Search

The formation conditions of maximum- and minimum-wave jumps were experimentally investigated. A total of 110 wave-type jump experiments were carried out for several discharges, supercritical upstream and subcritical downstream water depths and drop heights. The experimental results revealed that the influential parameters on wave-type jumps are the upstream Froude number and the relative drop height. As the classical hydraulic jump equation is not sufficient to define conjugate depths of wave-type flow, empirical equations were developed for defining the conjugate depths of maximum-wave jumps and minimum-wave jumps (for which insufficient experimental data are available in the literature). The agreement between calculated and measured conjugate depths was good. It was also found that the value of the lower limit for the upstream Froude number is not constant for the formation of a maximum-wave jump – it depends on the relative drop height. Furthermore, the experimental results showed that the energy-dissipation ratios of maximum- and minimum-wave jumps are equal to or larger than those of classical hydraulic jumps. For this reason, wave-type jumps may be preferred at stilling basins with drops along with A-jumps. [ABSTRACT FROM AUTHOR]

This work presents an experimental study of the fluctuating properties of hydraulic jump rollers for high-Froude-number and pre-aerated inflow conditions, to investigate the validity of empirical relationships in the literature that are derived typically from experiments for smaller Froude numbers and clear-water approach flows. The jump roller fluctuations are evaluated in terms of the dimensions of the roller surface profile, the fluctuation magnitudes and frequencies of the instantaneous jump toe positions and water elevations, including at the tailwater surface, and the formation frequency and advection velocity of internal vortices in the shear layer. The effects of pre-aeration are found primarily in the length-scale properties such as jump length and surface fluctuation magnitudes, while the time-scale properties such as characteristic frequencies of the unsteady motions are not affected. Extrapolation of existing quantitative prediction of jump roller dynamic properties to high-Froude-number flow conditions should be performed carefully. An assessment of the fluctuating bubble counts within fixed time intervals yields close frequencies between the bubble grouping motions in the shear layer and the jump toe and tailwater wave motions, thus implying possible correlations between the roller surface deformations and air entrainment. [ABSTRACT FROM AUTHOR]

Some basic characteristics of a classic hydraulic jump flow over a pebbled rough bed, as well as on a smooth bed as a reference, are presented in this experimental study. For the experiments, an inflow Froude number Fr1 from 1.54 to 4.94 and inflow Reynolds number Re1 from 42 000 to 230 000 were considered. Visual observations and measurements suggested some differences between the formation of a hydraulic jump on rough and smooth bed configurations, including different air entrainment processes, larger vortical structures in the roller length and stronger backward flow in the upper layer. Furthermore, the jump roller and aerated flow lengths were shorter on a pebbled rough bed than on a smooth bed, while the dimensionless advection velocity of large vortices was the same for both bed types. The instantaneous jump toe perimeter showed the largest variation at the largest Fr1 and was generally larger on rough bed than on smooth bed. Larger oscillations of the free-surface profile were observed on smooth bed, highlighting that roughness resulted in smaller free-surface oscillations, suggesting the higher rate of energy dissipation. [ABSTRACT FROM AUTHOR]

The present work studies the hydro-gasdynamic analogy between a shock wave, occurring in supersonic internal or external compressible flows, and a hydraulic jump, a sort of normal shock occurring in open-channel flows. It consists of an extensive theoretical framework followed by a practical analysis, the aim of which was to experimentally trigger the hydraulic jump, both normal and oblique, while using a low-cost designed lab prototype. The assembly development, called 'water table', arises from the necessity of economical alternatives to expensive supersonic wind tunnels in the experimental study of compressible fluid dynamics. With this objective in mind, a hydraulic canal based on a Laval nozzle was constructed where water flow could accelerate from subcritical to critical to supercritical regime and then return to subcritical regime through a hydraulic jump. In addition, multiple design alternatives were evaluated considering environmental, economic, functional and aesthetics factors. A low-cost implementation was the critical criterion in the design process. The measurements have revealed that the geometry of the nozzle and the wedges designed as obstacles to cause obliquity are the most significant and influential elements in the formation of a hydraulic jump in the experimental set-up. Regarding the experimental variables, the experiments demonstrate the effect of the upstream and downstream heights of the hydraulic jump in the data collection. This experience is a step forward in supporting students in the understanding of compressible flow and its principles by providing an in-house experimental set-up that promotes active learning, motivation and interest in fluid mechanics. [ABSTRACT FROM AUTHOR]

