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.     

Steady open channel flows with curved streamlines: the Fawer approach revised

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.     

Flow and drag force around a free surface piercing cylinder for environmental applications

This paper investigates flows around a free surface piercing cylinder with Froude number F > 0.5 and Reynolds number around Re = 50,000. The aim of this work is to gain a better understanding of the flow behaviour in environmental systems such as fishways. The advances are based upon experimental and numerical results. Several flow discharges and slopes are tested to obtain both subcritical and supercritical flows. The drag force exerted on the cylinder is measured with the help of a torque gauge while the velocity field is obtained using particle velocimetry. For the numerical part, two URANS turbulence models are tested, the k-\(\omega\) SST and the RNG k-\(\varepsilon\) models using the OpenFOAM software suite for subcritical cases, and then compared with the corresponding experimental results. With fishways applications in mind, the changes in drag coefficient \(C_d\) versus Froude number and water depth are studied and experimental correlations proposed. We conclude that the most suitable URANS turbulence model for reproducing this kind of flow is the k-\(\omega\) SST model.     

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.     

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.     

Global patterns of epipelagic gelatinous zooplankton biomass

There is concern that overfishing may lead to a proliferation of jellyfish through a process known as fishing down the food web. However, there has been no global synthesis of patterns of gelatinous zooplankton biomass (GZB), an important first step in determining any future trends. A meta-analysis of epipelagic-GZB patterns was undertaken, encompassing 58 locations on a global scale, and spanning the years 1967–2009. Epipelagic-GZB decreased strongly with increasing total water column depth (r ² = 0.543, p < 0.001, n = 58): in shallow (<50 m) coastal waters, epipelagic-GZB was typically 742× the levels in deep ocean (>2,000 m) sites. However, the ratio of GZB to primary productivity showed high values across a range of depths, i.e. this measure of the relative abundance of gelatinous zooplankton did not co-vary with depth.     

On the fine structure of the thermal bar front

The thermal bar—a hydrodynamic phenomenon, arising in natural basins due to successive changes of the water temperature across the temperature of maximum density (T_m, which is close to 4°C)—has been studied in laboratory experiments and by numerical simulations. The experiments were performed in a rectangular tank with an inclined bottom, filled with water with initial temperature T₀ < T_m and then heated at the surface. During the heating a basin-wide circulation develops, consisting of down-slope cascades in regions where T < T_m, a subsurface off-shore jet in the region where T > T_m, and a compensating flow at intermediate depths towards the shallow part of the tank, supplying both off-shore flows with waters from deeper regions. Analysis of the water temperature and density fields as well as the currents has revealed that the location of the convergence zone of the surface current (when formed) does not coincide with that of the Tm-isotherm. The thermal bar front is typically understood as a convergence zone near the 4°C-isotherm, formed due to the effect of cabbeling. Our experiments demonstrate, however, that the front is associated with the leading edge of the subsurface current. The increasing distance between the 4°C-isotherm and the subsurface jet has been recorded in the laboratory experiments. Numerical simulation results corroborate the laboratory experiments. A scaling analysis predicts the speed of propagation of this frontal zone to be U ~ [g × Δρ/ρ × H]^1/2, where H is the depth (increasing with time) of the upper thermo-active layer, ρ₀ a reference density, and Δρ is the characteristic horizontal density difference across the front. A combined analysis of laboratory, field and numerical data has corroborated this law.     

Experimental study of a positive surge. Part 2: comparison with literature theories and unsteady flow field analysis

A positive surge is a unsteady open channel flow resulting from the rapid rise of the free-surface. The phenomenon may be observed in water supply canals and channels as well as in some estuaries during spring tidal conditions. The formation and development of positive surges can be predicted using the method of characteristics and shallow water equations. The paper is the second part of a study presenting 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. A comparison between main features of the undular surges with literature theories demonstrated that the experimental data were mostly in agreement with Andersen’s theory. The analysis of unsteady flow field including Reynolds stresses confirmed and extended previous findings about positive surge hydrodynamics.     

Mass-based depth and velocity scales for gravity currents and related flows

Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET’s entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET’s parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which—unlike in open channel flows—generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plumes.     

