On the front conditions for gravity currents in channels of general cross-section

We consider the propagation of a high-Reynolds-number gravity current in a horizontal channel with general cross-section whose width is \(f(z), 0 \le z\le H\), and the gravity acceleration g acts in \(-z\) direction. (The classical rectangular cross-section is covered by the particular case \(f(z) =\) const.) We assume a two-layer system of homogeneous fluids of constant densities \(\rho _{c}\) (current, of height \(h < H \)) and smaller \(\rho _{a}\) (ambient, filling the remaining part of the channel). We focus attention on the calculation and assessment of the nose Froude-number condition \(Fr = U/(g' h)^{1/2}\); here U is the speed of propagation of the current and \(g' = (\rho _{c}/\rho _{a}-1) g\) is the reduced gravity. We first revisit the steady-state current, and derive compact insightful expressions of Fr and energy dissipation as a function of \(\varphi \) (\(=\) area fraction occupied by the current in the cross-section). We show that the head loss \(\delta _0\) on the stagnation line is formally a degree of freedom in the determination of \(Fr(\varphi )\), and we clarify the strong connections with the head loss \(\delta \) in the ambient fluid, and with the overall rate of dissipation \(\dot{{\mathcal{D}}}\). We demonstrate that the closure \(\delta _0 = 0\) [suggested by Benjamin (J Fluid Mech 31, 209–248, 1968) for the rectangular cross-section] produces in general the smallest Fr for a given \(\varphi \); the results are valid for a significant range \([0, \varphi _{\max }]\), in which the current is dissipative, except for the point \(\varphi _{\max }\) where \(\delta = \dot{{\mathcal{D}}} = 0\). We show that imposing the closure \(\delta = \dot{{\mathcal{D}}} = 0\), which corresponds to an energy-conserving or non-dissipative current, produces in general unacceptable restrictions of the range of validity, and large values of Fr; in particular, deep currents (\(\varphi < 0.3\) say) must be excluded because they are inherently dissipative. On the other hand, the compromise closure \(\delta (\varphi ) =\delta _0(\varphi )\) produces the simple \(Fr(\varphi ) = \sqrt{2}(1 - \varphi )\) formula whose values and dissipation properties are very close, and the range of validity is identical, to these obtained with Benjamin’s closure (moreover, we show that this corresponds to circulation-conservation solutions). The results are illustrated for practical cross-section geometries (rectangle, \(\Delta \) and \(\nabla \) triangle, circle, and the general power-law \(f(z) = b z ^\alpha \) (\(b>0, \alpha \ge 0, 0< z \le H\)). Next, we investigate the connection of the steady-state results with the time-dependent current, and show that in a lock-released current the rate of dissipation of the system is equal to, or larger than, that obtained for Fr corresponding to the conditions at the nose of the current. The results and insights of this study cover a wide range of cross-section geometry and apply to both Boussinesq and non-Boussinesq systems; they reveal a remarkable robustness of Fr as a function of \(\varphi \).     

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness \(h_{\ell }\), via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air–water interface, \(\eta _{\ell }\), inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter, \({\mathcal{A}}_{*} = \eta _{0}/h_{\ell }\), where \(\eta _{0}\) was the initial displacement of the air–water interface, and by the strength of the background rotation controlled by the Burger number, \({\mathcal{S}}\). We set the experiments to explore a transitional regime from moderate- to weak-rotational environments, \(0.65\le {\mathcal{S}} \le 2\), for a wide range of initial perturbations, \(0.05\le {\mathcal{A}}_{*}\le 1.0\). The evolution of \(\eta _{\ell }\) was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, \(T_{d}\), and the seiche period of the basin, \(T_{g}\), has a median value of \(T_{d}/T_{g}\approx 11\), a maximum value of \(T_{d}/T_{g}\approx 10^{3}\) and a minimum value of \(T_{d}/T_{g}\approx 5\). The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid- to small-size lakes.     

