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This study employs an explicit scheme of solving the pressure Poisson equation based on the moving particle semi-implicit (MPS) method to simulate forced hydraulic jumps on different slopes. To accurately calculate velocity, a mixed source term is used in the discretized pressure Poisson equation. The mesh-free model is validated to simulate a forced hydraulic jump on a slope, and the free surface and velocity profiles are reproduced. The numerical model is then implemented to simulate the forced hydraulic jumps by varying the channel slope, inlet velocity, and height of the bottom sill. The free surface and velocity profiles in the flows are investigated and the effect on the forced hydraulic jumps by the Froude number and height of the sill are analyzed. The developing process of the hydraulic jumps including developing flow patterns and eddy formation is analyzed. It is found there are four flow stages in the developing process of the flow. [ABSTRACT FROM AUTHOR]

The three-dimensional MITgcm (MIT general circulation model) was applied to simulate wind-induced baroclinic oscillations in Cayuga Lake, to obtain an understanding of the internal seiche/surge dynamics and associated mixing in long narrow lakes. The MITgcm has not been rigorously validated for closed basins against field observations. Thus, qualitative and quantitative methods were used to validate the model and study the sensitivity to different model parameters against observed temperature data. The linear equation of state (EoS) yielded poor results, in comparison to the polynomial EoS formulations where the density gradient was large. The vertical density stratification was strongly sensitive to the background vertical viscosity and diffusivity (when > 10–5 m2s−1), because the prescribed background values control mixing in the KPP scheme, except on the surface and bottom boundary layers. After calibration, the model correctly simulated the vertical stratification, upwelling, basin-scale seiche (with a horizontal mode-one period T1 = 80 h) and surge formation with a basin-wide root-mean-square-error 1.9 °C. Flow visualization indicated that internal surges evolved due to (i) a wind-induced locally downwelled thermocline (wind duration < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (wind duration > T1/4) and (iii) internal hydraulic jumps. Article Highlights: The MITgcm was extensively validated against field data in simulation of Cayuga Lake A polynomial equation-of-state and space–time variable turbulence closure scheme were applied Three distinct processes were found to generate internal surges [ABSTRACT FROM AUTHOR]

The kilometer-long sub-surface mooring 'KmT', densely instrumented with 760 high-resolution temperature 'T-'sensors, demonstrates details of turbulent mixing in the vicinity of a large seamount. Away from the internal wave breaking zone above the seafloor, turbulence is observed in two cases. It is found in thin layers along isopycnals providing non-smooth dispersal, as well as induced by internal wave breaking following strongly non-linear interaction as in a hydraulic jump more than 500 m above the local seafloor. Turbulence levels for these cases are relatively low and high, respectively, but always one to two orders of magnitude larger than in the ocean interior far from topography. Both cases imply the importance of underwater topography like a seamount for deep-sea turbulence. The seamount functions as a lens focusing internal waves into a turbulence-generator. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the physical features of hydraulic jump oscillations at an abrupt drop with high Froude numbers reaching values up to 9.92. In order to emphasize the importance of the bottom shape, different relative step heights in the range between 0.9 and 3.4 have been analysed, leading to the occurrence of different jump regimes (A-wave, A-jump, B-wave and B-jump). For the case of the B-jump type, the jump toe is drifted downstream when the Froude number increases. For the A-jump type with high Froude, the surface roller is made up of an increasing several number of vortices and thus the jump toe is drifted upstream, when the Froude number increases. In particular, for the case of the A-jump type at the highest simulated Froude number, when the toe of the jump is at its most upstream location, the maximum number of anticlockwise vortices (with decreasing sizes) is observed. At the same time, the turbulence levels decrease much faster due to the dominance of viscous forces at the small scales. Instead, when the toe of the jump is moving downstream, the neighbouring vortices tend to influence each other with their rotation and to coalesce into one larger vortex and the turbulence levels increase rapidly due to the dominance of inertial forces. A statistical analysis indicates that turbulent pressure fluctuations increase rapidly from the toe of the jump and reach a peak in the roller region, downstream of which they decrease again. The structure of the turbulent pressure fluctuations depends on the Froude number. [ABSTRACT FROM AUTHOR]