Air–water mixing associated with high turbulence is a common hydraulic phenomenon, where the transport of entrained air bubbles and the dissipation of turbulent energy are key processes affecting the air–water mass transfer. Herein hydraulic jumps were selected as a seminal case of self-air-entrainment in transitional water flow, and the air–water flow properties were investigated at high Froude numbers from 10.5 to 13.5. The analysis of air concentration distributions and bubble size spectra enabled deviation of the rates of bubble diffusion and turbulence dissipation. The study was facilitated with re-analyses of earlier experimental data for smaller Froude numbers between 3.8 and 10. The spatial evolution of the diffusion and dissipation rates suggested that the diffusion of air bubbles and dissipation of turbulent structures were not independent processes, and, at high Froude numbers, the mix of air and water was subject to re-aeration of the turbulent shear layer by the roller. [ABSTRACT FROM AUTHOR]

This document is a response to a previous article titled "Investigation of flow structure with moat acting as a water cushion at the toe of an overflowing levee." The response paper numerically investigates the effects of geometric parameters of the moat downstream of the overflowing levee on its hydraulic characteristics and energy reduction. The authors validate their model using the previous paper but argue that the validation is insufficient. They suggest that more information is needed to reach conclusions on the optimal geometric parameters. The publisher remains neutral on jurisdictional claims and institutional affiliations. [Extracted from the article]

Laboratory measurements of turbulence in submerged hydraulic jumps with blocks downstream of a sluice gate are presented. As observed previously two flow regimes were distinguished; the deflected surface jet (DSJ) and the reattaching wall jet (RWJ) regimes. In the DSJ regime considerable turbulent kinetic energy (TKE) was generated just downstream of the blocks and the rate of dissipation of TKE was found to be very high resulting in a rapid decay of TKE. In the RWJ flow regime the magnitude of both the TKE and the dissipation rate were considerably lower but because the TKE decayed more slowly higher levels of TKE persisted farther downstream. This study provides insights into the production and dissipation of turbulence in submerged flows and helps to explain why a submerged jump with blocks with a low submergence factor; i.e., the DSJ flow regime, is as effective as a free jump in dissipating energy. [ABSTRACT FROM AUTHOR]

Free surface, axially symmetric shallow flow is analyzed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterized by a unique value of specific energy, the analytical sub- and supercritical solutions are determined. Furthermore, the sub- and supercritical steady solutions for the flow with friction over a flat plate are determined, provided that inertial terms are important compared with frictional terms. In the inviscid case, the sub- and supercritical solutions over a bottom topography are determined, provided that the bottom unevenness is compatible with a continuous solution. In the fundamental case of inviscid flow over a flat plate, the discontinuous solution also is analyzed for a direct hydraulic jump imposed by proper boundary conditions. In the simple scheme of an inviscid shock of zero length, the jump position and the sequent depths are analytically derived, thus indicating that all results are uniquely functions of one dimensionless number, i. e., the specific energy ratio between the sub- and supercritical flows. [ABSTRACT FROM AUTHOR]

The heat transfer and fluid flow between a horizontal heated plate and impinging circular double jets were studied experimentally. The parameters investigated are the Reynolds number of each jet and jet-to-jet spacing. Experiments are carried out covering a range for Reynolds number from 7100 to 30,800 for each jet, the dimensionless jet-to-jet spacing from 22.73 to 90.1. During experimental phases, the right jet Reynolds number was higher than the left jet Reynolds number. The isothermal contours were plotted for different cases as well as the distribution of water film thickness over the heated plate. The results indicated that increasing the Reynolds number of one jet than the other increases both local and average Nusselt numbers. In addition, increasing the jet-to-jet spacing at the same Reynolds number increases the average Nusselt number. [ABSTRACT FROM AUTHOR]