Thin-layer models for gravity currents in channels of general cross-section area,a review

We present a brief review of the recent investigations on gravity currents in horizontal channels with non-rectangular cross-section area (such as triangle, \(\bigvee \)-valley, circle/semi-circle, trapezoid) which occur in nature (e.g., rivers) and constructed environment (tunnels, reservoirs, canals). To be specific, we discuss the propagation of a gravity current (GC) in a horizontal channel along the horizontal coordinate x, with gravity g acting in the \(-z\) direction, and y the horizontal–lateral coordinate. The bottom and top of the channel are at \(z=0,H\). The “standard” problem is concerned with 2D flow in a channel with rectangular (or laterally unbounded) cross-section area (CSA). Recent investigations have successfully extended the standard knowledge to the channels of CSA given by the quite general \(-f_1(z)\le y \le f_2(z)\) for \(0 \le z \le H\). This includes the practical \(\bigvee \)-valley, triangle, circle/semi-circle and trapezoid; these geometries may be in “up” or “down” setting with respect to gravity, e.g., \(\bigtriangleup \) and \(\bigtriangledown \). The major objective of the extended theory is to predict the height of the interface \(z=h(x,t)\) and the velocity (averaged over the CSA) u(x, t), where t is time; the prediction includes the speed and position of the nose \(u_N(t), x_N(t)\). We show that the motion is governed by a set of simplified equations, called “model,” that provides versatile and insightful solutions and trends. The emphasis in on a high-Reynolds-number current whose motion is dominated by buoyancy–inertia balance; in particular a GC released from a lock, which also contains general effects such as front and internal jumps (shocks), and reflected bore. We discuss two-layer, one-layer, and box models; Boussinesq and non-Boussinesq systems; compositional and particle-driven cases; and the effect of stratification of the ambient fluid. The models are self-contained, and admit realistic initial and boundary conditions. The governing equations are amenable to analytical solutions in some special circumstances. Some salient features of the buoyancy-viscous regime, and the estimate for the length at which transition to this regime takes place, are also presented. Some experimental support to the theory, and open questions for further investigations, are also mentioned. The major conclusions are (1) The CSA geometry has significant influence on the motion of the GC; and (2) The new theory is a useful, very significant, extension of the standard two-dimensional GC problem. The standard current is just a particular case, \(f_{1,2} =\) constants, among many other covered by the new theory.     

Fitting the truncated negative binomial distribution to count data

Modeling empirical distributions of repeated counts with parametric probability distributions is a frequent problem when studying species abundance. One must choose a family of distributions which is flexible enough to take into account very diverse patterns and possess parameters with clear biological/ecological interpretations. The negative binomial distribution fulfills these criteria and was selected for modeling counts of marine fish and invertebrates. This distribution depends on a vector \(\left( K,\mathfrak {P}\right) \) of parameters, and ranges from the Poisson distribution (when \(K\rightarrow +\infty \)) to Fisher’s log-series, when \(K\rightarrow 0\). Moreover, these parameters have biological/ecological interpretations which are detailed in the literature and in this study. We compared three estimators of K, \(\mathfrak {P}\) and the parameter \(\alpha \) of Fisher’s log-series, following the work of Rao CR (Statistical ecology. Pennsylvania State University Press, University Park, 1971) on a three-parameter unstandardized variant of the negative binomial distribution. We further investigated the coherence underlying parameter values resulting from the different estimators, using both real count data collected in the Mauritanian Exclusive Economic Zone (MEEZ) during the period 1987–2010 and realistic simulations of these data. In the case of the MEEZ, we first built homogeneous lists of counts (replicates), by gathering observations of each species with respect to “typical environments” obtained by clustering the sampled stations. The best estimation of \(\left( K,\mathfrak {P}\right) \) was generally obtained by penalized minimum Hellinger distance estimation. Interestingly, the parameters of most of the correctly sampled species seem compatible with the classical birth-and-dead model of population growth with immigration by Kendall (Biometrika 35:6–15, 1948).     

