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.     

Particle laden flows through an inverted chimney with applications to ocean carbon sequestration

Plumes of negatively buoyant hydrate particles, formed by reacting liquid CO₂ with seawater at ocean depths of 1000–1500 m, have been suggested as a way to help sequester CO₂. The vertical flux of CO₂ can be increased by constructing a shroud around the hydrate particle source to shelter the plume from effects of ambient stratification and current. The shroud also serves as an inverted chimney, inducing a down draft that will transport the dissolving particles to a depth of lower ambient disturbance. Laboratory PIV measurements are compared to an analysis of an idealized shroud that is long, frictionless and driven by a single phase source of buoyancy distributed uniformly over the shroud base. Results indicate that induced draft, and hence dilution of dissolved CO₂, increases with plume buoyancy, and shroud length and diameter, but efficiency decreases with increasing ratio of particle slip velocity divided by the characteristic induced draft velocity. While larger particles show reduced plume-like behavior and hence are less efficient in inducing draft, they still generated about half of the theoretically predicted flow.     

Simulation of Jeddah multi-port sea outfall

Jeddah wastewater multi-port outfall was analyzed using CORMIX2 for average ambient conditions. The numerical analysis of the outfall shows that the near-field mixing extends 187.5 m downstream of the diffuser and the dilution at the end of near-field reaches 1,047.8. The concentration of the plume drops sharply from 100 at the exit point to 0.0954 at the end of near-field zone. In the far-field zone the reduction in concentration is gradual and will reach 0.0061 at a distance of 20,000 m downstream of the diffuser, while dilution exceeds 16,440 at this point. The plume rises rapidly due to the buoyancy and touches the water surface at a distance of 187.5 m downstream. The thickness of the plume reaches a maximum value of 37.5 m at the interface of near-field and far-Field zones, and then it starts spreading horizontally maintaining a thickness of about 13 m over a distance of about 4 km. As the plume mixes with ambient sea water, it starts spreading again in vertical direction and fills the entire water depth at a distance of 18,927 m down stream. The plume maintains nearly a constant width in the near-field zone but spreads progressively horizontally in the far-field zone till the plume touches the left bank at a distance of 18,482.52 m downstream. The plume spreads at a distance of 2,069 m from the coastline at the end of simulation zone. It can be concluded from numerical results that if the discharged water meets local and international standards for treated wastewater, the plume will not pose any threats to the local venerable environment as the dilution is considerably high due to high exit momentum and favorable cross current.     

Experimental Study of the Criteria of Flow Laminarization in Two-Dimensional Dense Gas Plumes

Laminarization of flow in a two-dimensional dense gas plume was experimentally investigated in this study. The plume was created by releasing CO₂ through a ground-level line source into a simulated turbulent boundary layer over an aerodynamically rough surface in a meteorological wind tunnel. The bulk Richardson number (Ri_*), based on negative plume buoyancy, plume thickness, and friction velocity, was varied over a wide range so that the effects of stable stratification on plume laminarization could be observed. A variety of ambient wind speeds as well as three different sizes of roughness arrays were used so that possible effects of roughness Reynolds number (Re_*) on plume laminarization could also be identified. Both flow visualization methods and quantitative measurements of velocity and intermittency of turbulence were used to provide quantitative assessments of plume laminarization.Flow visualization provided an overall picture of how the plume was affected by the negative buoyancy. With increasing Ri_*, both the plume depth and the vertical mixing were significantly suppressed, while upstream propagation of the plume from the source was enhanced. The most important feature of the flow revealed by visualization was the laminarization of flow in the lower part of the plume, which appeared to be closely related to both Ri_* and Re_*.Measurements within the simulated dense gas plumes revealed the influence of the stable stratification on mean velocity and turbulence intensity profiles. Both the mean velocity and turbulence intensity were significantly reduced near the surface; and these reductions systematically depended on Ri_*. The roughness Reynolds number also had considerable influence on the mean flow and turbulence structure of the dense gas plumes.An intermittency analysis technique was developed and applied to the digitized instantaneous velocity signals. It not only confirmed the general flow picture within the dense plume indicated by the flow visualization, but also clearly demonstrated the changes of flow regime with variations in Ri_* and Re_*. Most importantly, based on this intermittency analysis, simple criteria for characterizing different flow regimes are formulated; these may be useful in predicting when plume laminarization might occur.     

