Alternating skimming flow over a stepped spillway

The study of stepped spillways in laboratory scales has been essentially focused on two separated sub-regimes within skimming flow. In this paper we investigate the appearance of an unclassified alternating skimming flow regime in a 0.5 m wide stepped spillway which does not fit on these earlier definitions, and which does not occur in a 0.3 m wide spillway. Our aim is to explain the genesis of this unclassified flow which is visualised in the physical stepped spillway, by using 3D numerical modelling. Flow depths and velocities are measured using an ultrasonic sensor and Bubble Image Velocimetry in the wider flume (0.5 m). The numerical model is validated with the experimental data from the 0.5 m wide spillway. After validation, the channel width of the same numerical model is reduced to 0.3 m wide spillway in order to characterise (compare) the case without (with) alternating skimming flow. Both cases are solved using Reynolds-Averaged Navier–Stokes equations together with the Volume-of-Fluid technique and SST k-\(\omega\) turbulence model. The experimental results reveal that the alternating skimming flow regime is characterised by an evident seesaw pattern of flow properties over consecutive steps. In turn, the numerical modelling clarified that this seesaw pattern is due to the presence of a complex system of cross waves along the spillway. These cross waves are also responsible for a mass and momentum exchange in the transversal direction and for the formation of the alternating skimming flow in the spillway.     

Characterization of turbulence statistics on the non-aerated skimming flow over stepped spillways: a numerical study

Environmental Fluid Mechanics - In this work we address the mean flow and turbulence statistics in the non-aerated region of a stepped spillway by using two different numerical strategies in two...     

Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments

The design floods of several reservoirs were recently re-evaluated and the revised spillway outflow could result in dam overtopping with catastrophic consequences for some embankment structures. Herein a physical study was performed on flat and pooled stepped spillways with a slope typical of embankments $(\uptheta = 26.6^{\circ })$ and four stepped configurations were tested: a stepped spillway with flat horizontal steps, a pooled stepped spillway, and two stepped spillways with in-line and staggered configurations of flat and pooled steps. The focus of the study was on the flow aeration, air–water flow properties, cavity flow processes, and energy dissipation performances. The results demonstrated the strong aeration of the flow for all configurations. On the in-line and staggered configurations of flat and pooled steps, the flow was highly three-dimensional. The residual head and energy dissipation rates at the stepped chute downstream end were calculated based upon the detailed air–water flow properties. The results showed that the residual energy was the lowest for the flat stepped weir. The data for the stepped spillway configuration with in-line and staggered configurations of flat and pooled steps showed large differences in terms of residual head in the transverse direction. Altogether the present results showed that, on a $26.6^{\circ }$ slope stepped chute, the designs with in-line and staggered configurations of flat and pooled steps did not provide any advantageous performances in terms of energy dissipation and flow aeration, but they were affected by three-dimensional patterns leading to some flow concentration.     

Wind- and tide-induced currents in the Stagnone lagoon (Sicily)

The hydrodynamic circulation is analyzed in the coastal lagoon of Stagnone di Marsala, a natural reserve located in the north-western part of Sicily, using both experimental measurements and numerical simulations. Field measurements of velocities and water levels, carried out using an ultrasound sensor (3D), are used to validate the numerical model. A 3D finite-volume model is used to solve the Reynolds-averaged momentum and mass balance differential equations on a curvilinear structured grid, employing the k–e{\varepsilon} turbulence model for the Reynolds stresses. The numerical analysis allows to identify the relative contribution of the forces affecting the hydrodynamic circulation inside the lagoon. In the simulations only wind and tide forces are considered, neglecting the effects of water density changes. Two different conditions are considered. In the first both the wind stress over the free-surface and the tidal motion are imposed. In the second the wind action is neglected, to separately analyze the tide-induced circulation. The comparison between the two test cases highlights the fundamental role of the wind on the hydrodynamics of the Stagnone lagoon, producing a strong vertical recirculation pattern that is not observed when the flow is driven by tides only.     

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.     

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.     

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( $K^{E})$ and macrodispersivity ( $\alpha ^{E})$ for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of $K^{E}$ and $\alpha ^{E}$ on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal $K^{E}$ and $\alpha ^{E}$ are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical $K^{E}$ and $\alpha ^{E}$ are found to be reduced slightly when the density factor ( $\gamma $ ) is less than 0.01, whereas significant decreases occur when $\gamma $ exceeds 0.01. Of note, the variation of $K^{E}$ and $\alpha ^{E}$ is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.     