In flows where the ratio of inertia to gravity varies strongly, large variations in the fluid thickness appear and hydraulic jumps arise, as depicted by Rayleigh. We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. The Bond number – which measures the importance of gravitational body forces compared to surface tension – must be small in order to observe such objects using capillarity as a driving force. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses, which dominate inertia, and capillary jumps should not be described by the inertial shock wave theory that one would deduce from Bélanger or Rayleigh for hydraulic jumps. In order to get rid of viscous shears, we consider Plateau borders, which are the microchannels defined by the merging of three films inside liquid foams, and we show that capillary jumps propagate along these deformable conduits. We derive a simple model that predicts the velocity, geometry and shape of such fronts. A strong analogy with Rayleigh’s description is pointed out. In addition, we carried out experiments on a single Plateau border generated with soap films to observe and characterize these capillary jumps. Our theoretical predictions agree remarkably well with the experimental measurements. [ABSTRACT FROM PUBLISHER]

The implementation of roughened channels with cross beams (RCCB) in drainage systems reduces the negative effects of high kinetic energy on flood flows, such as the increased erosion of infrastructures or of the ground. This paper aims to highlight the importance of using RCCB in drainage systems and to contribute to a better knowledge of flow characteristics in RCCB. The performance of RCCB was studied under diverse conditions through the use of a physical model in which several cross beams were installed with different thickness, longitudinal spacing between them, and at different heights. Results of free-surface profile, pressure head, and velocity measurements for different arrangements of slopes, cross-beam dimensions, and spacing were compared with the scarce data available in literature and put together to form empirical relations to predict flow characteristics in the engineering practice dealing with RCCB design, such as discharge limit, maximum flow, water depth, and friction factor. In particular, it shows that energy dissipation in roughened channels with cross beams increases approximately 30% in relation to channels where cross beams are not used. [ABSTRACT FROM AUTHOR]

An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady-state flow equation. It is established that the undular hydraulic jump phenomenon takes place because of the instability of the flow and can be described by the instability principle. The threshold of an undular hydraulic jump can be represented by a monotonic increasing curve of approaching flow Froude number versus boundary inclination. The elevation of the undular free surface increases with an increase in boundary inclination, but the amplitude of the free surface waves decreases with downstream distance. The theoretical results are well comparable with the experimental data. [ABSTRACT FROM AUTHOR]

An open channel flow with a flow depth close to the critical depth is characterised by a curvilinear streamline flow field that results in steady free surface undulations. Near critical flows of practical relevance encompass the undular hydraulic jump when the flow changes from supercritical (F > 1) to subcritical (F < 1), and the undular weir flow over broad-crested weirs where the flow changes from subcritical (F < 1) to supercritical (F > 1). So far these flows were mainly studied based on ideal fluid flow computations, for which the flow is assumed irrotational and, thus, shear forces are absent. While the approach is accurate for critical flow conditions (F = 1) in weir and flumes, near-critical flows involve long distances reaches, and the effect of friction on the flow properties cannot be neglected. In the present study the characteristics of near-critical free-surface flows are reanalysed based on a model accounting for both the streamline curvature and friction effects. Based on the improved model, some better agreement with experimental results is found, thereby highlighting the main frictional features of the flow profiles. [ABSTRACT FROM AUTHOR]

Abstract: It can be seen in the literature that the fundamental factors governing oblique shock wave development, typically in very large channels with straight sidewalls, have not yet been completely understood and remain at the level of indicating its presence and formation. In this study, in addition to an analysis of various properties of hydraulic jump behaviour in very large channels, some aspects of boundary layer development and its detachment from the channel lateral sidewall are also investigated. At the detachment point of the lateral shock waves, it was noted that the displacement thickness experiences a significant increase; this is accompanied by a significantly reduced gradient normal to the channel sidewalls of the flow velocity as well as the occurrence of a strong, sudden adverse pressure gradient. An analysis of the flow velocity distribution and the background turbulence intensity of both the streamwise and spanwise velocity components was also carried out. Furthermore, it is argued that the supersonic flow separation analogy with a supercritical free surface flow can be applied to this case study and that the behaviour of the supercritical flow during separation can be interpreted by the free interaction theory typically used in aerodynamics. [Copyright &y& Elsevier]