The principle theme of this study is to introduce a novel countermeasure to reduce the energy of the overflowing floodwater by utilization of a water cushion. For this purpose, laboratory experiments including "LW" cases (levee with water cushion) and "OL" cases (only levee) were conducted to elucidate the role of a water cushion in the flow structure variation after a levee is overflowed and to reduce energy. A moat (a deep and wide trench) with varying non-dimensional length (Lm* = Lm/hL; Lm is the length of the moat where hL is the levee height) and depth (Dm* = Dm/hL; Dm is the moat depth) acting as a water cushion was provided at the toe of a levee with varied landward slopes (SL). The energy reductions in the LW and OL systems were found to be very close to each other at lower overflow water depths, while it was 25% greater in the LW system than in the OL system at higher overflow water depths. Changes in the landward slope (SL) of the levee, non-dimensional length (Lm*), and depth (Dm*) of moat significantly changed the flow structure and created six different flow structures. However, 1–6%, 1–3%, and 1–5% differences in energy reduction rate were observed by varying SL, Lm*, and Dm*, respectively, in LW cases. All flow structures contributed greatly to energy reduction, but the energy reduction rate was maximum in flow structure named as T-2. Flow structures named as T-2 and T-6 are preferable due to increased water depth inside the moat and presence of submerged hydraulic jump which can be achieved during landward slopes SL = 1:1, 1:2 and by decreasing Lm* Dm*, of moat during Landward slope SL = 1:3. Article Highlights: The water cushion function of moat was utilized at toe of overflowing levee. The effect of different non-dimensional overflow water depths, non-dimensional length, depth of moat and varying landward slope of levee on flow structure was investigated. Different flow structure was classified based on non-dimensional length and depth of moat. Relation between flow structure and energy reduction rate was investigated. [ABSTRACT FROM AUTHOR]

Hydraulic jumps are commonly employed as energy dissipators to guarantee long-term operation of hydraulic structures. A comprehensive and in-depth understanding of their main features is therefore fundamental. In this context, the current study focused on hydraulic jumps with low Froude numbers, i.e. Fr1 = 2.1 and 2.4, at relatively high Reynolds number: Re ~2 × 105. Experimental tests employed a combination of dual-tip phase-detection probes and ultra-high-speed video camera to provide a comprehensive characterisation of the main air-water flow properties of the hydraulic jump, including surface flow features, void fraction, bubble count rate and interfacial velocities. The current research also focused on the transverse distributions of air-water flow properties, i.e. across the channel width, with the results revealing lower values of void fraction and bubble count rate next to the sidewalls compared to the channel centreline data. Such a spatial variability in the transverse direction questions whether data near the side walls may be truly representative of the behaviour in the bulk of the flow, raising the issue of sidewall effects in image-based techniques. Overall, these findings provide new information to both researchers and practitioners for a better understanding of the physical processes inside the hydraulic jump with low Froude numbers, leading to an optimised design of hydraulic structures. Article Highlights: Experimental investigation of air-water flow properties in hydraulic jumps with low Froude numbers Detailed description of the main air-water surface features on the breaking roller Transversal distribution of the air-water flow properties across the channel width and comparison between centreline and sidewall. [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]

A hydraulic jump forming in the stilling basin at the base of a high-head dam spillway is often characterized by high Froude number and inflow pre-aeration conditions. Although the air entrainment in hydraulic jump has been studied extensively, the effects of the inflow pre-air-entrainment on the downstream air–water flow properties and energy dissipation performance have not been investigated systematically, especially for high-Froude-number cases. This paper presents a comparative study of the pre-aeration effects on the air–water flow characteristics of high-Froude-number hydraulic jumps. Two pre-aeration levels were achieved using a smooth sloping chute and a ramp aerator on the chute. Apart from the change in jump length required for the same amount of energy dissipation, the major impact of the variation in pre-aeration was observed for the void fraction and air entrainment flux within the jet-shear region, whereas the bubble count rate and interfacial velocity were less affected. Differences were also observed from the prediction of previous studies under smaller Froude number and negligible pre-air-entrainment conditions. The pre-air-entrainment was found to affect the scale effects on the bubble counts and the interfacial area between air and water phases. This study may facilitate a bridging between the laboratory findings and the cases closer to the real engineering application of large-scale hydraulic jumps. [ABSTRACT FROM AUTHOR]