Population genetics of the nurse shark (Ginglymostoma cirratum) in the western Atlantic

The nurse shark, Ginglymostoma cirratum, inhabits shallow, tropical, and subtropical waters in the Atlantic and the eastern Pacific. Unlike many other species of sharks, nurse sharks are remarkably sedentary. We assayed the mitochondrial control region and eight microsatellite loci from individuals collected primarily in the western Atlantic to estimate the degree of population subdivision. Two individuals from the eastern Atlantic and one from the Pacific coast of Panama also were genotyped. Overall, the mtDNA haplotype (h = 48 ± 5%) and nucleotide (π = 0.08 ± 0.06%) diversities were low. The microsatellite data mirror the mitochondrial results with the average number of alleles ([`(N)]<sub>A</sub> \bar{N}_{A}  = 9) and observed heterozygosity ([`(H)]_O \bar{H}_{O}  = 0.58) both low. The low levels of diversity seen in both the mtDNA and the microsatellite may be due to historical sea level fluctuations and concomitant loss of shallow water habitat. Eight of the 10 pair-wise western Atlantic F _ST estimates for mtDNA indicated significant genetic subdivision. Pair-wise F _ST values for the microsatellite loci indicated a similar pattern as the mtDNA. The western Atlantic population of nurse sharks is genetically subdivided with the strongest separation seen between the offshore islands and mainland Brazil, likely due to deep water acting as a barrier to dispersal. The eastern and western Atlantic populations were closely related. The eastern Pacific individual is quite different from Atlantic individuals and may be a cryptic, sister species.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

Numerical simulation and optimization study of the wind flow through a porous fence

Three turbulence closure models (RNG k-ε, SST k-ω and RSM) were used to investigate the flow characteristics around a two-dimensional isolated porous fence. The comparison between the numerical results and the experimental measurements indicated that RSM model shows a better performance than the other two models. The aim of this paper is to accurately and efficiently determine the optimum porosity that attain the best shelter effect of the wind fence in the near wake region (0–4h_b) and in the far wake region (4h_b–10h_b) respectively, where h_b is the height of the fence. The gradient algorithm was adopted as the optimization algorithm and the RSM model was used to model turbulent features of the flow. The shelter effect was parameterized by the peak velocity ratio involving velocity and turbulence. The objective was to reduce the peak velocity ratio in the near or far wake region by changing the design variable porosity (?) of the fence, which ranged between 2 and 60%. The results revealed that a porosity of 10.2% was found as the optimum value giving rise to the best shelter effect in the near wake region, and ? = 22.1% was determined in the case of the far wake region. In addition, based on the proposed optimization method, it is found that the recirculating bubble behind the fence can only be detected when ? < 29.9%.     

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $(\overline{\hbox {Ri}_\mathrm{g} } >1)$ , but sometimes at smaller values $(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $\hbox {z/L}<1$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $\hbox {z/L}>1$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $\overline{\hbox {Ri}_\mathrm{g} }$ was identified. Eddy diffusivities of momentum $\hbox {K}_\mathrm{M}$ and heat $\hbox {K}_\mathrm{H}$ were dependent on wave activities, notably when $\overline{\hbox {Ri}_\mathrm{g} } > 1$ . The ratio $\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$ dropped well below unity at high $\overline{\hbox {Ri}_\mathrm{g} }$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.     

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.     

On the heating environment in street canyon

This study investigates the impact of building aspect ratio (building-height-to-street-canyon-width-ratio), wind speed and surface and air-temperature difference (Δθ_s−a) on the heating environment within street canyon. The Reynolds-averaged Navier-Stokes (RANS) and energy transport equations were solved with Renormalization group (RNG) theory version of k-e{\varepsilon} turbulence model. The validation process demonstrated that the model could be trusted for simulating air-temperature and velocity trends. The temperature and velocity patterns were discussed in idealized street canyons of different aspect ratios (0.5–2.0) with varying ambient wind speeds (0.5–1.5 m/s) and Δθ_s−a (2–8 K). Results show that air-temperatures are directly proportional to bulk Richardson number (R _b ) for all but ground heating situation. Conversely, air-temperatures increase significantly across the street canyon with a decrease in ambient wind speed; however, the impact of Δθ_s−a was negligible. Clearly, ambient wind speed decreases significantly as it passes over higher AR street canyons. Notably, air-temperatures were the highest when the windward wall was heated and the least during ground heating. Conversely, air-temperatures were lower along the windward side but higher within the street canyon when the windward wall was heated.     