The gradually diverging stilling basin is attractive to the designer due to its compatibility with a large range of upstream and downstream sections, and to having a small sequent depth ratio and jump length. However, the hydraulic jump in such stilling basins often encounters instability and asymmetrical flow problems. In the present study, the effect of broad and sharp-crested sills in improving hydraulic jump characteristics, including sequent depth ratio, jump length and the free surface profile of a jump in a gradually diverging stilling basin was investigated. For this purpose, sills with various heights and different locations relative to the jump toe were installed in stilling basins with diverging angles of 3, 5 and 9°. In total, 284 tests were carried out in the range of initial Froude numbers of 3·1 to 10·4. The results indicate that the end sill has an insignificant effect on the sequent depth ratio, but it may considerably decrease the length of the hydraulic jump. It was also found that the sill could considerably improve the general conditions and features of an expanding hydraulic jump and could stabilise the position of this type of jump. [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]

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]

Hydraulic jumps in an inclined rectangular chute contraction were studied in this paper. Theoretical equations for the sequent-area and sequent-depth ratios for hydraulic jumps in the contraction were developed considering the effects of contracting width and sloping bottom. The equation of the sequent-area ratio (instead of the sequent-depth ratio) has the same form as the traditional Belanger equation for the sequent-depth ratio for hydraulic jumps in a horizontal rectangular constant-width channel (HRCW channel). A modified approach Froude number M, including the effects of contracting width and sloping bottom, was introduced to replace the approach Froude number F1 in analyzing hydraulic jumps in the contraction. Laboratory experiments of hydraulic jumps in inclined contractions were also conducted to verify the theoretical sequent-area ratio and also to develop the empirical equations of the location of the start of the jump, flow depth of the start of the jump, length of the jump, and energy loss of the jump. The calculation procedure for the application of the presented equations is also provided in this paper. [ABSTRACT FROM AUTHOR]

Hydraulic jumps on the steps of a stepped spillway were investigated analytically, physically, and numerically. Using classic hydraulic formulae, a conceptual prototype was designed. A large scale model was adapted and an experimental study was conducted to examine similarity of hydraulic jumps on each step, minimizing hydraulic jump length and maximizing discharge per unit width. A numerical model based on the 2D Reynolds averaged equations, where the free-surface is represented using a refined volume-of-fluid algorithm, the internal obstacles are described by means of the fractional area-volume obstacle representation method, and the turbulence is represented by a specially developed RNG (Renormalization Group) k-[variant_greek_epsilon] closure model was used for evaluating velocities and pressures, and for characterizing hydrodynamic forces on the baffles and sills. Preliminary design criteria are proposed for stepped spillways with hydraulic jump formation of simple shapes and adequate relations of critical depth/step height and the application of computational fluid dynamics to such problems is studied. [ABSTRACT FROM AUTHOR]

A tangential vortex intake is a compact structure that can convey storm water efficiently as a swirling flow down a vortex dropshaft. It has been studied in physical models and successfully employed in urban drainage and hydroelectric plant applications, but a comprehensive account of the key flow characteristics has not been reported and a theoretical design guideline of a tangential intake is not available. In this study the hydraulics of tangential slot vortex intakes is investigated via extensive experiments. It is found that the flow in the tapering and downward sloping vortex inlet channel is strongly dependent on the geometry of the inlet and dropshaft. Under some conditions, hydraulic instability and overflow can occur, rendering the design ineffective. It is shown that the hydraulic stability depends on the discharge at which flow control shifts from upstream to downstream (Qc), as well as the free drainage discharge (Qf). A theoretical design criterion for stable flow is developed in terms of Qf and Qc as a function of the vortex inlet geometry. For a “stable” design, the flow in the tapering inlet evolves from supercritical flow to subcritical flow smoothly as the discharge increases. Fifteen different tangential vortex intake models are tested. The experimental observations are in excellent agreement with the theoretical prediction. The present study provides a general guideline for designing a tangential vortex intake that can convey the flow smoothly without unstable fluctuating flow associated with a hydraulic jump. [ABSTRACT FROM AUTHOR]

