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.     

Influence of planform geometry and momentum ratio on thermal mixing at a stream confluence with a concordant bed

The effects of planform geometry and momentum flux ratio on thermal mixing at a stream confluence with concordant bed morphology are investigated based on numerical simulations that can capture the dynamics of large-scale turbulence. In two simulations, the bathymetry and asymmetrical planform geometry are obtained from field experiments and the momentum flux ratio is set at values of one and four. These two conditions provide the basis for studying differences in thermal mixing processes at this confluence when the wake mode and the Kelvin–Helmholtz mode dominate the development of coherent structures within the mixing interface (MI). The effects of channel curvature and angle between the two incoming streams on thermal mixing processes are investigated based on simulations conducted with modified planform geometries. Two additional simulations are conducted for the case where the upstream channels are parallel but not aligned with the downstream channel and for the zero-curvature case where the upstream channels are parallel and aligned with the downstream channel. The simulations highlight the influence of large-scale coherent structures within the MI and of streamwise-oriented vortical (SOV) cells on thermal mixing processes within the confluence hydrodynamics zone. Simulation results demonstrate the critical role played by the SOV cells in promoting large-scale thermal mixing for cases when such cells form in the immediate vicinity of the MI and in modifying the shape of the thermal MI within cross sections of the downstream channel—predictions consistent with empirical measurements of thermal mixing at the confluence. The set of numerical simulations reveal that the degree of thermal mixing occurring within the confluence hydrodynamic zone varies dramatically with planform geometry and incoming flow conditions. In some cases thermal mixing at the downstream end of the confluence hydrodynamic zone is limited to the MI and its immediate vicinity, whereas in others substantial thermal mixing has occurred over most of the cross-sectional area of the flow. Overall, the simulations highlight the flow conditions and the controls of these conditions that influence mixing within the immediate vicinity of a confluence.     

Turbulent flow characteristics and drag over 2-D forward-facing dune shaped structures with two different stoss-side slopes

The present paper explores the characteristics of turbulent flow and drag over two artificial 2-D forward-facing waveform structures with two different stoss side slopes of $50^{\circ }$ and $90^{\circ },$ respectively. Both structures possessed a common slanted lee side slope of $6^{\circ }.$ Flume experiments were conducted at the Fluvial Mechanics Laboratory of Indian Statistical Institute, Kolkata. The velocity data were analyzed to identify the spatial changes in turbulent flow addressing the flow separation region with recirculating eddy, the Reynolds stresses, the turbulent events associated with burst-sweep cycles and the drag over two upstream-facing bedforms for Reynolds number $Re_h=1.44\times 10^5.$ The divergence at the stoss side slope between the two structures revealed significant changes in the mean flow and turbulence. Comparison showed that during the flood-tide condition there was no flow separation region on the gentle lee side of the structure with smaller slope at the stoss side, while for the other structure with vertical stoss side slope a thick flow separation region with recirculating eddy was observed at the gentle lee side just downstream of the crest. The recirculating eddy induced on the lee-side had a strong influence on the resistance that the structure exerts to the flow due to loss of energy through turbulence. In contrast, a great amount of reduction in drag was observed in the case of smaller stoss side sloped structure as there was no flow separation. The quadrant analysis was also used to highlight the turbulent event evolution along the bed form structures under flood-tide conditions.     

Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

Numerical simulation of particle-driven gravity currents

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) ${k-\epsilon}$ scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG ${k-\epsilon}$ and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration C _o /C _i by the gravity current varies as a function of the particle diameter d _s . We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (d _s is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm < d _s <40 μm) where deposition rates significantly change the flow dynamics; and (3) a deposition regime (d _s ?> 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG ${k-\epsilon}$ turbulence closure scheme for field scale investigation of particle-driven gravity currents.     

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.     