Reductive dechlorination of chlorobenzene in supercritical water catalyzed by Fe/ZrO<Subscript>2</Subscript>

Reductive dechlorination of chlorobenzene by Fe/ZrO₂ in supercritical water was investigated. The effects of the operation conditions were studied. The dechlorination of chlorobenzene obeyed pseudo-first-order kinetics models. In supercritical water, the rate constant increases more rapidly with temperature than those in subcritical water. The results showed that the rate-determining step of dechlorination in subcritical water is diffusion; whereas the rate-determining of dechlorination in supercritical water is chemical reaction. The reaction mechanism in subcritical water might involve with an ionic mechanism; whereas the reaction mechanism in supercritical water might involve with a homolytic reaction.     

Dressler’s theory for curved topography flows: iterative derivation,transcritical flow solutions and higher-order wave-type equations

The Dressler equations are a system of two non-linear partial differential equations for shallow fluid flows over curved topography. The theory originated from an asymptotic stretching method formulating the equations of motion in terrain-fitted curvilinear coordinates. Apparently, these equations failed to produce a transcritical flow profile changing from sub- to supercritical flow conditions. Further, wave-like motions over a flat bottom are excluded because the bed-normal velocity component is not accounted for. However, the theory was found relevant for several environmental flow problems including density currents over mountains and valleys, seepage flow in hillslope hydrology, the development of antidunes, the formation of geological deposits from hyper-concentrated flows, and shallow-water flow modeling in hydraulics. In this work, Dressler’s theory is developed in an alternative way by a systematic iteration of the stream and potential functions in terrain-fitted coordinates. The first iteration was found to be the former Dressler’s theory, whereas a second iteration of the governing equations results in velocity components generalizing Dressler’s theory to wave-like motion. Dressler’s first-order theory produces a transcritical flow solution over topography only if the total head is fixed by a minimum value of the specific energy at the transition point. However, the theory deviates from measurements under subcritical flow conditions, given that the bed-normal velocity component is significant. A second iteration to the velocity field was used to produce a second-order differential equation that resembles the cnoidal-wave theory. It accurately produces flow over an obstacle including the critical point and the minimum specific energy as part of the numerical solution. The new cnoidal-wave model compares well with the theory of a Cosserat surface for directed fluid sheets, whereas the Saint-Venant theory appears to be poor.     

Drag coefficient for rigid vegetation in subcritical open-channel flow

Drag coefficient has been commonly used as a quantifying parameter to represent the vegetative drag, i.e., resistance to the flow by vegetation. In this study, the measured data on the drag coefficient for rigid vegetation in subcritical open-channel flow reported in previous studies are collected and preprocessed for multi-parameter analysis. The effect of Froude number (Fr) on the drag coefficient for rigid vegetation in subcritical flow cannot be ignored, especially when \(Fr < 0.12\). The drag coefficient is observed to exponentially decrease with the stem Reynolds number (R _d ) and logarithmically decreased with the vegetation density (λ) when \(0.012 < \lambda < 0.12\). The relative submergence (h ^* ) has a significant effect on the drag coefficient, and a positive logarithmic relationship is summarized. A simplified three-stage empirical formula is obtained based on the divisions of Fr. Laboratory tests (with \(Fr < 0.02\)) prove that the present empirical model has higher precision compared with existing models.     

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.     

Effects of spatial variability and colony size on the reproductive output and gonadal development cycle of the Mediterranean red coral (Corallium rubrum L.)