Partially filled pipes have many applications in hydraulic and environmental engineering; such as sewer and storm water collection pipes and circular culverts. Hydraulic jump can lead to scouring at hydraulic structures and thus excess energy should be dissipated to prevent scour and erosion. Calculation of conjugate depths in circular pipes and culverts is important in hydraulic engineering. The conjugate flow depths are commonly used to estimate the length of the hydraulic jump and the energy loss in the jump. Available relationships to estimate the conjugate depths in circular pipes are not accurate and wide application range. In comparison to easily available numerical solutions, a closed-form solution is a function of all input independent variables; and thus the dependence of the conjugate depth on each input independent variable can be easily interpreted. This study presents explicit solutions for the conjugate depths (pre- and post-jump depths) in partially filled pipes. The proposed solutions are examined over a wide range of the Froude number and geometric conditions, providing satisfactory estimations when compared with the exact solution obtained from the specific force relation. If the prejump flow depth of the hydraulic jump is known, the postjump flow depth can be determined using the proposed solution with a maximum relative error less than 1.4%. Inversely, if postjump flow depth is known, the prejump flow depth can be determined with a maximum relative error less than 2.3%. The proposed direct solutions are general, accurate, simple, and useful for studying the partially filled circular open channels. [ABSTRACT FROM AUTHOR]

The aim of the present study is to numerically investigate the scouring phenomenon downstream of a stilling basin for a wide range of Froude number and size of bed material. The numerical model was first verified. The results obtained from the numerical model concerning the maximum depth and profiles of the scoured hole were in agreement with the long-term experimental data. Thereupon, the verified numerical model was employed to simulate the profile of the scour hole for various Froude numbers and bed material sizes downstream of the stilling basin. According to the results of the numerical model as well as experimental data, it was revealed that by using dimensionless scour depth, the upstream profile of the scour hole is independent of time and size of the material. Results show that the bottom of the scour hole in the oscillating jump is of greater length than the steady jump. Moreover, both the numerical and available experimental data were used to propose a relationship for calculation of long-term maximum scour depth in a wide range of affecting parameters. Article highlights: Scour hole depth and geometry downstream of a stilling basin were studied with a verified numerical model. Numerical simulations were made in a wide range of Froude number and bed material size which were not available in the literature. Using available experimental data and numerical model results, an equation was developed for estimating the scour depth. [ABSTRACT FROM AUTHOR]

In plunging jets and at hydraulic jumps, large amounts of air bubbles are entrained at the impingement of the liquid jet into the receiving body. Air is entrapped and advected into a turbulent shear layer with strong interactions between the air bubble advection process and momentum shear flow. In this new physical study, air–water flow measurements were systematically repeated with identical inflow length, inflow depth and inflow velocity in a vertical supported jet (PJ) and a horizontal hydraulic jump (HJ). Detailed measurements were conducted with the same instrumentation. Both similarities and differences were observed between the two multiphase gas–liquid shear flows. Visual observations showed a key difference in the outer region, with a buoyancy-driven flow in the plunging jet with negligible void fraction, versus a strong recirculation motion with uncontrolled interfacial aeration in the hydraulic jump. Differences were also observed at the impingement perimeter, in terms of fluctuation frequencies and amplitudes, for identical inflow conditions. Both flow conditions yielded intense local singular air entrainment and close results were observed in terms of void fraction, bubble count rate, bubble chord sizes and interfacial area in the shear layer, in both the plunging jet and hydraulic jump. The transfer of momentum between impinging jet and receiving water, as well as the effect of buoyancy, were however affected by the flow geometry. [ABSTRACT FROM AUTHOR]