Vertical Buoyant Jets in a Linearly Stratified Ambient Cross-Stream

In this study a numerical simulation is performed to investigate the effect of ambient density stratification on the characteristic of a vertical buoyant jet in a stably linearly stratified ambient cross-stream. Based on the ensemble integral method, the theoretical formulation for such a flow field consists of a set of elliptic Reynolds-averaged equations incorporating with the k– transport equations for the turbulence closure. An oscillating motion can be observed in the computed jet trajectory, and the corresponding alternative variation of dominant quantities for the induced momentum and buoyancy of the jet are examined by direct integration on a cross-section along the jet axis. The influences on the jet development both by the ambient cross-stream and the stratification are investigated. The oscillation characteristic shows that a linear relation holds between the wavenumber of jet trajectory, crossflow velocity and the Brunt–Väisälä frequency of ambient stratification. Computational results indicate that the formation of the secondary and a third pairs of vortices, which are not induced in the unstratified environment, causes the jet flow oscillation from its maximum height-of-rise in the flowing direction. The ambient stratification prohibits the growth of the plume radius and reduces the mixing rate as well as the plume rise. The developed flow indicates the transformation of entrainment mechanism in stratified crossflow.     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows Part 2: Plane Jet Dynamics Resulting from Multiport Diffuser Jets

An integral model for the plane buoyant jet dynamics resulting from the interaction of multiple buoyant jet effluxes spaced along a diffuser line is considered as an extension of the round jet formulation that was proposed in Part I. The receiving fluid is given by an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions. Applications for this situation are primarily for submerged multiport diffusers for discharges of liquid effluents into ambient water bodies, but also for multiple cooling tower plumes and building air-conditioning. The CorJet model formulation describes the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow in the plane jet geometry. It employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear and of internal instability mechanisms, and contains a quadratic law turbulent pressure force mechanism. But the model formulation also includes several significant three-dimensional effects that distinguish actual diffuser installations in the water environment. These relate to local merging processes from the individual multiple jets, to overall finite length effects affecting the plume geometry, and to bottom proximity effects given by a “leakage factor” that measures the combined affect of port height and spacing in allowing the ambient flow to pass through the diffuser line in order to provide sufficient entrainment flow for the mixing downstream from the diffuser. The model is validated in several stages: First, comparison with experimental data for the asymptotic, self-similar stages of plane buoyant jet flows, i.e. the plane pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with data for many types of non-equilibrium flows with a plane geometry support the proposed functional form of the entrainment relationship, and also the role of the pressure force in the jet deflection dynamics. Third, the observed behavior of the merging process from different types of multiport diffuser discharges in both stagnant and flowing ambient conditions and with stratification appears well predicted with the CorJet formulation. Fourth, a number of spatial limits of applicability, relating to terminal layer formation in stratification or transition to passive diffusion in a turbulent ambient shear flow, have been proposed. In sum, the CorJet integral model appears to provide a mechanistically sound, accurate and reliable representation of complex buoyant jet mixing processes, provided the condition of an unbounded receiving fluid is satisfied.     

2D brine sewage after impinging on a shallow sea free surface

We consider the problem of the vertically upwards disposal of heavy brine sewage from a two-dimensional diffuser in a lighter, homogeneous, motionless and shallow ambient sea. The rejected high salinity water of seawater desalination plants for urban and agricultural uses is such a case of a two dimensional fountain. The disposal of brine sewage produces a negative buoyant jet due to its initial momentum, which impinges on the free surface, spreads laterally on it and then sinks downwards, because of the negative buoyancy. Laboratory experiments and dimensional considerations are used in this paper in order to investigate the spreading behavior (width) of the vertical fountain which impinges on the free surface of the shallow ambient fluid. The experimental results have been used to derive an equation relating the width at the free surface with the initial parameters of the flow. In addition, the experimentally measured dilution of the heavier brine sewage on the recipient’s surface is compared with the dilution which was calculated by a numerical simulation of a well-known commercial software package, CORJET (a CORMIX sub model).     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet

The mechanics of buoyant jet flows issuing with a general three-dimensional geometry into an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions is investigated. An integral model is formulated for the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow. The model employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear (leading to jet, plume, or wake internal flow dynamics) and of azimuthal shear mechanisms (leading to advected momentum puff or thermal flow dynamics), respectively. Furthermore, it contains a quadratic law turbulent drag force mechanism as suggested by a number of recent detailed experimental investigations on the dynamics of transverse jets into crossflow. The model is validated in several stages: First, comparison with basic experimental data for the five asymptotic, self-similar stages of buoyant jet flows, i.e., the pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice and magnitude of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with many types of non-equilibrium flows support the proposed transition function within the entrainment relationship, and also the role of the drag force in the jet deflection dynamics. Third, a number of spatial limits of applicability have been proposed beyond which the integral model necessarily becomes invalid due to its parabolic formulation. These conditions, often related to the breakdown of the boundary layer nature of the flow, describe features such as terminal layer formation in stratification, upstream penetration in jets opposing a current, or transition to passive diffusion in a turbulent ambient shear flow. Based on all these comparisons, that include parameters such as trajectories, centerline velocities, concentrations and dilutions, the model appears to provide an accurate and reliable representation of buoyant jet physics under highly general flow conditions.     

Large-eddy simulation of starting buoyant jets

A series of Large Eddy Simulations (LES) are performed to investigate the penetration of starting buoyant jets. The LES code is first validated by comparing simulation results with existing experimental data for both steady and starting pure jets and lazy plumes. The centerline decay and the growth rate of the velocity and concentration fields for steady jets and plumes, as well as the simulated transient penetration rate of a starting pure jet and a starting lazy plume, are found to compare well with the experiments. After validation, the LES code is used to study the penetration of starting buoyant jets with three different Reynolds numbers from 2000 to 3000, and with a wide range of buoyancy fluxes from pure jets to lazy plumes. The penetration rate is found to increase with an increasing buoyancy flux. It is also observed that, in the initial Period of Flow Development, the two penetrative mechanisms driven by the initial buoyancy and momentum fluxes are uncoupled; therefore the total penetration rate can be resolved as the linear addition of these two effects. A fitting equation is proposed to predict the penetration rate by combining the two independent mechanisms.     

On thermally forced flows in urban street canyons

During sunny days with periods of low synoptic wind, buoyancy forces can play a critical role on the air flow, and thus on the dispersion of pollutants in the built urban environments. Earlier studies provide evidence that when a surface inside an urban street canyon is at a higher temperature than that of local ambient air, buoyancy forces can modify the mechanically-induced circulation within the canyons (i.e., gaps between buildings). The aspect ratio of the urban canyon is a critical factor in the manifestation of the buoyancy parameter. In this paper, computational fluid dynamics simulations are performed on urban street canyons with six different aspect ratios, focusing on the special case where the leeward wall is at a greater temperature than local ambient air. A non-dimensional measure of the influence of buoyancy is used to predict demarcations between the flow regimes. Simulations are performed under a range of buoyancy conditions, including beyond those of previous studies. Observations from a field experiment and a wind tunnel experiment are used to validate the results.     

Dynamics of the buoyant plume off the Pearl River Estuary in summer

Field measurements of salinity, wind and river discharge and numerical simulations of hydrodynamics from 1978 to 1984 are used to investigate the dynamics of the buoyant plume off the Pearl River Estuary (PRE), China during summer. The studies have shown that there are four major horizontal buoyant plume types in summer: Offshore Bulge Spreading (Type I), West Alongshore Spreading (Type II), East Offshore Spreading (Type III), and Symmetrical Alongshore Spreading (Type IV). River mouth conditions, winds and ambient coastal currents have inter-influences to the transport processes of the buoyant plume. It is found that all of the four types are surface-advected plumes by analysing the vertical characteristic of the plumes, and the monthly variations of the river discharge affect the plume size dominantly. The correlation coefficient between the PRE plume size and the river discharge reaches 0.85 during the high river discharge season. A wind strength index has been introduced to examine the wind effect. It is confirmed that winds play a significant role in forming the plume morphology. The alongshore wind stress and the coastal currents determine the alongshore plume spreading. The impact of the ambient currents such as Dongsha Current and South China Sea (SCS) Warm Current on the plume off the shelf has also assessed. The present study has demonstrated that both the river discharge and wind conditions affect the plume evolution.     

