Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

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_z/d₁ < 0.8 in the shear layer, where L_z is the integral turbulent length scale and d₁ the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations.     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

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.     

Coupling between free-surface fluctuations,velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges,bores and compression waves

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.     

Modelling hydraulic jump using the bubbly two-phase flow method

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.     

Characteristics of clustered particles in skimming flows on a stepped spillway

Air–water flows at hydraulic structures are commonly observed and called white waters. The free-surface aeration is characterised by some intense exchanges of air and water leading to complex air–water structures including some clustering. The number and properties of clusters may provide some measure of the level of particle-turbulence and particle–particle interactions in the high-velocity air–water flows. Herein a re-analysis of air–water clusters was applied to a highly aerated free-surface flow data set (Chanson and Carosi, Exp Fluids 42:385–401, 2007). A two-dimensional cluster analysis was introduced combining a longitudinal clustering criterion based on near-wake effect and a side-by-side particle detection method. The results highlighted a significant number of clustered particles in the high-velocity free-surface flows. The number of bubble/droplet clusters per second and the percentage of clustered particles were significantly larger using the two-dimensional cluster analysis than those derived from earlier longitudinal detection techniques only. A number of large cluster structures were further detected. The results illustrated the complex interactions between entrained air and turbulent structures in skimming flow on a stepped spillway, and the cluster detection method may apply to other highly aerated free-surface flows.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

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 6H, 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.     

Advanced post-processing and correlation analyses in high-velocity air–water flows

The interest in air–water flows has not diminished in recent years, but it is accompanied by frequent citations of early, sometimes outdated articles. A basic issue is the inadequate, incomplete interpretation of air–water flow instrumentation by hydraulic engineers and researchers. This article comments on high-velocity air–water flow measurements by means of intrusive phase detection probes. This article focus on the bubbly flow structure of high-velocity air–water flow based upon measurements by means of intrusive phase detection probes. It is shown that some advanced post-processing techniques may yield expanded information on the air–water turbulent flow properties and bubbly flow structures. The outcomes demonstrate simple techniques in high-velocity air–water flow analysis.     

Experimental study of a positive surge. Part 1: basic flow patterns and wave attenuation

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 m³/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.     

Analysis of the velocity field in a large rectangular channel with lateral shockwave

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.     

Experimental analysis of Froude number effect on air entrainment in the hydraulic jump

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.     

Characterization of bedload intermittency near the threshold of motion using a Lagrangian sediment transport model

At the smallest scales of sediment transport in rivers, the coherent structures of the turbulent boundary layer constitute the fundamental mechanisms of bedload transport, locally increasing the instantaneous hydrodynamic forces acting on sediment particles, and mobilizing them downstream. Near the critical threshold for initiating sediment motion, the interactions of the particles with these unsteady coherent structures and with other sediment grains, produce localized transport events with brief episodes of collective motion occurring due to the near-bed velocity fluctuations. Simulations of these flows pose a significant challenge for numerical models aimed at capturing the physical processes and complex non-linear interactions that generate highly intermittent and self-similar bedload transport fluxes. In this investigation we carry out direct numerical simulations of the flow in a rectangular flat-bed channel, at a Reynolds number equal to Re = 3632, coupled with the discrete element method to simulate the dynamics of spherical particles near the bed. We perform two-way coupled Lagrangian simulations of 48,510 sediment particles, with 4851 fixed particles to account for bed roughness. Our simulations consider a total of eight different values of the non-dimensional Shields parameter to study the evolution of transport statistics. From the trajectory and velocity of each sediment particle, we compute the changes in the probability distribution functions of velocities, bed activity, and jump lengths as the Shields number increases. For the lower shear stresses, the intermittency of the global bedload transport flux is described by computing the singularity or multifr actal spectrum of transport, which also characterizes the widespread range of transport event magnitudes. These findings can help to identify the mechanisms of sediment transport at the particle scale. The statistical analysis can also be used as an ingredient to develop larger, upscaled models for predicting mean transport rates, considering the variability of entrainment and deposition that characterizes the transport near the threshold of motion.     

Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects

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 ρ _w × q _w/μ _w up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.     

A closure approach with multi-scale mixing length,and its application to wind and shear stress profiles within the atmospheric boundary layer

A method to determine flow specific first-order closure for the turbulent flux of momentum in the atmospheric boundary layer (ABL) is presented. This is based on the premise that eddy viscosity is a flow rather than a fluid property, and the physically more realistic assumption that the transfer of momentum and other scalar quantities in a turbulent flow takes place by a large, but finite number of length scales, than the often used single length scale, the ‘mixing length’. The resulting eddy viscosity is flow specific and when applied to the study of the ABL, yields the vertical profiles of shear stress and mean wind velocity in good agreement with observations. The method may be extended to other types of turbulent flows, however it should be recognized that each type of flow may yield a different eddy viscosity profile. Using the derived eddy viscosity the paper presents simple analytical solutions of the ABL equations to determine observationally consistent wind speed and shear stress profiles in the ABL for a variety of practical applications including air pollution modelling.     

