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This article examines the impact of different inflow conditions on hydraulic jumps, specifically focusing on the free-surface properties and energy loss. The authors conducted experiments using LiDAR to measure jump characteristics under partially and fully developed inflow conditions. They also discuss the calculation of head loss in a jump and provide equations and data from previous studies to support their findings. The article concludes that energy loss is larger under fully developed inflow conditions compared to partially developed inflow conditions, but further research is needed to fully understand the effect of inflow conditions on energy dissipation in jumps. [Extracted from the article]

In the present study, a one-dimensional governing equation with a vertical acceleration term is used to analyse the free surface profile of various types of jumps. Initially, the surface profile of various types of jumps are reproduced analytically by using a suitable eddy diffusivity term. The approximations of the surface profile for various jumps are then verified numerically. Based on the comparisons, an empirical relationship between the Froude number and the turbulent diffusivity coefficient is established. The proposed empirical relationship is used in the governing equation to compute the various jumps, where an implicit two dimensional flow is assumed. The obtained results are compared with the experimental data to assure the transition of flow from undular jump to breaking jump. The comparisons of numerical results of wave profiles, pressure distribution, wave length and wave amplitude with the existing experimental data for various Froude numbers indicated the suitability of the proposed empirical relationship. Finally, the transitions of flow from undular jump to breaking hydraulic jump are discussed. [ABSTRACT FROM AUTHOR]

In high dam construction projects in China, stilling basin design with an abrupt bottom drop is sometimes introduced to reduce the bottom velocity and pressure loads by generating A-type hydraulic jumps. Although the stilling basin design is not new, A-type hydraulic jumps have not been studied taking into account the air entrainment and evolution of internal air–water flow structures. This paper presents an experimental study of self-aerated A-type jumps in terms of bubble transport and free-surface fluctuations over the bottom drop. Four Froude numbers from 4.1 to 10.3 are tested for three drop heights, in addition to the flat-bottom case. Compared to the classic hydraulic jumps, A-jumps are observed with longer jump lengths and weaker free-surface fluctuations. The downward deflection of the jet-shear flow and formation of a bottom roller in the step cavity require a modification to the analytical expression of velocity and void fraction distributions. The relationship between the bubble diffusivity and jump spreading rate differs from that in classic hydraulic jumps, suggesting a faster expansion of the bubble diffusion layer than the turbulent shear flow downstream of the drop, especially for large drop heights. At large approach velocities, the reattachment of the deflected jet-shear flow to the lowered bed may cause a local rise in bubble counts downstream the bottom roller. Further increase in drop height results in a W-jump with overwhelming bottom roller over the surface roller and an arced surface jet, which is beyond the scope of this study. [ABSTRACT FROM AUTHOR]

The article discusses the effect of inflow conditions on the properties of hydraulic jumps. It acknowledges the contributions of previous studies on the topic, including the importance of boundary layer development and jump toe fluctuations on free-surface characteristics. The article also highlights the significance of measuring instantaneous velocities in aerated flows for a better understanding of flow processes. It presents an equation for calculating energy dissipation efficiency in hydraulic jumps and compares the results with previous studies. The article challenges the assumption that hydraulic jumps with fully developed inflow conditions have better energy dissipation, suggesting that there is no evidence to support this claim. [Extracted from the article]

Study of hydraulic jumps following aerated supercritical flow has been limited, although this is a common scenario in stilling basins preceded by open-channel spillways. New experiments were performed in a concrete stilling basin model downstream of a sloping stepped chute, where hydraulic jumps were generated on the horizontal stilling basin bed and characterized by bubbly approach flow with Froude numbers 7.6 and 9.3 and Reynolds numbers in the order of 105. Measurements were focused on the jump toe oscillations, jump roller length, and air–water flow property distributions. Comparison of the results with literature data under non-aerated inflow conditions suggested overall insignificant pre-aeration effects on the investigated air–water flow properties, although some comparative analyses were subject to scale effects. The streamwise evolution of air flux suggested that the pre-entrained air did not intrude deeply into the jet-shear layer beyond 1/5 to 1/3 roller length from the jump toe. [ABSTRACT FROM AUTHOR]

Prototype hydraulic jump experiments were conducted at the Pei-bridge Gates in the Bao River, China. Two D-jumps formed on the 14° slope downstream one of the 5-m-wide sluice gates, followed by a sudden expansion of flow cross-section in the stilling basin. With the Froude numbers Fr = 7.47 and 3.18, the Reynolds numbers reached Re = 1.16 × 106 and 1.88 × 106, respectively. The fluctuating jump toe and free-surface characteristics were analysed and compared with existing model tests of classic and D-type jumps. The air–water flow properties were measured intrusively with phase-detection probes and compared to the laboratory data. The prototype jumps exhibited three-dimensional roller motions with shorter roller lengths than classic hydraulic jumps in prismatic channels. Scale effects were noted for the bubble frequency and bubble size distributions among the influences of other measuring factors, implying the need to revisit the model-based prediction relationship at prototype conditions. [ABSTRACT FROM AUTHOR]

