled by a broad-crested weir and critical flow conditions were observed along most of the weir crest, although the pressure distributions were not hydrostatic at the upstream and downstream ends. Downstream of the broad crest and upstream of the inception point, the free surface was smooth, although some significant free-surface curvature was observed for all discharges. The boundary ...

On a gabion stepped chute, the steps contribute to the dissipation of turbulent kinetic energy, free-surface aeration may be intense, and there are complex interactions between the free-surface flow and seepage motion. Detailed measurements were conducted in a relatively large gabion stepped spillway model. Using a combination of high-speed movies and phase-detection probe measurements, the air–water flow properties in the step cavities and in the gabions were documented. Strong air–water exchanges between seepage and stepped cavity flows were observed. The data showed a complex bubbly seepage motion in the gabions associated with a high level of interactions between seepage and free-surface flows, leading to a modification of the step cavity recirculation and lesser flow resistance.

The stepped spillway design is associated with significant flow resistance and associated energy dissipation on the steps, yielding smaller, more economical downstream dissipation structures. A number of design guidelines were developed for steep stepped spillways typical of concrete gravity dams. The focus of this study is on embankment stepped spillways. A large set of air-water flow data is compared with reanalyzed data sets to provide a simple unifying design approach for the residual energy at the stepped chute’s downstream end and to highlight the uncertainties involved. The results provided some simple design criteria in terms of the dimensionless residual energy of stepped chutes with flat steps. It is believed that a stepped design with a 1V:2.5H slope (θ=21.8°) might be optimum in terms of energy dissipation performances. The Darcy-Weisbach friction factors were close for all stepped data ranging between 0.1≤fe≤0.4.

Basic experiments were conducted on a large-size broad-crested weir with a rounded corner. Detailed free-surface, velocity, and pressure measurements were performed for a range of flow conditions. The results showed the rapid flow distribution at the upstream end of the weir and next to the weir brink at large flow rates. The flow properties above the crest were analyzed taking into account the nonuniform velocity and nonhydrostatic pressure distributions. Introducing some velocity and pressure correction coefficients, it is shown that critical flow conditions were achieved above the weir crest for 0.1

A tidal bore is a positive surge taking place during the flood tide with a large tidal range and the bore corresponds to the leading edge of the tidal wave propagating upstream. In this study, some physical modelling was performed to investigate the upstream bore propagation over fixed and movable gravel beds. Both undular and breaking bores were tested. The free-surface and velocity measurements were complemented by some observations of particle motion beneath the bore front. In the initially-steady flow and beneath undular bores, no sediment motion was observed for the experimental set-up. Beneath breaking bores, on the other hand, some upstream gravel bed load motion was observed behind the bore. The gravel bed particles were de-stabilized by the roller toe passage and advected upstream. The unsteady velocity data showed some damping of the transient recirculation on the movable gravel bed.

A tidal bore is an unsteady flow motion generated by the rapid water level rise at the river mouth during the early flood tide under macrotidal and appropriate bathymetric conditions. This paper presents a study that physically investigates the turbulent properties of tidal bores. Results from some experimental measurements of free-surface fluctuations and turbulent velocities conducted on smooth and rough beds are reported. The free-surface measurements were conducted with Froude numbers of 1-1.7. Both undular and breaking bores were observed. Using an ensemble-averaging technique, the free-surface fluctuations of breaking tidal bores are characterized. Immediately before the roller, the free-surface curves gradually upwards. The passage of the bore roller is associated with some largewater elevation fluctuations; the largest free-surface fluctuations are observed during the first half of the bore roller. The turbulent velocity measurements were performed at several vertical elevations during and shortly after the passage of breaking bores. Both the instantaneous and ensemble-averaged velocity data highlight a strong flow deceleration at all elevations during the bore passage. Close to the bed, the longitudinal velocity component becomes negative immediately after the roller passage, implying the existence of a transient recirculation. The height and duration of the transient are a function of the bed roughness, with a higher and longer recirculation region above the rough bed. The vertical velocity data presented some positive, upward motion beneath the front with increasing maximum vertical velocity with increasing distance from the bed. The transverse velocity data show some large fluctuations with nonzero ensemble average after the roller passage that highlight some intense secondary motion advected behind the bore front. DOI: 10.1061/(ASCE)HY.1943-7900.0000542. © 2012 American Society of Civil Engineers.

A tidal bore may develop in an estuary during the spring tide conditions when the tidal range exceeds 5–6 m and the flood tide is confined to a narrow funnelled estuary with low freshwater levels. The tidal bore is of great importance for the geomorphology of the estuarine zone. In this study, some physical modelling was performed to investigate the sediment motion inception beneath a tidal bore on a movable gravel bed. The results show the significant impact of breaking bore propagation on the gravel bed motion. The dominant contribution to sediment transport inception is the longitudinal pressure gradient force, while the transient recirculation motion next to the bed yields to a drag force acting in the upstream direction and contributing to sediment motion.

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-averaged void-fraction data highlight a rapid deaeration of the jump roller. The results suggest that the hydraulic jumps are effective aerators and that the rate of detrainment is comparatively smaller at the largest Froude numbers.

Jean-Baptiste Bélanger (1790–1874) worked as a hydraulic engineer at the beginning of his career. He developed the backwater equation to calculate the free-surface profile of gradually varied, steady open channel flow. He also introduced the concept of critical flow and the numerical technique called the direct step method. Later, as an academic staff member at the leading French engineering schools (Ecole Centrale des Arts et Manufactures, Ecole des Ponts et Chaussées and Ecole Polytechnique), he developed a new university curriculum in mechanics and wrote several textbooks including a seminal text in hydraulic engineering. His influence on his contemporaries was considerable, and his name is written on the border of one of the four façades of the Eiffel Tower. Bélanger's leading role demonstrated the dynamism of practising engineers at the time, and his contributions paved the way to many significant works in hydraulics and fluid dynamics during the late nineteenth and early twentieth centuries.

The present study examines the free-surface properties of undular tidal bores observed for 1 < F < 1.5-1.8. The analysis is based on some new experimental results together with a reanalysis of both field and laboratory data. The free-surface profiles followed a pattern somehow similar to the sinusoidal and cnoidal wave shapes, although neither captures the fine details of the undulation profiles. The wave properties highlighted some maxima in amplitude and steepness for a Froude number of about 1.3-1.4 corresponding to the apparition of some wave breaking at the first wave crest.