A Numerical Study of the Dynamics of the Riverine Thermal Bar in a Deep Lake

A numerical model based on a Finite Volume formulation of the Navier–Stokes equations is used to simulate a range of scenarios leading to a thermal bar formed by a river inflow to an idealised deep lake. The results presented here show that small riverine salinity increases have a profound effect on the dynamics of the thermal bar, suppressing horizontal propagation of the plume and raising the possibility of a thermal bar which is capable of sinking to great depths. This finding is particularly relevant to Lake Baikal in Siberia, where the vigorous deep-water renewal is still not fully understood. An analysis of the buoyancy forces governing the depth of penetration of the thermal bar plume shows that realistic salinity gradients are an important factor in determining the circulation of Baikal waters. Observations of the saline curtailment of the thermal bar's horizontal propagation also reveal a potential for reduced productivity in the ecosystem of any temperate river delta during the Spring renewal period.     

Filament-Based Atmospheric Dispersion Model to Achieve Short Time-Scale Structure of Odor Plumes

This article presents the theoretical motivation, implementation approach, and example validation results for a computationally efficient plume simulation model, designed to replicate both the short-term time signature and long-term exposure statistics of a chemical plume evolving in a turbulent flow. Within the resulting plume, the odor concentration is intermittent with rapidly changing spatial gradient. The model includes a wind field defined over the region of interest that is continuous, but which varies with location and time in both magnitude and direction. The plume shape takes a time varying sinuous form that is determined by the integrated effect of the wind field. Simulated and field data are compared. The motivation for the development of such a simulation model was the desire to evaluate various strategies for tracing odor plumes to their source, under identical conditions. The performance of such strategies depends in part on the instantaneous response of target receptors; therefore, the sequence of events is of considerable consequence and individual exemplar plume realizations are required. Due to the high number of required simulations, computational efficiency was critically important.     

Effects of the Resolution and Kinematics of Olfactory Appendages on the Interception of Chemical Signals in a Turbulent Odor Plume

A variety of animals use olfactory appendages bearing arrays of chemosensory neurons to detect chemical signatures in the water or air around them. This study investigates how particular aspects of the design and behavior of such olfactory appendages on benthic aquatic animals affect the patterns of intercepted chemical signals in a turbulent odor plume. We use virtual olfactory `sensors' and `antennules' (arrays of sensors on olfactory appendages) to interrogate the concentration field from an experimental dataset of a scalar plume developing in a turbulent boundary layer. The aspects of the sensors that we vary are: (1) The spatial and temporal scales over which chemical signals arriving at the receptors of a sensor are averaged (e.g., by subsequent neural processing), and (2) the shape and orientation of a sensor with respect to ambient water flow. Our results indicate that changes in the spatial and temporal resolution of a sensor can dramatically alter its interception of the intermittency and variability of the scalar field in a plume. By comparing stationary antennules with those sweeping through the flow (as during antennule flicking by the spiny lobster, Panulirus argus), we show that flicking alters the frequency content of the scalar signal, and increases the likelihood that the antennule encounters peak events. Flicking also enables a long, slender (i.e., one-dimensional) antennule to intercept two-dimensional scalar patterns.     

Stratification and Tidal Current Effects on Larval Transport in the Eastern English Channel: Observations and 3D Modeling