Spatial–temporal structure of mixing interface turbulence at two large river confluences

Converging flows at stream confluences often produce highly turbulent conditions. The shear layer/mixing interface that develops within the confluence hydrodynamic zone (CHZ) is characterized by complex patterns of three-dimensional flow that vary both spatially and temporally. Previous research has examined in detail characteristics of mean flow and turbulence along mixing interfaces at small stream confluences and laboratory junctions; however few, if any, studies have examined these characteristics within mixing interfaces at large river confluences. This study investigates the structure of mean velocity profiles as well as spatial and temporal variations in velocity, backscatter intensity, and temperature within the mixing interfaces of two large river confluences. Velocity, temperature, and backscatter intensity data were obtained at stationary locations within the mixing interfaces and at several cross sections within the CHZ using acoustic Doppler current profilers. Results show that mean flow within the mixing interfaces accelerates over distance from the junction apex. Turbulent kinetic energy initially increases rapidly over distance, but the rate of increase diminishes downstream. Hilbert–Huang transform analysis of time series data at the stationary locations shows that multiple dominant modes of fluctuations exist within the original signals of velocity, backscatter intensity, and temperature. Frequencies of the largest dominant modes correspond well with predicted frequencies for shallow wake flows, suggesting that mixing-interface dynamics include wake vortex shedding—a finding consistent with spatial patterns of depth-averaged velocities at measured cross sections. Spatial patterns of temperature and backscatter intensity show that the converging flows at both confluences do not mix substantially, indicating that turbulent structures within the mixing interfaces are relatively ineffective at producing mixing of the flows in the CHZ.     

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.     

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.     

One-dimensional modelling of sediment deposition in reservoirs with sinking streams

It is common in karst regions that rivers are occasionally cut by mountains, resulting in the alternate appearances of open channel flow and pressurized flow. With more and more reservoirs being built in this region, the complicated sediment transport processes of such mixture flow are urgently needed to study. In this paper a one-dimensional numerical model with free surface and pressurized flows coupled together is presented. The simulated results are analyzed to explore deposition process in reservoirs with sinking streams; impacts of different hydraulic conditions on the sedimentation are also studied. To verify the computed results, a flume experiment is also conducted. The results show that deposition of sediments mainly occurs in open channel reaches where the longitudinal profile is similar to that of conventional reservoirs, i.e. typical delta has formed, demonstrating characteristics of deltaic deposition morphology in that the crest of delta moves to the downstream direction over time. The model provided by this paper is not only proved to simulate the characteristics of deposition in karst reservoirs successfully, but also reveal the impacts of hydraulic conditions in such circumstances.     

Using surface drifter observations to measure tidal vortices and relative diffusion at Aransas Pass,Texas

Tidal vortices play an important role in the flushing of coastal regions. At the mouth of a tidal inlet, the input of circulation by the ebb tide may force the formation of a starting-jet dipole vortex. The continuous ebb jet current also creates a periodic sequence of secondary vortices shed from the inlet mouth. In each case, these tidal vortices have a shallow aspect ratio, with a lateral extent much greater than the water depth. These shallow vortices affect the transport of passive tracers, such as nutrients and sediment from the estuary to the ocean and vice versa. Field observation of tidal vortices primarily relies on ensemble averaging over several vortex events that are repeatable in space and can be sampled by a fixed Eulerian measurement grid. This paper presents an adaptive approach for locating and measuring within tidal vortices that propagate offshore near inlets and advect along variable trajectories set by the wind-driven currents. A field experiment was conducted at Aransas Pass, Texas to measure these large-scale vortices. Locations of the vortices produced during ebb tide were determined using near real-time updates from surface drifters deployed near or within the inlet during ebb tide, and the paths of towed acoustic Doppler current profiler (ADCP) transects were selected by analysis of the drifter observations. This method allowed ADCP transects to be collected within ebb generated tidal vortices, and the paths of the drifters indicated the presence of both the starting-jet dipole and the secondary vortices of the unstable ebb tidal jet. Drifter trajectories were also used to estimate the size of each observed vortex as well as the statistics of relative diffusion offshore of Aransas Pass. The field data confirmed the starting-jet spin-up time (time until the vortex dipole begins to propagate offshore) measured in the laboratory by Bryant et al. [6] and that the Strouhal condition of \(St=0.2\) predicts the shedding of secondary vortices from the inlet mouth. The size of the rotational core of the vortex is also shown to be approximated physically by the inlet width or by \(0.02UT\) , where U is the maximum velocity through the inlet channel and T is the tidal period, and confirms results found in laboratory experiments by Nicolau del Roure et al. [23]. Additionally, the scale of diffusion was approximately 1–15 km and the apparent diffusivity was between 2–130  \(m^2/s\) following Richardsons law.     