In recent decades, stepped chutes followed by a stilling basin became a standard for spillways of dams. The comprehensive knowledge of stepped chute approach flows on internal air–water flow properties of the hydraulic jump is still too limited for an appropriate design of stilling basins. Therefore, an experimental campaign was performed on a large-scale physical model of a plain stilling basin preceded by a 30° sloping smooth or stepped chute. Stepped chute approach flows induce lower deaeration rates along the jump roller as compared to smooth chute approach flows, indicating longer dimensionless jump lengths, normalized by the tailwater depth. Pronounced bottom air concentrations were observed within the first 40% of the jump length in the stilling basin downstream of the stepped chute. Thus, despite the significantly higher pressure fluctuations, this zone seems better protected against cavitation damage than in stilling basins following a smooth chute. [ABSTRACT FROM AUTHOR]

Under a flow in supercritical regime, depending on the pier width to water depth ratio, the flow pattern around a bridge pier can take the form of a wall-jet-like bow wave or a detached hydraulic jump. The present work aims at analysing the maximum scour depth at piers in both flow patterns. A dedicated experimental set-up was used to produce the live-bed scour experiments, varying the inflow velocity and pier diameter. During the experiments, scour developed very rapidly, achieving equilibrium conditions after few minutes. No major differences between the maximum scour depth in the wall-jet-like bow wave and detached hydraulic jump cases were observed. Measured scour depths were of comparable magnitude and followed similar tendencies with controlling parameters as in subcritical flows. Scour formulas for piers in subcritical flow thus achieve a good accuracy in prediction of maximum scour depth at piers in supercritical flows. [ABSTRACT FROM AUTHOR]

The low-level bottom outlet operates in a long tunnel type, indicating that the air discharge is independent of the tunnel length and the air flow is supplied totally by the upstream air vent. The total air demand discharge in the bottom tunnel is the sum of the entrained air discharge and the air discharge above the flow surface. To validate the prediction of air supply performance in bottom tunnels, the two aspects of the total air discharges should be clarified carefully, including the coupling effect between the air vent size and tunnel length on complex air supply patterns. [Extracted from the article]

Previous research has shown that the inflow conditions upstream of hydraulic jumps can affect flow aeration, bed pressures and turbulence. However, studies of the effects of inflow conditions on free-surface properties have not been conclusive and have lacked a comparison of partially and fully developed inflow conditions. Detailed measurements of the free-surface features in fully aerated hydraulic jumps with partially and fully developed inflow conditions have been conducted using a LIDAR. The results showed that the free-surface profile, the roller length, the free-surface and jump toe movements are strongly influenced by the inflow conditions. Hydraulic jumps with fully developed inflow conditions were of comparatively shorter length compared to partially developed hydraulic jumps, while they were characterized by stronger fluctuations, jump toe motions and frequencies as well as stronger energy loss across the hydraulic jump. Inflow conditions must be considered in determining the envelope of hydraulic jump motions with consequences for dissipator design. [ABSTRACT FROM AUTHOR]

Measuring flow depths in free-surface turbulent flows can be challenging due to their fast dynamics and the presence of aeration. This study analyses the suitability of a low-cost sensor, the Intel® RealSense™ D435 RGB-D camera, for characterization of a highly aerated case study: the hydraulic jump. As with all instrumentation, special care must be taken to ensure accurate measurements. In this case, two different methods to calibrate depth estimations (accounting for set-up and any instrument precision) are presented, both leading to similar results. The main advantage of the presented instrumentation is its capability to measure 3D surfaces with high temporal and spatial resolution. Results are presented primarily in 2D in order to evaluate the flow depth estimation quality of this new technique with 2D data available in literature. The employed sensor showed a similar level of uncertainty as previous, well-established instrumentation for the study of free-surface elevations, amplitudes and frequencies of turbulent fluctuations. [ABSTRACT FROM AUTHOR]

Accurate prediction of the discharge through radial gates is difficult. Existing calibration methods typically provide sufficient accuracy for free flows and submerged flows with jet Froude number at vena contracta larger than 1.7. However, their predictions are poor for submerged flows with jet Froude number less than 1.7. Based on the analysis of experimental data collected by the US Bureau of Reclamation, an empirical indicator was proposed to predict the approximate range of jet Froude number for submerged flows. Accordingly, submerged flows were subdivided into partially submerged flows with fully developed hydraulic jump, and totally submerged flows with undular or no jump. A new discharge calibration method, referred to as the identification method, was developed for the three distinct flow conditions. Verification of the proposed method indicated the discharge prediction accuracies were significantly improved for totally submerged flows. [ABSTRACT FROM AUTHOR]