We study how the combination of tides and freshwater buoyancy affects the marine organisms accumulation and horizontal transport in the ROFI system of the eastern English Channel. The Princeton Ocean Model coupled with a particle-tracking module is used to study the migration of fish eggs and larvae under different forcing conditions. Results of modeling are validated against observed concentrations of Flounder (Pleuronectes flesus) larvae. Numerical Lagrangian tracking experiments are performed with passive and active particles, representing sea-water organisms. Passive particles are neutrally buoyant whereas active particles are able to exercise light dependent vertical migrations equating to the swimming behavior of larvae. The experiments reveal that the strongest accumulation of particles occurs along the French coast on the margin of the ROFI. This happens because the interaction between the turbulence, the freshwater buoyancy input, and tidal dynamics, produces particle trapping and vertical spreading within the frontal convergence zone. Tides and freshwater input induce net alongshore horizontal transport toward the North. Tidal currents modulate the magnitude of horizontal transport whereas the fresh water input controls more the location of accumulation zones. Tracking experiments with active particles indicate that the vertical migration leads to a significant departure from the passive particle transport pattern. Differences lie in the shape of the particle transport pattern and the rate of the northward migration. In particular, vertically migrating particles travel slower. To find possible Flounder migration pathways, particles are released within the assumed spawning area of Flounder. The model predicts larvae drift routes and demonstrates that throughout the entire particle-tracking period the horizontal structure of the particle distribution is consistent with the larvae concentrations observed during the field experiments.     

Plume rise and spread in buoyant releases from elevated sources in the lower atmosphere

This study focuses on the influence of emission conditions—velocity and temperature—on the dynamics of a buoyant gas release in the atmosphere. The investigations are performed by means of wind tunnel experiments and numerical simulations. The aim is to evaluate the reliability of a Lagrangian code to simulate the dispersion of a plume produced by pollutant emissions influenced by thermal and inertial phenomena. This numerical code implements the coupling between a Lagrangian stochastic model and an integral plume rise model being able to estimate the centroid trajectory. We verified the accuracy of the plume rise model and we investigated the ability of two Lagrangian models to evaluate the plume spread by means of comparisons between experiments and numerical solutions. A quantitative study of the performances of the models through some suitable statistical indices is presented and critically discussed. This analysis shows that an additional spread has to be introduced in the Lagrangian trajectory equation in order to account the dynamical and thermal effects induced by the source conditions.     

Calculation of search volume on cruise-searching planktivorous fish in foraging model

Search volume of cruising planktivorous fish was calculated based on its detailed behavior Th examine the factors influencing search volume, a series of experiments were conducted by varying ambient conditions, such as structural complexity light intensity and turbidity Pseudorasbora parva were used in experiment as predator and Daphnia pulex was selected as prey The shape of scanning area of P parva showed elliptic and the search volume changed drastically depending on ambient conditions. Compared with the results of previous foraging model, the search volumes of the fish under previous study were larger (1.2 to 2.4 times) than those from our study These results on the changes in feeding rate can be useful in determining microhabitat requirement of P parva and othercyprinids with a similar foraging behavior The calculated search volume is compared with other foraging model andthe effect of zooplankton-planktivore interactions on aquatic ecosystem is discussed.     

Factors affecting buoyancy in the eggs of Bairdiella icistia (Pisces: Sciaenidae)

Several aspects of buoyancy were studied in the normally pelagic eggs of the sciaenid fish Bairdiella icistia (Jordan and Gilbert). Spawning fish acclimated to a low salinity (15‰) produced larger, more buoyant eggs which had a higher water content than eggs produced by fish living in ordinary sea water (33‰ S). Eggs fertilized in lower salinities were larger and more buoyant than eggs fertilized in higher salinities. The salinity of the medium during the first 5 to 7 min after fertilization had a lasting effect on egg buoyancy, but subsequent transfer to a different salinity also influenced buoyancy. Although egg buoyancy in this species can be influenced by the ambient salinity both before and after spawning, the capacity for adjusting buoyancy is limited, and eggs spawned in salinities lower than 30‰ would probably sink.     

Generation of internal waves by sheared turbulence: experiments

A series of experiments is presented that model the generation of internal gravity waves in the ocean by the forcing of turbulent eddies in the surface mixed layer.The experimental setup consists of a shallow mixed upper layer and a deep continuously stratified lower layer. A source of turbulence is dragged through the upper layer. Internal waves can freely propagate in the lower layer. The internal waves are measured using synthetic schlieren to determine the frequencies of the generated waves. Consistent with other studies, it is found that the characteristic frequencies of internal waves generated by turbulence are an approximate constant fraction of the buoyancy frequency.     

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.