Variations of bed elevations due to turbulence around submerged cylinder in sand beds

This paper presents the spatio-temporal variations in bed elevations and the near-bed turbulence statistics over the deformed bed generated around the submerged cylindrical piers embedded vertically on loose sediment bed at a constant flow discharge. Experiments were carried out in a laboratory flume for three blockage ratios in the range of 0.04–0.06 using three different sizes of submerged cylinders individually placed vertically at the centerline of the flume. Clear-water experimental conditions were maintained over the smooth sediment bed surface with a constant flow discharge (\(Q = 0.015\,{\rm m}^3/{\rm sec}\)), thereby giving three different cylinder Reynolds numbers \(Re_{D_c} = \frac{U_mD_c}{\nu }\) (=10200, 12750, 15300) away from the cylinder locations, where \(U_m\) is the maximum mean velocity, \(D_c\) is the cylinder diameter and \(\nu\) is the kinematic viscosity of fluid. Instantaneous sand bed elevations around the cylinders were recorded using a SeaTek 5MHz ultrasonic ranging system of net 24 transducers to estimate bed form migration, and the near-bed velocity data at transducer locations over the stable deformed bed around the pier-like structures were collected using down-looking three-dimensional (3D) Micro-acoustic Doppler velocimeter to estimate the bottom Reynolds shear stresses and the contributions of bursting events to the dominant shear stress component. The flow perturbation generated due to relatively lower flow blockage ratio favored to achieve the stable bed condition more rapidly than the others, and larger upstream scour-depth and deformed areas were noticed for greater flow blockage ratio due to larger cylinder diameter. For larger blockage ratio in the upstream of scour-hole near the bed, occurrences of probabilities of both boundary-ward interactions (Q1 and Q3) were the dominant; whereas in the downstream of the scoured region, occurrences of probabilities of second and third quadrant events (Q2 and Q4) were dominant. On the other hand, for the lower blockage ratio, quadrant (Q2) was dominant over Q4 in the downstream of scour-hole, and in the upstream of scour-hole, quadrant Q4 was the dominant.     

Penetrative convection in slender containers

An experimental study was conducted to investigate the penetration of a convective mixed layer into an overlying stably (solutally) stratified layer contained in a narrow, tall vessel when the fluid is subjected to a destabilizing heat flux from below. The interest was the evolution of the bottom mixed-layer height (\(h\)) with time (\(t\)) in the presence of side-wall effects, but without the formation of conventional double-diffusive layers. The side-wall effects are expected at small mixed-layer aspect ratios, \(\varGamma_{h} = (W/h)\), where \(W\) is the container width. This case has not been studied hitherto, although there are important environmental and industrial applications. The mixed-layer growth laws for low aspect ratio convection were formulated by assuming a balance between the vertical kinetic energy flux at the interface and the rate of change of potential energy of the fluid system due to turbulent entrainment. The effects of sidewalls were considered using similarity arguments, by taking characteristic rms velocities to be a function of \(\varGamma_{h}\), in addition to buoyancy flux (\(q_{0}\)) and \(h\). In all stages of evolution, the similarity variables \(\xi = h/W\) and \(t^{\prime } = Nt/A\), where \(A = N^{3} W^{2} /4q_{0}\) and \(N\) is the buoyancy frequency, scaled the mixed-layer evolution data remarkably well. Significant wall effects were noted when \(\varGamma_{h} < 1\), and for this case the interfacial vertical turbulent velocity and length scales were identified via scaling arguments and experimental data.     

Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

Wind-induced pressure at a tunnel portal

In order to properly size the mechanical ventilation system of a tunnel, it is essential to estimate the wind-driven pressure difference that might rise between its two portals. In this respect, we explore here the pressure distribution over a tunnel portal under the influence of an incident atmospheric boundary layer and, in particular, its dependency on wind direction and on tunnel geometry. Reduced scale models of generic configurations of a tunnel portal are studied in an atmospheric wind tunnel. Pressure distributions over the front section of different open cavities are measured with surface taps, which allows us to infer the influence of the tunnel aspect ratio and wind direction on a pressure coefficient \(C_{P}\), defined as a spatially and time averaged non-dimensional pressure. Experiments reveal that the magnitude of the coefficient \(C_{P}\), as a function of the wind direction, is significantly influenced by the portal height-to-width ratio and almost insensitive to its length. The experimental data set is completed by hot-wire anemometry measurements providing vertical distribution of velocity statistics. The same configurations are simulated by numerically solving the Reynolds-averaged Navier–Stokes equations, adopting the standard \(k - \varepsilon\) turbulence model. Despite some discrepancies between numerical and experimental estimates of some flow parameters (namely the turbulent kinetic energy field), the numerical estimates of the pressure coefficients \(C_{P}\) show very good agreement with experimental data. The latter is also compared to the predictions of an analytical model, based on the estimate of a spatially averaged velocity within an infinitely long street canyon. The results of the model, which takes into account varying canyon aspect ratios, are in reasonable agreement with experimental data for all cases studied. Notably, its predictions are significantly better than those provided by the simple analytical relations usually adopted as a reference in tunnel ventilation studies.     

Development of similarity relationships for energy dissipation rate and temperature structure parameter in stably stratified flows: a direct numerical simulation approach

In this study, a newly developed direct numerical simulation (DNS) solver is utilized for the simulations of numerous stably stratified open-channel flows with bulk Reynolds number (Re _b ) spanning 3400–16,900. Overall, the simulated bulk Richardson number (\(Ri_b\)) ranges from 0.08 (weakly stable) to 0.49 (very stable). Thus, both continuously turbulent and (globally) intermittently turbulent cases are represented in the DNS database. Using this comprehensive database, various flux-based and gradient-based similarity relationships for energy dissipation rate (ε) and temperature structure parameter (\(C_T^2\)) are developed. Interestingly, these relationships exhibit only minor dependency on Re _b . In order to further probe into this Re _b -effect, similarity relationships are also estimated from a large-eddy simulation (LES) run of an idealized atmospheric boundary layer (very high Re _b ) case study. Despite the fundamental differences in the estimation of ε and \(C_T^2\) from the DNS- and the LES-generated data, the resulting similarity relationships, especially the gradient-based ones, from these numerical approaches are found to be remarkably similar. More importantly, these simulated relationships are also comparable, at least qualitatively, to the traditional observational data-based ones. Since these simulated similarity relationships do not require Taylor’s hypothesis and do not suffer from mesoscale disturbances and/or measurement noise, they have the potential to complement the existing similarity relationships.     

The CPCAT as a novel tool to overcome the shortcomings of NOEC/LOEC statistics in ecotoxicology: a simulation study to evaluate the statistical power

Species reproduction is an important determinant of population dynamics. As such, this is an important parameter in environmental risk assessment. The closure principle computational approach test (CPCAT) was recently proposed as a method to derive a NOEC/LOEC for reproduction count data such as the number of juvenile Daphnia. The Poisson distribution used by CPCAT can be too restrictive as a model of the data-generating process. In practice, the generalized Poisson distribution could be more appropriate, as it allows for inequality of the population mean \(\mu\) and the population variance \(\sigma ^2\). It is of fundamental interest to explore the statistical power of CPCAT and the probability of determining a regulatory relevant effect correctly. Using a simulation, we varied between Poisson distribution (\(\mu =\sigma ^2\)) and generalized Poisson distribution allowing for over-dispersion (\(\mu <\sigma ^2\)) and under-dispersion (\(\mu >\sigma ^2\)). The results indicated that the probability of detecting the LOEC/NOEC correctly was \(\ge 0.8\) provided the effect was at least 20% above or below the mean level of the control group and mean reproduction of the control was at least 50 individuals while over-dispersion was missing. Specifically, under-dispersion increased, whereas over-dispersion reduced the statistical power of the CPCAT. Using the well-known Hampel identifier, we propose a simple and straight forward method to assess whether the data-generating process of real data could be over- or under-dispersed.     