Eddy diffusivity: a single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 h to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth <3 m). Taylor’s diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 and 0.02 m²/s during the flood tide experiment. The diffusivity showed strong dependence (R² > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo’s scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.     

Near-critical free-surface flows: real fluid flow analysis

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.     

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air–water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3–4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.     

Energy dissipation, flow resistance and gas-liquid interfacial area in skimming flows on moderate-slope stepped spillways

With the re-evaluation and revision of a number of design floods, several embankment overtopping protection systems have been developed and a common technique is the construction of a stepped spillway on the downstream slope. For such moderate slope stepped channels, detailed air–water flow measurements were performed in a large facility with a focus on the rate of energy dissipation, flow resistance, air–water interfacial areas and re-aeration rates. Past and present experimental results showed a significant aeration of the flow. The median dimensionless residual head was about 3 × d_c for the 21.8° sloping chute and smaller than that for flatter slopes (θ = 3.4° and 15.9°). The flow resistance results yielded an equivalent Darcy friction factor of about 0.25 implying a larger flow resistance for the 21.8° slope angle than for smaller slope angles. The re-aeration rate was deduced from the integration of the mass transfer equation using measured air–water interfacial areas and air–water flow velocities. The results suggested an increasing re-aeration rate with increasing rate of energy dissipation. The stepped invert contributed to intense turbulence production, free-surface aeration and large interfacial areas. The experimental data showed however some distinctive seesaw pattern in the longitudinal distribution of air–water flow properties with a wave length of about two step cavities. While these may be caused by the interactions between successive adjacent step cavities and their interference with the free-surface, the existence of such “instabilities” implies that the traditional concept of normal flow might not exist in skimming flows above moderate-slope stepped spillways.     

Blockage of saline intrusions in restricted,two-layer exchange flows across a submerged sill obstruction

Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.     

Seasonal concentrations of lead in outdoor and indoor dust and blood of children in Riyadh,Saudi Arabia

Because detrimental effects of exposure to lead (Pb) on human health have been observed, we previously investigated concentrations of Pb in water supplies and blood of adult residents of Riyadh, Saudi Arabia. The objectives of the present study were to: (1) examine seasonal rates of deposition of Pb in dust in several areas of Riyadh city, (2) measure concentrations of Pb in both outdoor and indoor dust, (3) compare concentrations of Pb in dust in Riyadh with those reported for other cities, and (4) quantify Pb in blood of children living in Riyadh. Mean, monthly deposition of PB in outdoor dust was 4.7 × 10¹ ± 3.6 tons km^?2, with a mean Pb concentration of 2.4 × 10² ± 4.4 × 10¹ μg/g. Mean, monthly deposition of Pb in indoor dust was 2.7 ± 0.70 tons km^?2, with a mean concentration of 2.9 × 10¹ ± 1.5 × 10¹ μg Pb/g. There was a significant (P < 0.01) correlation between concentrations of Pb in outdoor and indoor dust. There was no correlation between concentrations of Pb in indoor dust and that in blood of children of Riyadh, whereas there was a weakly significant (P < 0.05) correlation between concentrations of Pb in outdoor dust and that in blood of children. The mean (±SD) concentration of Pb in blood of children in Riyadh was 5.2 ± 1.7, with a range of 1.7–1.6 × 10¹ μg/dl. Concentrations of Pb in blood of 17.8 % of children in Riyadh were greater than 10 μg/dl, which is the CDC’s level of concern.     

Spatial distributions,source apportionment and ecological risk of SVOCs in water and sediment from Xijiang River,Pearl River Delta

Xijiang River is an important drinking water source in Guangxi Province, China. Along the Xijiang River and surrounding tributary, the pollution profile of three important groups of semi-volatile organic compounds, including polycyclic aromatic hydrocarbons (PAHs), organochlorine pesticides (OCPs) and phthalate esters (PAEs), was analyzed. Relatively low levels of PAHs (64–3.7 × 10² ng L^?1) and OCPs (16–70 ng L^?1), but high levels of PAEs (7.9 × 10²–6.8 × 10³ ng L^?1) occurred in the water. Comparatively, low levels of OCPs (39–1.8 × 10² ng g^?1) and PAEs (21–81 ng g^?1), but high levels of PAHs (41–1.1 × 10³ ng g^?1) were found in sediment. Principal component analyses for source identification indicated petroleum-derived residues or coal and biomass combustion, and vehicular emission was the main sources for PAHs. The OCPs sources of each category were almost independent, whereas the new input of HCHs and p,p′-DDTs probably existed in some areas. PAEs were mainly originated from personal care products of urban sewage, plastic and other industrial sources. Ecological risk through the risk quotient analysis indicated a small or significant potential adverse effect on fish, daphnia and green algae. Nevertheless, the integrated risk of all pollutants should be taken into account in future study.