Under large unit discharges, cavitation damage may occur and energy dissipation may remarkably decline in stepped chutes due to absence of air entrainment. Herein, a pre-aeration device, entraining air by contracting the flow locally by walls without special air vent, is proposed for increasing the maximum available unit discharges. The test results demonstrate that the aerator proposed in this paper generates a ski-jump and a local hydraulic jump to entrain air into flow. It provides fully aerated flows for the stepped chutes, and significantly increases the energy dissipation with large unit discharges. [ABSTRACT FROM AUTHOR]

Hydraulic jumps are characterized by three-dimensional motions, air entrainment and energy dissipation. While extensive air–water flow research has been conducted for classical hydraulic jumps, the air–water flow properties in hydraulic jumps on slopes remain widely unexplored. New air–water flow experiments were conducted of Type B and D jumps for slopes of 1.25°, 2.5° and 5°. Comparative analyses of the sloped jumps with classical hydraulic jumps for the same Froude and Reynolds numbers showed that hydraulic jumps on slopes were more stable. Close similarities in aeration and energy dissipation performances were found between the classical hydraulic jumps and Type B jumps while Type D jumps showed lower energy dissipation efficiency and aeration. Combining the observations of flow aeration and stability, the present results suggested that a Type B jump may be an optimum hydraulic jump achieving large energy dissipation while providing increased jump toe stability. [ABSTRACT FROM AUTHOR]

When Eqs (1) and (2) are applied, the detailed parameters of the spillway tunnel of Jinping-I dam are listed in Table 1, in which I s i is the gate opening percentage, I h SB gate sb i the height of gate opening, I h SB c sb i the water depth of the contraction section downstream the gate (Henry, [3]), I B i the tunnel width, Graph HT ht the equivalent tunnel height and Graph HT ht m SP 2 sp the sectional area all along the tunnel. [Extracted from the article]

Prototypal and 3D numerical model data of the total air demand, I Q SB air sb i , along the spillway tunnel, and of the air discharge along three air ducts installed on the tunnel ceiling were evaluated. The Authors presented a fascinating research work on the air demand in spillways. Additionally, the present discussion highlights that, if practitioners must rapidly estimate the air demand of a spillway tunnel, then the utilization of Eq. (1) is feasible because its prediction accuracy is larger than other empirical formula considered by the Authors. [Extracted from the article]

Hydraulic jumps are often employed as energy dissipators below hydraulic structures. If a high-velocity conduit drains into an expanding open channel a spatial hydraulic jump can be formed. Even though this type of hydraulic jump is common in civil engineering practice, it has not received sufficient consideration by researchers. Three-dimensional, unsteady detached eddy simulation of a symmetric submerged spatial hydraulic jump was carried out to evaluate the turbulent flow features. The volume of fluid multiphase model was used to capture the free surface. The complete three-dimensional flow features of symmetric submerged hydraulic jump are reported herein for the first time. The three-dimensional jump roller was found to be stronger near the side walls than at the centre. The instantaneous vortex shedding from the conduit outlet was also captured by the simulations. To describe the internal structure of turbulence within a symmetric submerged spatial hydraulic jump, the coherent flow structures are qualitatively and quantitatively examined using a vortex identification technique and proper orthogonal decomposition. [ABSTRACT FROM AUTHOR]

These recommendations are herein used to estimate the maximum shock wave heights and the discharge capacity of 45° and 90° three-branched supercritical junction manholes with variable inlet branch diameters. All these research studies analysed junction manholes approached by two circular inlet branches and with a circular outlet branch (subscript I u i ) of diameter I D SB u sb i = 0.240 m. A similar scenario was observed in 45° and 90° three-branched junction manholes by Del Giudice and Hager ([2]) and Gisonni and Hager ([3]). 3, the four-branched junction manhole experienced the choking condition for Froude numbers smaller than in Del Giudice and Hager ([2]), Gisonni and Hager ([3]) and Pfister and Gisonni ([10]). [Extracted from the article]

Hydraulic jumps cause significant flow energy dissipation and generally occur in association with hydraulic structures. Nevertheless, the dissipative mechanisms occurring with this hydraulic phenomenon still require investigation. There are no systematic studies analysing the hydraulic jump energy dissipation for a large range of hydraulic and geometric conditions. To the authors’ knowledge, no studies provide a complete and exhaustive analysis of the dissipative mechanism for rough sloped channels. This study proposes a novel semi-theoretical and general approach to estimate energy dissipation at hydraulic jumps in rough sloped rectangular channels, involving a large range of both hydraulic conditions and bed configurations. Two relationships were derived and their predictive capability has been tested with approximately 500 experimental data points from different studies. [ABSTRACT FROM AUTHOR]