Effect of atmospheric boundary layer stability on the inclination angle of turbulence coherent structures

Coherent structures in the atmospheric boundary layer are fundamental to the transport of momentum and heat as well as to the production of turbulence. The present work attempts to investigate the behavior of the inclination angle of the vortex packet structures (\(\gamma\)) under different stability conditions. The data were collected from the Marine Ecosystem Research Centre (EKOMAR) site at the east coast of Peninsular Malaysia. The main measurements were conducted by placing two hotwires 3 and 12 m above ground. The two-point correlation method was used to calculate the vortex packet structure inclination angle, while the one-point correlation method was employed to calculate its length-scale. The inclination angle was found to increase under both stable and unstable conditions. As the Obukhov stability parameter (\(\zeta\)) approaches 0, the inclination angle ranged between \(\gamma = 15^\circ\) to \(\gamma = 18^\circ\) for the stable and unstable conditions, respectively, which agrees with the findings of previous research. The vertical gradient of velocity is the dominant parameter affecting the inclination angle under different stability conditions.     

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).     

Integral models for bubble,droplet, and multiphase plume dynamics in stratification and crossflow

We present the development and validation of a numerical modeling suite for bubble and droplet dynamics of multiphase plumes in the environment. This modeling suite includes real-fluid equations of state, Lagrangian particle tracking, and two different integral plume models: an Eulerian model for a double-plume integral model in quiescent stratification and a Lagrangian integral model for multiphase plumes in stratified crossflows. Here, we report a particle tracking algorithm for dispersed-phase particles within the Lagrangian integral plume model and a comprehensive validation of the Lagrangian plume model for single- and multiphase buoyant jets. The model utilizes literature values for all entrainment and spreading coefficients and has one remaining calibration parameter \( \kappa \), which reduces the buoyant force of dispersed phase particles as they approach the edge of a Lagrangian plume element, eventually separating from the plume as it bends over in a crossflow. We report the calibrated form \( \kappa = [(b - r) / b]^4 \), where b is the plume half-width, and r is the distance of a particle from the plume centerline. We apply the validated modeling suite to simulate two test cases of a subsea oil well blowout in a stratification-dominated crossflow. These tests confirm that errors from overlapping plume elements in the Lagrangian integral model during intrusion formation for a weak crossflow are negligible for predicting intrusion depth and the fate of oil droplets in the plume. The Lagrangian integral model has the added advantages of being able to account for entrainment from an arbitrary crossflow, predict the intrusion of small gas bubbles and oil droplets when appropriate, and track the pathways of individual bubbles and droplets after they separate from the main plume or intrusion layer.     

On the periodicity of atmospheric von Kármán vortex streets

For over 100 years, laboratory-scale von Kármán vortex streets (VKVSs) have been one of the most studied phenomena within the field of fluid dynamics. During this period, countless publications have highlighted a number of interesting underpinnings of VKVSs; nevertheless, a universal equation for the vortex shedding frequency ( \(N\) ) has yet to be identified. In this study, we have investigated \(N\) for mesoscale atmospheric VKVSs and some of its dependencies through the use of realistic numerical simulations. We find that vortex shedding frequency associated with mountainous islands, generally demonstrates an inverse relationship to cross-stream obstacle length ( \(L\) ) at the thermal inversion height of the atmospheric boundary layer. As a secondary motive, we attempt to quantify the relationship between \(N\) and \(L\) for atmospheric VKVSs in the context of the popular Strouhal number ( \(Sr\) )–Reynolds number ( \(Re\) ) similarity theory developed through laboratory experimentation. By employing numerical simulation to document the \(Sr{-}Re\) relationship of mesoscale atmospheric VKVSs (i.e., in the extremely high \(Re\) regime) we present insight into an extended regime of the similarity theory which has been neglected in the past. In essence, we observe mesoscale VKVSs demonstrating a consistent \(Sr\) range of 0.15–0.22 while varying \(L\) (i.e, effectively varying \(Re\) ).     