Red coral (Corallium rubrum, L. 1758) is an over-exploited Mediterranean gorgonian. The gonadal development cycle of this gorgonian is examined at the Costa Brava (NW Mediterranean) taking into account for the first time colony size, depth and spatial horizontal variability. This study compares the gonad development and fertility in two colony size classes (colonies <6-cm height, and >10-cm height, both at 40–45-m depth), and two populations at different depths (16–18-m depth, and 40–45-m depth, both consisting of <6-cm high colonies) in a 15-month period. The fertility of seven size classes (<2 cm to >12 cm high colonies, in 2 cm intervals) was examined in the deep population, where large colonies were present. Furthermore, reproductive output was compared in 6 populations (distributed along more than 70-km coastline) one month before spawning (June). Red coral was found to be dioecious and gonochoric with a sex ratio of 1:1, which differs from other NW Mediterranean populations. On the other hand, fertility of different size classes indicates that small colonies of 2-cm height already produce gonads, which is in line with previous studies. Female and male polyp fertility and sperm sac size increase significantly with colony size [sperm sac diameter: 476±144 μm (mean±SD) and 305±150 μm in the >10-cm and <6-cm height colonies, respectively), whereas no significant effect on oocyte diameter was found (oocyte diameter: 373.7±18.7 μm). Depth staggered spawning, that is, an earlier release of gonads in the shallow populations, was observed in summer 2003, coinciding with the highest temperature gradient between shallow and deep water during the study period. Colonies of <6-cm height were significantly less fertile than colonies >12 cm, thus the recommendation of this study is that a minimum height should be incorporated into fishing regulations. The six studied populations at the Costa Brava showed a comparable reproductive potential, which demonstrates little variability within the homogenous population structure and range of size classes (due to overharvesting) found at the Costa Brava. The study of reproductive output is an important tool for ecosystem management, and this work recommends basing specific exploitation laws for distinctive populations on colony size, which is found to have a larger effect on reproductive potential than mesoscale variability. An erratum to this article can be found at     

Mixing layer in open-channel junction flows

When two open-channel flows merge in a three-branch subcritical junction, a mixing layer appears at the interface between the two inflows. If the width of the downstream channel is equal to the width of each inlet channel, this mixing layer is accelerated and is curved due to the junction geometry. The present work is dedicated to simplified geometries, considering a flat bed and a \(90^{\circ }\) angle where two configurations with different momentum ratios are tested. Due to the complex flow pattern in the junction, the so-called Serret–Frenet frame-axis based on the local direction of the velocity must be employed to characterize the flow pattern and the mixing layer as Cartesian and cylindrical frame-axes are not adapted. The analysis reveals that the centerline of the mixing layer, defined as the location of maximum Reynolds stress and velocity gradient, fairly fits the streamline separating at the upstream corner, even though a slight shift of the mixing layer towards the center of curvature is observed. The shape of the mixing layer appears to be strongly affected by the streamwise acceleration and the complex lateral confinement due to the side walls and the corners of the junction, leading to a streamwise increase of the mean velocity along the centerline and a decrease of the velocity difference. This results in a specific streamwise evolution of the mixing layer width, which reaches a plateau in the downstream region of the junction. Finally, the evaluation of the terms in the Reynolds-Averaged-Navier–Stokes equations reveals that the streamwise and normal acceleration and the pressure gradient remain dominant, which is typical of accelerated and rotational flows.     

Satellite tagging of blue sharks (Prionace glauca) and other pelagic sharks off eastern Australia: depth behaviour, temperature experience and movements

Satellite telemetry was used to study the movements and behaviour of ten blue sharks and one individual each of shortfin mako, thresher and bigeye thresher off eastern Australia. The tracks showed latitudinal movements of up to 1,900 km, but none of the sharks travelled away from the eastern Australian region. Tracking periods did not exceed 177 days. All species showed oscillatory dive behaviour between the surface layers to as deep as 560–1,000 m. Blue sharks spent 35–58% of their time in <50 m depths and 10–16% of their time in >300 m. Of these four species, the bigeye thresher spent the least time in the surface layers and the most time at >300 m depth. All four species showed clear diel behaviour generally occupying shallower depths at night than during the day. Blue sharks were mainly in 17.5–20.0°C water, while the thresher sharks showed a more bimodal temperature distribution.     

Reproductive biology of the deep-sea octocoral Drifa glomerata in the Northwest Atlantic