The present work attempts to investigate the effects of jet obliquity on the spatial patterns formed as a consequence of hydraulic jumps due to the impingement of circular liquid jets on continuously moving but nonaccelerating horizontal flat plates. Both the normal and the oblique impinging jets are considered, in order to characterize the contrasting features of the associated hydraulic jump mechanisms. Theoretical calculations are executed to obtain the locations of the jump, for different jet and plate velocities and jet inclination angles, using a depth-averaged momentum integral equation for shallow-free surface flows. Comparisons are subsequently made between the theoretical predictions and experimental observations reported in the literature, and a good agreement between these two can be observed. Special cases of a circular hydraulic jump when the target plate is stationary and the impinging jet is vertical, and elliptic hydraulic jumps when the target plate is stationary and the impinging jet is obliquely inclined, are also discussed. It is conjectured that flow due to impinging jets on a horizontal moving plate can be modeled as an equivalent flow due to an inclined impinging jet on stationary horizontal flat plates, with appropriate alterations in the jet velocity and the jet inclination angles. [ABSTRACT FROM AUTHOR]

We present a study of hydraulic jumps with flow predominantly in one direction, created either by confining the flow to a narrow channel with parallel walls or by providing an inflow in the form of a narrow sheet. In the channel flow, we find a linear height profile upstream of the jump as expected for a supercritical one-dimensional boundary layer flow, but we find that the surface slope is up to an order of magnitude larger than expected and independent of flow rate. We explain this as an effect of turbulent fluctuations creating an enhanced eddy viscosity, and we model the results in terms of Prandtl's mixing-length theory with a mixing length that is proportional to the height of the fluid layer. Using averaged boundary-layer equations, taking into account the friction with the channel walls and the eddy viscosity, the flow both upstream and downstream of the jump can be understood. For the downstream subcritical flow, we assume that the critical height is attained close to the channel outlet. We use mass and momentum conservation to determine the position of the jump and obtain an estimate which is in rough agreement with our experiment. We show that the averaging method with a varying velocity profile allows for computation of the flow-structure through the jump and predicts a separation vortex behind the jump, something which is not clearly seen experimentally, probably owing to turbulence. In the sheet flow, we find that the jump has the shape of a rhombus with sharply defined oblique shocks. The experiment shows that the variation of the opening angle of the rhombus with flow rate is determined by the condition that the normal velocity at the jump is constant. [ABSTRACT FROM AUTHOR]

Abstract: SERR-1D is a 4th-order finite volume 1D Boussinesq model including wave breaking energy dissipation through extra diffusive-like terms. This model has been primarily conceived to compute wave propagation in coastal areas and has been validated for breaking and non-breaking waves propagating over uneven bathymetries (Cienfuegos et al., 2005, 2006a, b, 2007). The present paper aims at investigating the ability of SERR-1D to simulate challenging fluvial hydraulic applications such as sudden gate operation in open channels generating short waves, dam-break flows and a steady hydraulic jump over a bump. The performance of the absorbing-generating boundary condition implemented in SERR-1D is first analysed in the context of fluvial applications where relatively short waves must be evacuated from the computational domain without producing spurious reflection. Next, by comparing numerical results to analytical and experimental dam-break test cases we show that the model is able to reproduce the overall features of these flows, but that additional care should be paid to the representation of energy dissipation and front speed in order to accurately represent bore dynamics. [Copyright &y& Elsevier]

Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoretical predictions, with finite-amplitude internal hydraulic jumps and overturning forming during strong offslope tidal flow over steep slopes. These results suggest that internal hydraulic jumps may be an important mechanism for local tidally generated mixing at tall steep topography. [ABSTRACT FROM AUTHOR]

Abstract: Oblique impingement of a circular liquid jet with a horizontal target gives rise to hydraulic jumps of unique no-circular shapes. Hydrodynamics of this phenomenon have been experimentally investigated in the present work. Hydraulic jumps of two broad categories have been observed. At higher angles of jet inclination, the jumps are bounded by a smooth curve. However, at lower angles of inclination, typical jump profiles with corners have been observed. Effect of jet inclination angle on jump the profile and jump area has been investigated. Measurements of stagnation pressure and film thickness for different jet inclination angles and volume flow rates of liquid are reported. Film thickness measurements are made using an innovative cylindrical conductive probe, at the forward (θ = π) and backward (θ =0) radial locations, for regions both before and after the jump. The striking difference between the non-circular and circular hydraulic jumps is also critically assessed. [Copyright &y& Elsevier]