Analysis and prediction of $$\mathrm{PM}_{10}$$ concentration levels in Tunisia using statistical learning approaches

Over the past years, the health impact of airborne particulate matter \(\mathrm{PM}_{10}\) has become a very topical subject. Thereby, a lot of research effort in the environmental sciences goes towards the modeling and the prediction of ambient \(\mathrm{PM}_{10}\) concentrations. In this paper, we are interested in the statistical classification of the daily mean \(\mathrm{PM}_{10}\) concentration in Tunisia according to the authority regulation. We consider two monitoring stations: a big industrial station and a traffic station. The main goal of this work is to determine the pertinent predictors of \(\mathrm{PM}_{10}\) concentration within a nonlinear multiclass framework. To do this, we used two popular statistical learning methods; the support vector machines (SVM) and the random forests (RF). The statistical results obtained on the real datasets, show that RF outperform SVM for the purpose of variable selection even with a reduced number of observations compared to the number of explicative variables. It was also demonstrated that the \(\mathrm{PM}_{10}\) concentration measured yesterday is the most relevant predictor of its present-day value. Moreover, we found that the more delayed values of \(\mathrm{PM}_{10}\) concentration may be crucial to get an accurate prediction.     

Effect of wastewater composition on the calcium carbonate precipitation in upflow anaerobic sludge blanket reactors

Calcium carbonate often precipitates in anaerobic reactors treating wastewater with high calcium content. The aim of this paper is to study the effect of wastewater composition on calcium carbonate precipitation in upflow anaerobic sludge blanket (UASB) reactors. Two laboratory-scale UASB reactors were operated with calcium-containing influents using acetate and carbohydrate as substrate, respectively. There was an obvious accumulation of inorganic precipitate observed in the biogranules. Observations via scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS) showed that the acclimated biogranules in the two reactors differed in microstructure. Calcium carbonate was found to have precipitated on the surface of acetate-degrading biogranules, but precipitated at the core of the carbohydrate-degrading biogranules. The results indicated that substrates had significant influence on the location of calcium carbonate precipitation in anaerobic granular sludge, which was expected due to the different methanogens distribution and pH gradient within the granular sludge degrading various substrates. Moreover, the location of calcium carbonate precipitation substantially affected the specific methanogenic activity (SMA) of the granular sludge. The SMA of the acetate-degrading biogranules dropped from \(1.96 gCOD_{CH_4 } \cdot gVSS^{ - 1} \cdot d^{ - 1} \) to \(0.61 gCOD_{CH_4 } \cdot gVSS^{ - 1} \cdot d^{ - 1} \) after 180-d of operation in the reactor. However, the SMA of the carbohydrate-degrading biogranules was not adversely affected by calcium carbonate precipitation.     

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.

     

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.     

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.     

Warm discharges in cold fresh water: 2. Numerical simulation of laminar line plumes

The behaviour of a discharge of warm water upwards into a homogeneous body of cold fresh water was investigated by means of a numerical model. The discharge has a parabolic velocity profile, with Reynolds number \(Re=50\), Prandtl number \(Pr=7\) and Froude number varied over the range \(0.2 \le {\rm Fr} \le 2.5\). Water density is taken to be a quadratic function of temperature, so that an initially positively buoyant discharge will experience buoyancy reversal as it mixes with an ambient below the temperature of maximum density. The resulting plume has some similarities to a fountain resulting from injection of negatively buoyant fluid upward into a less dense ambient. The plume is initially symmetric, but then its head detaches as it approaches its maximum height. The detached head is denser than the fluid in the plume below it, and the interaction between the sinking head and the rising plume causes a sideways deflection; as this cycle is repeated, the plume displays side-to-side flapping motion and vertical bobbing. As Froude number is increased (i.e. buoyancy reduced) the growth of the plume becomes slower, but the plume eventually reaches a greater height. We obtain empirical power-law scalings for maximum height and time taken to reach that height as functions of Froude number; these scalings are simlar to those for fountains with a linear dependence of density on temperature in the very weak regime.