The present paper analyses the advantages and limitations of using numerical modelling to simulate hydraulic jumps at high Froude numbers. Two hydraulic jumps of the same Froude number (7.5) but different Reynolds numbers were simulated using Improved Delayed Detached Eddy Simulation. The free surface was captured using the Volume of Fluid multiphase model with a High-Resolution Interface-Capturing technique. Flow properties including velocity, total pressure and air concentration profiles were compared with experimental results at different streamwise locations. It was observed that while the simulations were able to accurately capture the velocity and pressure fields, the air concentration values were over predicted, although the air concentration distribution was successfully reproduced. Since the simulations capture the complete three-dimensional flow field, further analysis of different physical mechanisms contributing to air entrainment are also carried out. The turbulent kinetic energy and the vorticity field were examined to understand the air–water flow dynamics. The coherent structures responsible for air entrainment were identified using vortex identification techniques. The influence of these structures on the air-entrainment mechanisms is presented with pertinent discussions. [ABSTRACT FROM AUTHOR]

In the present work, oscillating characteristics and cyclic mechanisms in hydraulic jumps are investigated and reproduced using a weakly-compressible XSPH scheme which includes both an algebraic mixing-length model and a two-equation turbulence model to represent turbulent stresses. The numerical model is applied to analyze oscillations of different hydraulic jump types based on the laboratory experiments. The comparison between SPH and experimental results shows an influence of different turbulence models on the amplitude spectrum and peak amplitude of the time-dependent surface elevation upstream and downstream of the hydraulic jump. By analyzing a single cycle of the oscillating phenomena of a hydraulic jump it is possible to indicate their correlation with the vortex structures of the roller. Furthermore, analysis of the oscillating phenomena indicates a correlation among the surface profile elevations, velocity components and pressure fluctuations. This observation leads to conclude that oscillations phenomena are particularly important for analysis of the turbulence characteristics. [ABSTRACT FROM AUTHOR]

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier-Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k-ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon. [ABSTRACT FROM AUTHOR]

A numerical model was developed based on a moving grid method for simulating three-dimensional turbulent flows affected by curvilinear free surface. Reynolds-Averaged Navier-Stokes equations with the k-ε turbulence model were solved in non-orthogonal curvilinear coordinates. In the free surface, the kinematic boundary condition was implicitly imposed in the pressure Poisson equation derived from the momentum and continuity equations. The water surface elevation was calculated at each time step without solving additional equations. The developed numerical model was validated using the experimental data of the strongly curved channels and submerged hydraulic jump. The numerical simulation of the flow field and free surface elevation in all cases were compared with the experimental results. The agreement between the simulated and measured results was satisfactory for three-dimensional turbulent flows in the strongly curved channels and submerged hydraulic jump. The secondary flow and dip phenomena were correctly simulated in strongly curved channels. This numerical model could accurately predict steep water surface gradients in a submerged hydraulic jump. The reasonable results of the numerical simulation demonstrate the capability of the presented Lagrangian method in hydraulic engineering applications. This model provides a suitable method for simulating the free surface in engineering and environmental problems. [ABSTRACT FROM AUTHOR]

A hydraulic jump is a turbulent shear flow with a free-surface roller. The turbulent flow pattern is characterised by the development of instantaneous three-dimensional turbulent structures throughout the air-water column up to the free surface. The length and time scales of the turbulent structures are key information to describe the turbulent processes, which is of significant importance for the improvement of numerical models and physical measurement techniques. However, few physical data are available so far due to the complexity of the measurement. This paper presents an investigation of a series of characteristic turbulent scales for hydraulic jumps, covering the length and time scales of turbulent flow structures in bubbly flow, on free surface and at the impingement point. The bubbly-flow turbulent scales are obtained for Fr = 7.5 with 3.4 × 10 < Re < 1.4 × 10 in both longitudinal and transverse directions, and are compared with the free-surface scales. The results highlight three-dimensional flow patterns with anisotropic turbulence field. The turbulent structures are observed with different length and time scales respectively in the shear flow region and free-surface recirculation region. The bubbly structures next to the roller surface and the free-surface fluctuation structures show comparable length and time scales, both larger than the scales of vortical structures in the shear flow and smaller than the scales of impingement perimeter at the jump toe. A decomposition of physical signals indicates that the large turbulent scales are related to the unsteady motion of the flow in the upper part of the roller, while the high-frequency velocity turbulence dominates in the lower part of the roller. Scale effects cannot be ignored for Reynolds number smaller than 4 × 10, mainly linked to the formation of large eddies in the shear layer. The present study provides a comprehensive assessment of turbulent scales in hydraulic jump, including the analyses of first data set of longitudinal bubbly-flow integral scales and transverse jump toe perimeter integral scales. [ABSTRACT FROM AUTHOR]