Similarity law is the conversion rule between model and prototype, on which a lot of research works have been done, with no agreement reached referring to the similarity law of fluctuating pressure frequency spectrum. Experimental data of peak frequency and dominant frequency range of fluctuating pressure spectrum beneath hydraulic jump obtained from serial models of scales 1:1, 1:2 and 1:5 are compared. As a result, similarity law of fluctuating pressure spectrum in the strongly rolling area agrees with the gravity law. As peak frequency and dominant frequencies of fluctuating pressures in hydraulic jump, toe and tail are rather low, and the similarity is often misunderstood to be λt = 1. However, the normalized spectrums of fluctuating pressures show that the similarity nearly agrees with the gravity law. [ABSTRACT FROM AUTHOR]

This study presents a novel, simple, but rather accurate approximation of the eigenvalues of the system formed by the Saint-Venant–Exner equations, based on the comparison between eigenvalues for the complete system and eigenvalues for the water phase only. Moreover, a strategy is proposed to compute efficiently the intercell fluxes by properly adapting a Harten, Lax, and van Leer scheme for each equation. Two examples of transient transcritical flows are developed: the erosive migration of a knickpoint induced by an increase in the bed slope, and the evolution of a hydraulic jump over a mobile bed. [ABSTRACT FROM AUTHOR]

This paper describes the flow structures that occur in a 90° junction of four open channels with supercritical flow in two orthogonal inlet channels. An experimental facility was constructed to permit the measurement of flow rates, water depths, and the positions of hydraulic jumps in the channels. The various flow patterns which appear depend on the characteristics of the incoming flows and can be classified into three main types, depending on the location and shape of the hydraulic jumps that develop. These jumps can either be normal to the flow and located in the upstream channels, or can be oblique and confined within the junction. The explanation for the existence of various flow patterns is derived from previous studies of the rapid deflection of supercritical flow. A detailed description of each flow regime is provided, with information on the surface elevations, the behavior of the hydraulic jumps, the deflections of the incoming flows, and the formation and characteristics of recirculation zones. [ABSTRACT FROM AUTHOR]

The technique and the results of an experimental investigation of the longitudinal force component and the vertical coordinate of the point of its application when bore-type waves impinge on a vertical cylinder are presented. The bore was generated by removing a vertical gate providing a difference of free surface levels in a channel with a smooth horizontal bottom. It was found that the presence of a free surface in the incident flow has a considerable effect on the force and its moment about the channel bottom. [ABSTRACT FROM AUTHOR]

The issue of the bed friction effect on the stability of a stationary hydraulic jump in a rectangular upward sloping channel is investigated through a combined theoretical and experimental approach. The theoretical stability criterion proposed by Defina and Susin [Phys. Fluids 15, 3883 (2003)] is generalized to include rough wall flows. The results of an extensive series of experiments are then presented. The adopted experimental procedure is detailed, and results are compared with theoretical predictions. It is shown that the proposed stability criterion successfully predicts both the stable and unstable behavior of the jump for smooth and rough wall flow, at least in the range of small upward bottom slopes. [ABSTRACT FROM AUTHOR]

A fuzzy logic model was constructed to predict hydraulic jump aeration efficiency. Fuzzy subsets and rules were created based on experimental observations and measurements carried out in a 0.5m wide flume with upstream Froude and Reynolds numbers of 2·3-6·4 and 1·4-5·4 × 104, respectively. A strong correlation was found between the aeration efficiency and Froude number. Upstream Froude and Reynolds numbers were selected as input parameters for the model. In this study, rather than mathematical equations, linguistic expressions were used to relate the upstream Froude and Reynolds numbers with aeration efficiency in an IF-THEN format. The proposed fuzzy model made good predictions and captured the system dynamic behaviour. Experimental observations confirmed the fact that hydraulic jump can be used as an aerator and mixing device in water treatment plants. Estimation of the aeration efficiency of a hydraulic jump could be made by any designer with the help of the fuzzy logic procedure described in this paper. [ABSTRACT FROM AUTHOR]