Sediment processes and flow reversal in the undular tidal bore of the Garonne River (France)

A tidal bore is a series of waves propagating upstream as the tidal flow turns to rising, and the bore front corresponds to the leading edge of the tidal wave in a funnel shaped estuarine zone with macro-tidal conditions. Some field observations were conducted in the tidal bore of the Garonne River on 7 June 2012 in the Arcins channel, a few weeks after a major flood. The tidal bore was a flat undular bore with a Froude number close to unity: $\hbox {Fr}_{1} = 1.02$ and 1.19 (morning and afternoon respectively). A key feature of the study was the simultaneous recording of the water elevation, instantaneous velocity components and suspended sediment concentration (SSC) estimates, together with a detailed characterisation of the sediment bed materials. The sediment was some silty material ( $\hbox {d}_{50} \approx 13~\upmu \hbox {m}$ ) which exhibited some non-Newtonion thixotropic behaviour. The velocity and SSC estimate were recorded simultaneously at high frequency, enabling a quantitative estimate of the suspended sediment flux at the end of the ebb tide and during the early flood tide. The net sediment flux per unit area was directed upstream after the bore, and its magnitude was much larger than that at end of ebb tide. The field observations highlighted a number of unusual features on the morning of 7 June 2012. These included (a) a slight rise in water elevation starting about 70 s prior to the front, (b) a delayed flow reversal about 50 s after the bore front, (c) some large fluctuations in suspended sediment concentration (SSC) about 100 s after the bore front and (d) a transient water elevation lowering about 10 min after the bore front passage. The measurements of water temperature and salinity showed nearly identical results before and after the tidal bore, with no evidence of saline and thermal front during the study.     

Passive scalar roughness lengths for atmospheric boundary layer flow over complex, fractal topographies

When modeling atmospheric boundary layer flow over rough landscapes, surface fluxes of flow quantities (momentum, temperature, etc.) can be described with equilibrium logarithmic law expressions, all of which require specification of a roughness length that is, physically, the elevation at which the flow quantity equals its surface value. In high Reynolds number flows, such as the atmospheric boundary layer, inertial forces associated with turbulent eddy motions are responsible for surface momentum fluxes (form, or pressure drag). Surface scalar fluxes, on the other hand, occur exclusively via diffusion in the immediate vicinity of the topography—the interfacial region—before being advected by turbulent eddy motions into the bulk of the flow. Owing to this difference in surface transfer mechanism, the passive scalar roughness length, $z_{0S}$ , is known to be less than the momentum roughness length, $z_0$ . In this work, classical relations are used to specify $z_{0S}$ during large-eddy simulation of atmospheric boundary layer flow over aerodynamically rough, synthetic, fractal topographies which exhibit power-law height energy spectrum, $E_h (k) \sim k^{\beta _s}$ , where $\beta _s$ is a (predefined) spectral exponent. These topographies are convenient since they resemble natural landscapes and $\beta _s$ can be varied to change the topography’s aerodynamic roughness (the study considers a suite of topographies with $-2.4 \le \beta _s \le -1.2$ , where $-2.4$ and $-1.2$ are the “most smooth” and “most rough” cases, respectively, corresponding with roughness Reynolds number, $Re_0 \approx 10$ and $300$ ). It is often assumed that $z_{0S}/z_{0} \approx 10^{-1}$ for all $Re_0$ . But results from this work show that the roughness length ratio, $z_{0S}/z_{0}$ , depends strongly on $Re_0$ , ranging between $10^{-3}$ and $10^{-1}$ .     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Experiments on gravity currents propagating on unbounded uniform slopes

Gravity currents propagating on \(12^\circ \), \(9^\circ \), \(6^\circ \), \(3^\circ \) unbounded uniform slopes and on an unbounded horizontal boundary are reported. Results show that there are two stages of the deceleration phase. In the early stage of the deceleration phase, the front location history follows \({(x_f+x_0)}^2 = {(K_I B)}^{1/2} (t+t_{I})\), where \((x_f+x_0)\) is the front location measured from the virtual origin, \(K_I\) an experimental constant, B the total buoyancy, t time and \(t_I\) the t-intercept. In the late stage of the deceleration phase for the gravity currents on \(12^\circ \), \(9^\circ \), \(6^\circ \) unbounded uniform slopes, the front location history follows \({(x_f+x_0)}^{8/3} = K_{VS} {{B}^{2/3} V^{2/9}_0 }{\nu }^{-1/3} ({t+t_{VS}})\), where \(K_{VS}\) is an experimental constant, \(V_0\) the initial volume of heavy fluid, \(\nu \) the kinematic viscosity and \(t_{VS}\) the t-intercept. In the late stage of the deceleration phase for the gravity currents on a \(3^\circ \) unbounded uniform slope and on an unbounded horizontal boundary, the front location history follows \({(x_f+x_0)}^{4} = K_{VM} {{B}^{2/3} V^{2/3}_0 }{\nu }^{-1/3} ({t+t_{VM}})\), where \(K_{VM}\) is an experimental constant and \(t_{VM}\) the t-intercept. Two qualitatively different flow morphologies are identified in the late stage of the deceleration phase. For the gravity currents on \(12^\circ \), \(9^\circ \), \(6^\circ \) unbounded uniform slopes, an ‘active’ head separates from the body of the current. For the gravity currents on a \(3^\circ \) unbounded uniform slope and on an unbounded horizontal boundary, the gravity currents maintain an integrated shape throughout the motion. Results indicate two possible routes to the final stage of the gravity currents on unbounded uniform slopes.