A physical study of hydraulic jump is often undertaken using down-scaled Froude-similar models with Reynolds numbers much smaller than in prototype (e.g. spillway stilling basins). The potential viscous scale effects may affect a number of physical processes including turbulence development and air entrainment, thus challenging the extrapolation of laboratory data to the prediction of prototype conditions or justification of numerical modelling. This paper presents an experimental study of hydraulic jumps with a particular focus on the scale effects in terms of free-surface fluctuation and deformation, bubble advection and diffusion, bubble-turbulence interaction and turbulence dissipation. A broad range of free-surface, air-water flow and turbulence properties were measured systematically for Froude numbers from 3.8 to 10 and Reynolds numbers from 2.1 × 10 to 1.6 × 10. Based upon self-similarities in the longitudinal evolution of a number of characteristic flow properties, the analytical expressions of time-averaged roller surface profile, void fraction distribution and longitudinal velocity distribution were derived for given Froude number. The roller surface dynamics were found free of scale effects in terms of fluctuation amplitudes but the characteristic frequencies were scale-sensitive. While some air-water flow parameters such as bubble count rate, bubble chord time distribution and bubble grouping behaviour could only be correctly quantified at full-scale prototype conditions, the aeration level and turbulent scales might be estimated with satisfactory accuracy for engineering applications given a model Reynolds number no less than 4 × 10 to 6 × 10. [ABSTRACT FROM AUTHOR]

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air-water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < L/d < 0.8 in the shear layer, where L is the integral turbulent length scale and d the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations. [ABSTRACT FROM AUTHOR]

A positive surge results from a sudden change in flow that increases the depth. It is the unsteady flow analogy of the stationary hydraulic jump and a geophysical application is the tidal bore. Positive surges are commonly studied using the method of characteristics and the Saint-Venant equations. The article presents the results from new experimental investigations conducted in a large rectangular channel. Detailed unsteady velocity measurements were performed with a high temporal resolution using acoustic Doppler velocimetry and non-intrusive free-surface measurement devices. Several experiments were conducted with the same initial discharge ( Q = 0.060 m/s) and six different gate openings after closure resulting in both non-breaking undular and breaking bores. The analysis of undular surges revealed wave amplitude attenuation with increasing distance of surge propagation were in agreement with Ippen and Kulin theory. Also, undular wave period and wave length data were relatively close to the values predicted by the wave dispersion theory for gravity waves in intermediate water depths. [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]

Rapidly varied open channel flows are characterized by curvilinear streamlines, thereby resulting in a pressure field different from the hydrostatic approach proposed in the standard gradually varied flow theory. This problem is related to environmental hydraulic problems such as the undular hydraulic jump and flow over round-crested weirs, for which streamline curvature effects are significant. The inclusion of the curvilinear streamline effect in an extended energy equation was firstly by Fawer. Most of the extended energy equations currently employed are therefore modified forms of the original Fawer approach. The aim of the present study is to highlight and remind engineers of the outstanding theory presented by Fawer. Herein, his approach for steady open channel flow with curved streamlines is revised and compared with experimental observations. Computational methods are presented in detail and based on present results, it can be observed that more recent and complex models for these problems are similar to the original proposal of Fawer, and hardly more accurate in some instances. Based on the proposed study an useful framework for theoretical models for steady open channel flows with curved streamlines is proposed. [ABSTRACT FROM AUTHOR]

In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers ρw × qw/ μw up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated. [ABSTRACT FROM AUTHOR]

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure. [ABSTRACT FROM AUTHOR]

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer. [ABSTRACT FROM AUTHOR]

In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F 0 and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls. [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]

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]

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]