This paper presents the results of an experimental investigation on the hydraulic jump on horizontal rough beds. Experiments were carried out to study the effect of bed roughness on both the sequent depth ratio and the roller length. The investigation allowed the writers to positively test the reliability of a new solution of the momentum equation for the sequent depth ratio as a function of the Froude number and the ratio between the roughness height and the upstream supercritical flow depth. The applicability of some empirical relationships for estimating the roller length was also tested. [ABSTRACT FROM AUTHOR]

A three-dimensional (3D) study of spatial submerged hydraulic jumps (SSHJs) was carried out using a physical model for Froude numbers Fr1 = 2.00 and 3.75 and width ratios α = 0.20 and 0.33. Three orthogonal components of the velocity field were obtained with an acoustic Doppler velocimeter (ADV). The 3D velocity field has indicated that the jump consisted of a central jet-like flow, close to the channel bottom, surrounded by vertical and horizontal circulations (rollers). The circulation was predominantly in vertical planes in the channel central region of the flow and in horizontal planes close to the walls. Vertical and horizontal profiles of stream-wise velocity characterized the 3D roller with two length scales, Lrv and Lrh. The strength of the roller was stronger close to the walls than at the centreline of the jump. Sequent depth and energy head loss for submerged symmetric hydraulic jumps are discussed in terms of the submergence ratio S = y3/y2. [ABSTRACT FROM AUTHOR]

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves, and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in a rectangular horizontal flume with partially developed inflow conditions. The vertical distributions of the void fraction and the air bubbles count rate were recorded for inflow Froude number Fr 1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction C max increases with the increasing Fr 1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was derived. [ABSTRACT FROM AUTHOR]

A Godunov-type upwind finite volume solver of the non-linear shallow water equations is described. The shallow water equations are expressed in a hyperbolic conservation law formulation for application to cases where the bed topography is spatially variable. Inviscid fluxes at cell interfaces are computed using Roe's approximate Riemann solver. Second-order accurate spatial calculations of the fluxes are achieved by enhancing the polynomial approximation of the gradients of conserved variables within each cell. Numerical oscillations are curbed by means of a non-linear slope limiter. Time integration is second-order accurate and implicit. The numerical model is based on dynamically adaptive unstructured triangular grids. Test cases include an oblique hydraulic jump, jet-forced flow in a flat-bottomed circular reservoir, wind-induced circulation in a circular basin of non-uniform bed topography and the collapse of a circular dam. The model is found to give accurate results in comparison with published analytical and alternative numerical solutions. Dynamic grid adaptation and the use of a second-order implicit time integration scheme are found to enhance the computational efficiency of the model. [ABSTRACT FROM AUTHOR]

A large variety of hydraulic jumps on horizontal and sloping inverts at the end of an ogee standard weir is investigated. An ogee standard weir was used to create supercritical flow and slopes of 0.0, -0.025, -0.05, -0.075, and -0.10 were built downstream of the weir. Based on the momentum equation in the horizontal direction, a method to predict the sequent depth ratio is presented. The theory agrees well with the results of the writers and previous investigators. A correlation was developed to predict the minimum Froude number needed to establish jumps on negative slopes. Observations showed that in those cases where the gravity force component in the jump was opposite to the flow direction, the water surface of the surface roller became undular and unstable. The hydraulic jump on an entirely adverse slope was almost impossible to control. The analysis of experimental data showed that the negative slope of the basin reduces the sequent depth ratio, while a positive slope increases the sequent depth ratio. [ABSTRACT FROM AUTHOR]

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6 H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l M / H, regardless of downstream control. The near field jet stability criterion is determined to be l M / H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators. [ABSTRACT FROM AUTHOR]

In this work, is carried out a hydrodynamic study of the operation of the experimental channel of the Center of Hydraulics Research (CIH), taking into account the occurrence of certain local phenomena (hydraulics fall and hydraulic jump). Special attention is paid to the flow resistance of the conduction, being valued the results of precedent investigations. The authors introduce a law of specific resistance for all the length of the channel and validate a model of non stationary flow in this installation, which is based on the equations of Saint Venant, which are resolved with the method of the finite elements, according to the strategy of Szymkiewicz. [ABSTRACT FROM AUTHOR]