The evolution of large and small-scale structures in Kelvin–Helmholtz instabilities

To better understand the dynamics of Kelvin–Helmholtz instabilities in environmental flows, their evolution is investigated using direct numerical simulations (DNS). Two-dimensional DNS is used to examine the large-scale and small-scale structures of the instability at high Reynolds and Prandtl numbers that represent real environmental flows. The semi-analytical model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) is used to explain the physics of these simulations prior to saturation of the KH billow, and also provide a computationally efficient prediction of the vortex dynamics of the instability. The DNS results show that the large-scale structure of the billow does not depend on the Reynolds number for sufficiently high Reynolds numbers. The billow structure reveals a less straightforward dependence on the Prandtl number. Predictions of the model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) improve as Reynolds number and Prandtl number increase. The small-scale structure of the vorticity and density fields vary with both Reynolds and Prandtl numbers. Three-dimensional DNS of KH flows and their transition to turbulence are used to study small length scales. Based on the thickness of the braid, a simple method is introduced to estimate the Batchelor scale, which can be used as a guide for the resolution required for the direct numerical simulation of two and three-dimensional Kelvin–Helmholtz flow fields.     

Experimental study of recirculating flows generated by lateral shock waves in very large channels

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

Experimental and numerical study on the shear velocity distribution along one or two dunes in tandem

This paper investigates, experimentally and numerically, the shear velocity distribution along a single transverse dune and along two closely spaced dunes, analyzing the flow effects of one dune upon the other. The paper focuses on two-dimensional models simulating transverse sand dunes. The shape of the two pile geometries studied is described by sinusoidal curves, one having a maximum slope of $32^{\circ }$ and the other $27.6^{\circ }$ , with leeward flow separation. The tests were carried out for two undisturbed wind speeds and the experimental data obtained through wind-tunnel modeling encompass flow visualization and shear-velocity results. A generally good agreement is observed between the experimental measurements and computational results. From the inquiry between shear velocity distributions and published eroded contours for the same geometries, it appears the Bagnold’s approach is insufficient in the prediction of threshold conditions in wake flows formed in the dune’s leeward side.     

Gravity currents with tailwaters in Boussinesq and non-Boussinesq systems: two-layer shallow-water dam-break solutions and Navier–Stokes simulations

We consider the dam-break initial stage of propagation of a gravity current of density $\rho _{c}$ released from a lock (reservoir) of height $h_0$ in a channel of height $H$ . The channel contains two-layer stratified fluid. One layer, called the “tailwater,” is of the same density as the current and is of thickness $h_T (< h_0)$ , and the other layer, called the “ambient,” is of different density $\rho _{a}$ . Both Boussinesq ( $\rho _{c}/\rho _{a}\approx 1$ ) and non-Boussinesq systems are investigated. By assuming a large Reynolds number, we can model the flow with the two-layer shallow-water approximation. Due to the presence of the tailwater, the “jump conditions” at the front of the current are different from the classical Benjamin formula, and in some circumstances (clarified in the paper) the interface of the current matches smoothly with the horizontal interface of the tailwater. Using the method of characteristics, analytical solutions are derived for various combinations of the governing parameters. To corroborate the results, two-dimensional direct numerical Navier–Stokes simulations are used, and comparisons for about 80 combinations of parameters in the Boussinesq and non-Boussinesq domains are performed. The agreement of speed and height of the current is very close. We conclude that the model yields self-contained and fairly accurate analytical solutions for the dam-break problem under consideration. The results provide reliable insights into the influence of the tailwater on the propagation of the gravity current, for both heavy-into-light and light-into-heavy motions. This is a significant extension of the classical gravity-current theory from the particular $h_T=0$ point to the $h_T > 0$ domain.     