Results from large-eddy simulations and complementary flume experiments of turbulent open channel flows over bed-mounted square bars at intermediate submergence are presented. Scenarios with two bar spacings, corresponding to transitional and k-type roughness, and three flow rates, are investigated. Good agreement is observed between the simulations and the experiments in terms of mean free surface elevations and mean streamwise velocities. Contours of simulated time-averaged streamwise, streamfunction and turbulent kinetic energy are presented and these reveal the effect of the roughness geometry on the water surface response. The analysis of the vertical distribution of the streamwise velocity shows that in the lowest submergence cases no logarithmic layer is present, whereas in the higher submergence cases some evidence of such a layer is observed. For several of the flows moderate to significant water surface deformations are observed, including weak and/or undular hydraulic jumps which affect significantly to the overall streamwise momentum balance. Reynolds shear stress, form-induced stress and form drag are analysed with reference to the momentum balance to assess their contributions to the total hydraulic resistance of these flows. The results show that form-induced stresses are dominant at the water surface and can contribute significantly to the overall drag, but the total resistance in all cases is dominated by form drag due to the presence of the bars. [ABSTRACT FROM AUTHOR]

Local scour in the transition from super- to sub-critical flow without a hydraulic jump is investigated based on model experimentation. Supercritical flow was enforced by a box-culvert, passed a curved bed, and then flowed over the sediment bed. The scour processes and the initiation of sediment motion are discussed. Attempts are also made to explain similarities among scour processes and profiles. The temporal development of the maximum scour depth is evaluated. Results indicate that the maximum equilibrium scour depth and scour hole geometry in the transition from super- to sub-critical flow without a hydraulic jump significantly depend on the upstream supercritical approach flow, and the densimetric Froude numbers. Scour profiles were also compared with those resulting from equivalent hydraulic jumps, indicating that the geometrical characteristics of the scour holes are significantly smaller than those of the corresponding hydraulic jumps. Finally, relationships characterizing the equilibrium scour hole geometry are derived based on the experimental results. [ABSTRACT FROM AUTHOR]

The characteristics of air entrainment in hydraulic jumps below a sluice gate were systematically investigated. The air entrainment region is divided into the advective diffusion region and the breaking region. For the advective diffusion region, it was found that the air concentration for a fully developed inflow is larger than that for an undeveloped inflow under a given inflow Froude number. For a partially developed inflow, the air concentration in the advective diffusion region depends on the boundary layer development of the supercritical inflow. The air concentration in the breaking region is nearly independent of the inflow conditions of the boundary layer development. Regarding the effect of the inflow Froude number, the air concentration in both the advective diffusion and breaking regions increases with the inflow Froude number under a given boundary layer development. The air entrainment mechanism in jumps is explained for both the advective diffusion and breaking regions. [ABSTRACT FROM PUBLISHER]

In spite of some progress in the study of the transition from super- to subcritical flow without a hydraulic jump, many issues remain unclear, particularly in relation to the turbulence structure and dissipative mechanisms in the transition region. This paper therefore is focused on the experimental investigation of the turbulence characteristics in the transition region from super- to subcritical flow without a hydraulic jump. Instantaneous velocities were measured using an acoustic Doppler velocimeter and mean velocities, turbulence intensities, and Reynolds stresses were computed for different geometrical and hydraulic conditions. The turbulence intensities and Reynolds stresses were found to decrease in the transition region downstream and then approach the levels of the fully-developed turbulent open channel flow. The length of this transitional region was found to be three to seven times the tailwater depth for the range of Froude numbers between 1.3 and 4.5. The obtained results imply that the transition is driven by the longitudinal deceleration of the flow in the transition region. [ABSTRACT FROM PUBLISHER]

An undular hydraulic jump corresponds to the weak transition from super- to subcritical-flow in the form of steady free surface undulations. Previous models on undular hydraulic jumps employed the potential flow theory, i.e., the solitary and cnoidal wave theories. Experimental observations indicate the inadequacy of this theory, which motivated the development of more advanced approximations. Basic flow features including friction effects on the velocity profile, modelling of the bed-shear stress, and Reynolds stresses are considered. However, none of the models currently available include all these aspects. In this study, a general depth-averaged model is developed based on thek-ϵ turbulence closure. The general depth-averaged equations are applied to the undular jump problem, introducing a suitable time-averaged velocity distribution based on a composite power-law model, in which both streamline curvature and vorticity are accounted for. The bed-shear stress closure is included by a boundary layer method. Predictions of the depth-averaged Reynolds averaged Navier-Stokes (RANS) model are shown to be close to the 2D RANS solution and to experimental observations. [ABSTRACT FROM PUBLISHER]