A theory presented previously by the writer explained the asymmetric flow patterns occurring in symmetric rectangular expansions with subcritical flow. The theory is extended in the present paper to supercritical flows, in which the hydraulic jump is one of the flow features. The theory is shown to agree with available observations. Transverse oscillatory conditions are discussed in terms of a dynamic instability that can accompany static stability. The ranges for which experimental data are available with which to test the theory are identified, making it apparent where additional data would be useful for the full range of the problem. The phenomenological understanding provided by the present paper is important to the development of stabilization measures. In addition to stabilization by submergence, the hydraulic jump should be amenable to stabilization by other referenced methods, including various vane configurations and pipe communication between the eddy regions. [ABSTRACT FROM AUTHOR]

This study investigates energy dissipation due to air bubble entrainment for three typical phenomena; a hydraulic jump, a 2-D vertical plunging jet and a vertical circular plunging jet into water. A simple model is presented here which enables to estimate the energy transformation and dissipation achieved by air bubbles quantitatively for three above phenomena. The average rate of energy dissipation by air bubbles obtained from the experimental data are 25%, 1.4%, and 2.15% with respect to total energy loss for the hydraulic jump, 2-D vertical plunging jet and vertical circular plunging jet, respectively. [ABSTRACT FROM AUTHOR]

The energy-momentum (E-M) method for calibrating submerged radial gates was refined using a large laboratory data set collected at the Bureau of Reclamation hydraulics laboratory in the 1970s. The original E-M method was accurate in free flow, and when the gate significantly controls submerged flow, but for large gate openings with low head loss through the gate, discharge prediction errors were sometimes large (approaching 70%). Several empirical factors were investigated with the laboratory data, including the combined upstream energy loss and velocity distribution factor and the submerged flow energy correction. The utility of the existing upstream energy loss and velocity distribution factor relation was extended to larger Reynolds numbers. The relation between the relative energy correction and the relative submergence of the vena contracta was shown to be sensitive to the relative jet thickness. A refined energy correction model was developed, which significantly improved the accuracy of submerged flow discharge predictions. Although the focus of this work was radial gates, the energy correction concept and these refinements potentially have application to all submerged sluice gates. [ABSTRACT FROM AUTHOR]

A numerical model is developed for solving the depth-averaged, open-channel flow equations in generalized curvilinear coordinates. The equations are discretized in space in strong conservation form using a space-centered, second-order accurate finite-volume method. A nonlinear blend of first- and third-order accurate artificial dissipation terms is introduced into the discrete equations to accurately model all flow regimes. Scalar- and matrix-valued scaling of the artificial dissipation terms are considered and their effect on the accuracy of the solutions is evaluated. The discrete equations are integrated in time using a four-stage explicit Runge–Kutta method. For the steady-state computations, local time stepping, implicit residual smoothing, and multigrid acceleration are used to enhance the efficiency of the scheme. The numerical model is validated by applying it to calculate steady and unsteady open-channel flows. Extensive grid sensitivity studies are carried out and the potential of multigrid acceleration for steady depth-averaged computations is demonstrated. [ABSTRACT FROM AUTHOR]

Ski jumps are a major element of each dam spillway because these are the only structures able to accomplish satisfactory energy dissipation for takeoff velocities in excess of some 20 m/s. This research aims to add to several hydraulic problems with ski jumps that have not yet been systematically solved so far. Based on an experimental campaign, the following problems were addressed: (1) pressure head maximum and pressure distribution along a circular-shaped flip bucket; (2) takeoff characteristics for a certain bucket deflection and a relative bucket curvature including the jet trajectories of both the lower and the upper nappes; (3) impact characteristics in a prismatic tailwater channel with details of shock wave formation and height of recirculation depth; (4) energy dissipation across the ski jump, from the upstream channel to downstream of jet impact; and (5) choking flow conditions by the flip bucket. These results demonstrated the significant effect of the approach Froude number, the relative bucket curvature and the bucket angle. The results allow immediate application to the design of ski jumps in hydraulic engineering. [ABSTRACT FROM AUTHOR]