Statistical properties of concentration fluctuations in two merging plumes

The statistics of the fluctuating concentration field within a plume is important in the analysis of atmospheric dispersion of toxic, inflammable and odorous gases. Previous work has tended to focus on concentration fluctuations in single plumes released in the surface layer or at ground level and there is a general lack of information about the mixing of two adjacent plumes and how the statistical properties of the concentration fluctuations are modified in these circumstances. In this work, data from wind tunnel experiments are used to analyse the variance, skewness, kurtosis, intermittency, probability density function and power spectrum of the concentration field during the mixing of two identical plumes and results are compared with those obtained for an equivalent single plume. The normalised variance, skewness and kurtosis on the centre-lines of the combined plume increase with distance downwind of the stack and, in the two-source configuration, takes lower values than those found in the single plumes. The results reflect the merging process at short range, which is least protracted for cases in which the sources are in-line or up to 30 \(^{\circ }\) off-line. At angles of 45 \(^{\circ }\) and more, the plumes are effectively side-by-side during the merging process and the interaction between the vortex pairs in each plume is strong. Vertical asymmetry is observed between the upper and the lower parts of the plumes, with the upper part having greater intermittency (i.e. the probability that no plume material is present) and a more pronounced tail to the concentration probability distribution. This asymmetry tends to diminish at greater distances from the source but occurs in both buoyant and neutral plumes and is believed to be associated with the ‘bending-over’ of the emission in the cross-flow and the vortex pair that this generates. The results allowed us to identify three phases in plume development. The first, very near the stack, is dominated by turbulence generated within the plume and characterised by concentration spectra with distinct peaks corresponding to scales comparable with those of the counter-rotating vortex pair. A second phase follows at somewhat greater distances downwind, in which there are significant contributions to the concentration fluctuations from both the turbulence internal to the plume and the external turbulence. The third phase is one in which the concentration fluctuations appear to be controlled by the external turbulence present in the ambient flow.     

Analytical expression for predicting the reduced settling velocity of small particles in turbulence

The influence of turbulence on the settling velocity of small particles remains an inconclusive research subject. Both enhanced and retarded particle settling compared to quiescent settling have been reported in previous literature, and several theories have been proposed. Among the mechanisms that account for reduced settling velocities in turbulence, the loitering effect is an important one that generally exists in various conditions. This study focuses on an analytical prediction of reduced particle settling velocities due to the loitering effect. By considering the velocity autocorrelation function as a step function analogous to the free path theory, and using a modified integral time scale to capture the essence of the loitering effect, an analytical expression is derived for predicting the reduction in particle settling velocities in turbulent flows. Calculation results of the expression are then examined by comparing with the results of a random walk model, direct numerical simulations that conditionally captured the reduction of particle settling velocities due to the loitering effect, and several representative experiments. Major possible influencing factors on the prediction of the analytical expression and applicable conditions of the expression are then further discussed. The proposed analytical expression is shown to be suitable for predicting the reduced settling velocities of small particles with relatively weak inertia in turbulent flows and could provide a reasonable explanation for reported cases in which small to moderate reductions in particle settling velocities were observed.

     

Aeolian erosion of storage piles yards: contribution of the surrounding areas

Dust emissions from stockpiles surfaces are often estimated applying mathematical models such as the widely used model proposed by the USEPA. It employs specific emission factors, which are based on the fluid flow patterns over the near surface. But, some of the emitted dust particles settle downstream the pile and can usually be re-emitted which creates a secondary source. The emission from the ground surface around a pile is actually not accounted for by the USEPA model but the method, based on the wind exposure and a reconstruction from different sources defined by the same wind exposure, is relevant. This work aims to quantify the contribution of dust re-emission from the areas surrounding the piles in the total emission of an open storage yard. Three angles of incidence of the incoming wind flow are investigated ( $30^{\circ }, 60^{\circ }$ and $90^{\circ }$ ). Results of friction velocity from numerical modelling of fluid dynamics were used in the USEPA model to determine dust emission. It was found that as the wind velocity increases, the contribution of particles re-emission from the ground area around the pile in the total emission also increases. The dust emission from the pile surface is higher for piles oriented $30^{\circ }$ to the wind direction. On the other hand, considering the ground area around the pile, the $60^{\circ }$ configuration is responsible for higher emission rates (up to 67 %). The global emissions assumed a minimum value for the piles oriented perpendicular to the wind direction for all wind velocity investigated.