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 Sélune 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. [ABSTRACT FROM AUTHOR]

An experimental–analytical investigation was performed to explore whether a hydraulic jump in a transition from super- to subcritical flow regime can be avoided. As the free-surface profile passes the critical depth, the transitional point is a singular point. A transition structure was designed based on the energy principle and the singular point theory to gradually increase the flow depth, thereby eliminating the hydraulic jump. This profile was designed for approach flow Froude numbers between 1.5 and 7. To validate the analytical model, a comprehensive experimental study was conducted. Six hydraulic models of transition structures were experimentally investigated on the basis of the theoretical approach. The analytical results agreed well with the experimental results and those of former investigations. Observations indicated that the hydraulic jump is absent for a certain range of the Froude numbers. [ABSTRACT FROM AUTHOR]

This note is the final completion of a previously published work concerning the integral conservation of linear and angular momentum in the steady hydraulic jump in a linearly diverging channel [Valiani, A., Caleffi, V. (2011). Linear and angular momentum conservation in hydraulic jump in diverging channels.Adv. Water Res.34(2), 227–242]. The same reasoning is applied to a linearly converging channel, and the theoretical framework, which is almost completely the same, is shown to remain valid. Using a proper mechanical scheme, an analytical solution is obtained for the free surface profile of the flow. This solution allows the determination of the sequent depths and their positions. Thus, the length of the jump, which is assumed to be equal to the length of the roller, is also found. The mainstream and roller thicknesses can also be derived. This model may be used to derive the average shear stress exerted by the roller on the mainstream and the related exact expression for the total power loss in the jump, allowing to demonstrate the internal consistency of the proposed conceptual scheme. [ABSTRACT FROM PUBLISHER]

The analysis of bubble clustering in air–water flows may provide some measures of the bubble–turbulence interactions. A cluster of bubbles is as a group of two or more bubbles, with a distinct separation from other bubbles. This paper compares the results of a clustering study in a dropshaft and in a hydraulic jump to point out differences/similarities between those complex turbulent flows. The clustering process was studied through the analysis of the interparticle arrival time (IAT) of the bubbles. The results highlighted the presence of clustering in both bubbly flows due mostly to turbulent break-up. The range of bubbles sizes mainly affected by clustering was identified. The results showed that the bubbly flow in the dropshaft had a density of bubbles per unit flux larger than that in the hydraulic jump. Overall, the results demonstrated the relevance of the IATs analysis in the study of bubbly flows. [ABSTRACT FROM AUTHOR]

The formation of different undular hydraulic jumps in a very large channel is investigated and reproduced using a weakly-compressible XSPH scheme which includes a mixing-length turbulence model. An analysis of the ability and of the limits of the SPH method to reproduce undular hydraulic jumps is preliminarily performed on reference two-dimensional cases. The numerical description of the three-dimensional jump in a very large channel, where the hydraulic-jump front is trapezoidal and the lateral shock waves induce a large recirculation region along the side walls, is compared with experiments in a laboratory flume on two undular jumps at upstream Froude number equal to 3.9 and 8.3. Acoustic Doppler velocity measurements were compared with SPH instantaneous and time-averaged flow fields in order to evaluate whether the numerical method could help in having a clearer understanding of both hydraulic-jump development and lateral shockwave formation. The predicted free-surface elevations and velocity profiles show a satisfactory agreement with measurements and most of the peculiar features of the flow, such as the trapezoidal shape of the wave front and the flow separations at the toe of the oblique shock wave along the side walls, are qualitatively and quantitatively reproduced. [ABSTRACT FROM PUBLISHER]

An improved model for predicting oxygen transfer efficiency at gated sills is presented. An analysis of field measurements from eight gated sill structures is used to develop a dimensionless relationship between inflow conditions, dam geometry and oxygen transfer efficiency. The oxygen transfer coefficient is estimated from scaled formulations of the liquid film coefficient, mean bubble diameter, air entrainment rate and turbulent energy dissipation rate. The model is validated with additional field measurements adjusted for temperature and effective saturation concentration. A design parameter for gated sill dams is introduced giving a relationship between gate opening and oxygen transfer efficiency. Improved prediction of oxygen transfer in the field is a tool that can be used to successfully operate gated structures to meet oxygen concentration requirements and to assist in the design of remediation technologies. [ABSTRACT FROM PUBLISHER]