The present study examined the mode and timing of reproduction of poorly understood deep-water octocorals and the environmental factors that may influence their reproductive patterns. Data on reproductive characteristics of the octocoral Drifa glomerata (Alcyonacea: Nephtheidae) collected between 2004 and 2007 at ca. 100–330 m depth off Newfoundland and Labrador (eastern Canada) were compared among years, months and depth ranges. No male gonad was ever observed during the study. The ratio of fertile colonies possessing large pinkish polyps with oocytes/planulae was >50% throughout the year. The number of brooded planula larvae within a single fertile polyp varied between 1 and 10 for a total of approximately 40–3,000 in a whole colony. The size of oocytes and/or planulae was consistently greater in the polyps than in the branchlets, indicating that the development pathway of oocytes to planulae is from the branchlets to the polyps. Although larval production seemed to persist year round, the onset of major planulation events occurred in December–January of two consecutive years, when large mature planulae were released in correlation with the first increase of photoperiod and maximum temperature at 150 m. A second peak in planulation between April and early June followed the phytoplankton bloom. Seasonal trends were more apparent in colonies from <200 m, and the planula index varied among sampling depths and years. Larval release in a live colony under laboratory conditions occurred between January and June 2008, closely following predictions based on field samples.     

Genotypic variation in element concentrations in brown rice from Yunnan landraces in China

The mineral elements present in brown rice play an important physiological role in global human health. We investigated genotypic variation of eight of these elements (P, K, Ca, Mg, Fe, Zn, Cu, and Mn) in 11 different grades of brown rice on the basis of the number and distance coefficients of 282 alleles for 20 simple sequence repeat (SSR) markers. Six-hundred and twenty-eight landraces from the same field in Yunnan Province, one of the largest centers of genetic diversity of rice (Oryza sativa L.) in the world, formed our core collection. The mean concentrations (mg kg⁻¹) of the eight elements in brown rice for these landraces were P (3,480) > K (2,540) > Mg (1,480) > Ca (157) > Zn (32.8) > Fe (32.0) > Cu (13.6) > Mn (13.2). Mean P concentrations in brown rice were 6.56 times total soil P, so the grains are important in tissue storage of P, but total soil K is 7.82 times mean K concentrations in brown rice. The concentrations of the eight elements in some grades of brown rice, on the basis of the number and distance coefficients of alleles for 20 SSR markers for the landraces, were significantly different (P < 0.05), and further understanding of the relationship between mineral elements and gene diversity is needed. There was large variation in element concentrations in brown rice, ranging from 2,160 to 5,500 mg P kg⁻¹, from 1,130 to 3,830 mg K kg⁻¹, from 61.8 to 488 mg Ca kg⁻¹, from 864 to 2,020 mg Mg kg⁻¹, from 0.40 to 147 mg Fe kg⁻¹, from 15.1 to 124 mg Zn kg⁻¹, from 0.10 to 59.1 mg Cu kg⁻¹, and from 6.7 to 26.6 mg Mn kg⁻¹. Therefore, germplasm evaluations for Ca, Fe, and Zn concentrations in rice grains have detected up to sevenfold genotypic differences, suggesting that selection for high levels of Ca, Fe, and Zn in breeding for mass production is a feasible approach. Increasing the concentrations of Ca, Fe, and Zn in rice grains will help alleviate chronic Ca, Zn, and Fe deficiencies in many areas of the world.     

Gravity currents in two-layer stratified media

An analytical, experimental and numerical study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. Gravity currents are supposed to originate from a lock-release apparatus; the (heavy) gravity current fluid is assumed to span the entire channel depth, H, at the initial instant. Our theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, and follows from the classical analysis of Benjamin (J Fluid Mech 31:209?C248, 1968). In contrast to previous investigations, we argue that the interfacial disturbance must be parameterized so that its amplitude can be straightforwardly determined from the ambient layer depths. Our parameterization is based on sensible physical arguments; its accuracy is confirmed by comparison against experimental and numerical data. More generally, measured front speeds show positive agreement with analogue model predictions, which remain strictly single-valued. From experimental and numerical observations of supercritical gravity currents, it is noted that this front speed is essentially independent of the interfacial thickness, ??, even in the limiting case where ?? = H so that the environment is comprised of a uniformly stratified ambient with no readily discernible upper or lower ambient layer. Conversely, when the gravity current is subcritical, there is a mild increase of front speed with ??. Our experiments also consider the horizontal distance, X, at which the front begins to decelerate. The variation of X with the interface thickness and the depths and densities of the ambient layers is discussed. For subcritical gravity currents, X may be as small as three lock lengths whereas with supercritical gravity currents, the gravity current may travel long distances at constant speed, particularly as the lower layer depth diminishes.