Turbulent discontinuous open-channel flow appears in practice due to separation zones. The current practice overlooks the separation bubble by neglecting its velocity and by assuming static pressure on the active main stream. Based on the pioneering and so far unique work of Ralph Schröder, this approximation is compared with detailed computations of the energy and momentum velocity coefficients using his selected experiments. What would occur if their magnitude were 200 and 40 times greater than standard values? These extremes are demonstrated to occur and used to critically asses the “static bubble” approximation of roller flows. The data were also used to present generalized computations of the critical depth based on the energy and momentum equations, thereby proving that these differ in turbulent open-channel flow, although they are identical for potential flow. All these findings emerge from the outstanding experimental work of Schröder, which is critically reviewed to make his achievements available for the hydraulic community. [ABSTRACT FROM AUTHOR]

In vented closed conduit conveyance systems, air entrained through hydraulic jumps can be problematic for system operation. While various factors influencing air entrainment have been reported in the literature, no specific attention has been paid to the hydraulic jump location relative to the point of downstream air release. To better understand the effects of jump location on air entrainment, in this study, experiments were conducted in a vented, circular conduit with variable hydraulic jump locations relative to the pipe outlet. When the hydraulic jump was fully contained within the pipe, the air entrainment rate was dependent on the Froude number immediately upstream of the jump but was independent of the jump location within the pipe. The rate of air entrainment significantly increased, however, when the hydraulic jump was not fully contained within the pipe. For this condition, the distance from the toe of the jump to the pipe outlet significantly influences the air entrainment rate. [ABSTRACT FROM AUTHOR]

Near-critical flows in rivers and natural streams usually present a wavelike undular free surface, associated with dune-type bed-forms. The formation of this particular bed geometry is related to the shear stress acting on the river bed. The boundary shear stress distribution of undular flows was considered by Engelund and Hansen, stating that standing waves and their associated non-uniform shear stresses are responsible for bed-form generation in rivers. However, observations on movable-bed channels involving transcritical flow were not considered. In this note, an exploratory analysis is conducted to outline the analogy between the boundary shear in fixed-bed undular flows and the bed-form shape. Experimental observations reveal a strong analogy, supporting the original hypothesis of Engelund and Hansen. [ABSTRACT FROM PUBLISHER]

The article offers the authors' insights on a study which evaluates the effect of bottom friction on undular hydraulic jump. The authors mention that the study used energy balance equation with suitable auxiliary equations, Boussinesq-type equation, and nonlinear differential equation. They also note that the results obtained by the researcher are not an appropriate solution for the problem of the study, because the boundary conditions with Boussinesq-type equation are priori unknown.

Dam-break flows usually occur in domains with complex geometric and topographic features and involve abrupt flow patterns. A dam-break model must therefore be able to effectively handle different flow types including transcritical flows or hydraulic jumps, deal with complex domain topography, capture repeating wet-dry interface and represent high roughness values in the floodplain. Herein, all of these objectives are achieved by extending a recent one-dimensional finite volume Godunov-type model into two dimensions for solving the shallow-water equations. While doing so, a much simplified condition to maintain well-balanced solutions around a wet-dry front is proposed and a two-dimensional friction source term discretization is derived under a suitable stability condition in relation to practical simulations. The two-dimensional model is successfully validated against three analytical benchmark tests and then assessed for predicting realistic dam-break flood events. [ABSTRACT FROM AUTHOR]

The structure of turbidity currents released on a sloping bed below fresh water is investigated. Kaolin is used as a suspended material. Laboratory observations indicate that if a dense layer moves through the channel, the current thickness increases due to a hydraulic jump. This phenomenon occurs under special inlet conditions and has a significant effect on the current structure including velocity profile, current height and bed shear stress. Flows with different inlet Froude numbers based on various inlet concentrations behave more distinctly than those based on different inlet opening heights. Laboratory experiments indicate that an increase in the inlet Froude number causes an increase in the height of sediment-laden density currents and a decrease in the maximum cross-sectional velocity. The effects of the hydraulic jump on the bed shear stress are also investigated. A decrease in this stress and the average velocity is remarkable after the current has passed the jump. [ABSTRACT FROM AUTHOR]

This experimental investigation focuses on the turbulence features of weak hydraulic jumps in rectangular channels for two different approach flow lengths. The turbulent kinetic energy equation includes the turbulence production and dissipation terms, two advection and two turbulent transport terms and the pressure transport term, which could not be measured, however. For jumps with a limited approach flow length, the turbulence production is mostly confined to the shear layer, while for jumps with a longer approach flow length, an additional peak turbulence production region is observed at the near-wall region due to boundary layer separation. The turbulent energy is then transported by the mean flow both towards the free surface and into the downstream direction and is diffused by turbulent processes away from the energetic shear layer towards less energetic regions. Dissipation occurs mostly in the shear layer along the upstream portion of the jump and over most of the flow depth further downstream. [ABSTRACT FROM AUTHOR]

An experimental study of the characteristics of dividing critical flows in a 90° open-channel junction formed by three horizontal equal-width branches is presented, conducted for various inflow discharges and downstream boundary conditions. Outflow discharges and flow depths were also measured. Four main flow patterns are identified considering the location and length of the hydraulic jumps that develop across the main and lateral channels. A relationship between the discharge division ratio and the tailwater Froude number is found, reproducing well the experimental data. Practical applications of this relationship include the design of open channel and pipe networks and one-dimensional numerical modelling of flood propagation in urban areas. The study shows also that a two-dimensional depth-averaged numerical model hardly gives better predictions of the discharge ratios because of the presence of three-dimensional features at the junction. [ABSTRACT FROM AUTHOR]

While there has been a great deal of research in air entrainment at hydraulic jumps within closed conduits, limited research has specifically addressed size-scale effects. To determine the significance of these effects in closed conduits, air flow measurements were taken in four different-sized circular pipes with similar Froude numbers. Additionally, specific measurements were taken in one of the pipes with various water temperatures to identify any effects from changing fluid properties. The results indicated that the percentage of air entrainment was not affected by the pipe size if the full length of the hydraulic jump was contained within the pipe. For this condition, the data from four different pipes show that size-scale effects of air entrained into hydraulic jumps within closed conduits are negligible. However, air entrainment was significantly affected by water temperature. [ABSTRACT FROM AUTHOR]

Can a direct hydraulic jump also be generated if the surface roller is substituted with a corresponding inset? This and related questions are considered in the note, to understand the role of the roller. Based on recent findings relating to the classical hydraulic jump, its modification using bottom and surface insets is reconsidered using laboratory experimentation. The results of these tests are reported below using mainly photography and basic hydraulic computations. It is further demonstrated that the roller may not be separated from the hydraulic jump in a free surface arrangement. This would greatly simplify observations, because the standard two-phase flow including an air-water mixture flow would become a one-phase flow consisting of only water flow. The implications of this result are discussed. This work has exploratory character and should stimulate a further discussion on the main flow features of direct hydraulic jumps. [ABSTRACT FROM AUTHOR]

Knowledge of hydrodynamic processes is essential for engineers who assess the stability of energy dissipation structures undergoing extreme pressure fluctuations caused by turbulence during high discharge. Methods are in particular required to evaluate the frequencies of occurrence of extreme pressures. This work explores the use of the generalized extreme value (GEV) distribution to represent frequencies of instantaneous pressures recorded in a structure designed for energy dissipation by a hydraulic jump in a hydroelectric power station at Porto Colombia in central Brazil. The goodness of fit of the GEV distribution was evaluated using probability plots and the Kolmogorov-Smirnov test. The results indicate that it is appropriate for studying the maximum and minimum pressures for a range of discharges corresponding to Froude numbers between 3.88 and 6.42. [ABSTRACT FROM AUTHOR]

The behaviour of elongated air pockets in downward sloping pipes is investigated. The observed flow regimes in co-current air-water flow in downward sloping pipes are described. The effects of pipe diameter and surface tension on the air pocket motion are quantified and two criteria for the observed flow regime transitions are derived. One criterion stems from energy considerations and marks the transition from the presence of one elongated air pocket to multiple air pockets. The second criterion predicts the required water velocity to start the motion of elongated air pockets in the downward direction. Both criteria were validated with experimental data for a range of downward sloping pipe angles, lengths and diameters. [ABSTRACT FROM AUTHOR]

The study of bubble clustering processes may provide a significant insight into turbulent air-water flows. Previous studies investigated these processes in plunging jets, dropshafts and hydraulic jumps. This research investigates the bubble clustering process in hydraulic jumps using experimental data collected in a rectangular horizontal flume with partially developed inflow conditions for inflow Froude numbers in the range 6.5-14.3. Two criteria for cluster identification were applied: one criterion was based upon a comparison of the local instantaneous water chord time with the median water chord time, whereas the second identified a cluster if the water chord time was smaller than the air chord time of the preceding bubble, i.e. a bubble was in the near-wake of the leading bubble. The results highlight significant patterns in clusters production both over the flow depth and the distance from the jump toe. The effect of the inflow flow Froude number on the clustering process is also discussed. [ABSTRACT FROM AUTHOR]

Despite being widely used for the solution of one-dimensional subcritical flows governed by Saint-Venant's equations, the Preissmann's scheme cannot solve transcritical flows. This inability is due only to the solution methods created for non-transcritical flows. Transcritical transitions present specific properties that have to be adequately represented in the numerical method. A modified version of Preissmann's method is presented herein that changes the formulation only in transcritical zones, while keeping its conservative property and shock capturing form otherwise. A solution method is proposed for the implicit system, through storing the transcritical positions. This enables to solve the system with simple and double-sweep methods. The transcritical transition problem is solved locally, either by associating the cells involved in a bore and adding an equation to characterize the information transferred into the subcritical domain, or by the addition of an internal boundary condition to characterize the expansion fan at the critical point. [ABSTRACT FROM AUTHOR]

The undular hydraulic jump is a transitional flow phenomenon where both streamline curvature and frictional effects are important. In the past, streamline curvature effects were treated with the Boussinesq equations for the potential flow approach, thereby overlooking the real flow features. If friction is included, additional terms appear, because the specific energy variation along the undular jump is related to the boundary shear stress. However, these effects are neither addressed in the literature, nor compared with the classical Boussinesq-type solutions. Also, neither information on how boundary layer methods for adverse pressure gradients behave in undular flows is available, nor experimental data. Herein the frictional effects on the Boussinesq equations are systematically analysed using boundary layer methods for adverse pressure gradients. Based on these results, a new simplified approach is proposed to reasonably reproduce the oscillatory boundary layer characteristics in weakly undular hydraulic jumps under a steadily changing pressure gradient from adverse to favourable, and vice versa. [ABSTRACT FROM AUTHOR]

The Darcy-Weisbach equation was used in the analysis of flow over spillways, furnishing theoretical tools to design stilling basins. Predictions for the length of hydraulic jump stilling basins downstream of stepped and smooth spillways are presented, together with ranges of values for the Darcy-Weisbach friction factor of both spillways. The experimental data were compared with results of the theoretical solution of the gradually varied flow equation. All comparisons were made in non-dimensional form. The values of the Darcy-Weisbach friction factor were roughly five times smaller for smooth spillways than for stepped spillways. The theoretical predictions and the experimental data allow to present approximate equations for a preliminary evaluation of the length and the bed level of hydraulic jump stilling basins. In the same way, approximate equations were presented for the evaluation of the friction factor in smooth and stepped spillways, as a function of the Froude number at the downstream cross-section. [ABSTRACT FROM AUTHOR]

Universal probability density functions (PDFs) of two-dimensional turbulent velocity fluctuations, Reynolds shear stress and conditional Reynolds shear stresses in flows over smooth and rough beds are obtained using a Gram-Charlier series expansion based on the exponential distribution. To include skewness and kurtosis, the series is truncated up to moments of Order 4. The distributions of PDFs obtained theoretically and from the experimental data are in agreement. The conditional Reynolds shear stresses related to the ejections and sweeps are well represented by the exponential distribution, but those related to the outward and inward interactions depart from the theoretical distributions. [ABSTRACT FROM AUTHOR]

This note presents experimental measurements on the turbulence characteristics in the transition region from the end of a hydraulic jump to open channel flow in a rectangular channel. An acoustic Doppler velocimeter was used to measure mean velocities, turbulent intensities, Reynolds stress and turbulent kinetic energy for two supercritical Froude numbers. General correlations for the variation of the normalized maximum values of the Reynolds normal stresses as well as the shear stress and the turbulent kinetic energy have been developed, using the present results and those from the literature. The supercritical Froude number was found to be an effective scale in addition to the supercritical approach flow velocity in obtaining the general correlations. [ABSTRACT FROM AUTHOR]

The capability of Smoothed Particle Hydrodynamics (SPH) to reproduce a mobile hydraulic jump was investigated.A similar case was used to generate different upstream Froude numbers to obtain several jump shapes. A physical model was then constructed in a test flume to check the SPH outcomes. The results showed good agreement for Froude numbers <5. Higher Froude numbers require more sophisticated turbulence closure models to obtain better results. Good outcomes can be achieved with k-ε models, but the computational cost is higher than for basic SPH. Instead, a simple method was implemented to increase the viscosity in areas of higher vorticity. In this case, the main difference is related to the dependence of the viscosity on the vorticity. This approach yielded better adjustment. Finally, it was found that SPH provides correct estimates of the average pressures at the boundaries, but exhibits large dispersion for instantaneous water height values. This problem was considerably attenuated by introduction of a turbulence model. [ABSTRACT FROM AUTHOR]

The article reflects on two-dimensional physical model evaluating the effectiveness of baffles and sills along with its flow characteristics and energy dissipation. Topics discussed include hydraulic jump defined by total energy dissipation rate, energy dissipation rates causing formation of vortex zones and graphs representing several spillways. Also presented is a table featuring several abbreviations used for Sharp-stepped spillway, Rounded-stepped spillway and Sill-edged spillway.