Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

Influence of Downstream Control and Limited Depth on Flow Hydrodynamics of Impinging Buoyant Jets

Much study has been performed on the mixing properties of submerged, turbulent buoyant jets. It is safe to say that the problem of estimating dilution rates in vertical buoyant jets spreading in an `infinitely deep' ambient water has been more than adequately resolved by previous researchers. However, the majority of environmental applications involve discharges into ambient waters of finite depths in which a bounding surface serves to re-direct the impinging buoyant jet horizontally into a radial spreading layer. Previous research indicates that this impinging jet undergoes additional mixing before buoyancy stabilizes vertical mixing and confines the spreading layer to the vicinity of the bounding surface. Unfortunately, the conceptualization and subsequent mathematical modeling of this additional mixing phenomenon is surrounded by considerable amount of disagreement between researchers. The purpose of this study is to provide, by means of velocity and concentration profile measurements, independent experimental evidence for the existence of a critical flow state immediately downstream of the active mixing zone in the horizontally flowing, radial flow that forms after impingement. It is further shown that this critical flow state must be expressed in terms of a composite Froude Number that takes into account the possibility of a non-zero exchange layer flow. Finally, the influence of the presence of a sill-like topographic downstream control on the criticality of the radial flow immediately downstream of the active mixing zone is also investigated.     

Froude scaling limitations in modeling of turbidity currents

The scaling problem associated with the modeling of turbidity currents has been recognized but is yet to be explored systematically. This paper presents an analysis of the dimensionless governing equations of turbidity currents to investigate the scale effect. Three types of flow conditions are considered: (i) conservative density current; (ii) purely depositional turbidity current; and (iii) mixed erosional/depositional turbidity current. Two controlling dimensionless numbers, the Froude number and the Reynolds number, appear in the non-dimensional governing equations. When densimetric Froude similarity is satisfied, the analysis shows that the results would be scale-invariant for conservative density current under the rough turbulent condition. In the case of purely depositional flows, truly scale-invariant results cannot be obtained, as the Reynolds-mediated scale effects appear in the bottom boundary conditions of the flow velocity and sediment fall velocity. However, the scale effect would be relatively modest. The Reynolds effect becomes more significant for erosional or mixed erosional/depositional turbidity currents as Reynolds-mediated scale effects also appear in the sediment entrainment relation. Numerical simulations have been conducted at three different scales by considering densimetric Froude scaling alone as well as combined densimetric Froude and Reynolds similarity. Simulation results confirm that although the scaling of densimetric Froude number alone can produce scale-invariable results for conservative density currents, variations occur in the case of turbidity currents. The results become scale invariant when densimetric Froude and Reynolds similarities are satisfied simultaneously.     

Calculation of Entrainment in Density Jumps

The density jump in a two-layer channel flow of miscible fluids, in which one of the layers is infinitely deep and at rest, is analyzed using the momentum flux and mass flux conservation equations. The analysis yields simple equations relating the heights upstream and downstream of the jump with the upstream Froude number and the rate of entrainment into the moving layer, as well as a relation between the maximum possible entrainment and the upstream Froude number. The analysis also shows that when the flow down-stream of the jump is controlled by an obstruction or a contraction, the entrainment rate into the jump depends solely on the dimensionless obstruction height contraction ratio and the upstream Froude number.     

Surface signatures of submerged heated jet

The flow induced at the surface of a water body by a submerged heated horizontal turbulent jet was investigated experimentally with the aim of developing parameterizations for surface mean temperature/velocity fields. The jet nozzle diameter was fixed, the depth of the jet beneath the free surface was varied, and two jet Reynolds numbers (5020, 11300) were considered. The surface temperature was measured using a highly sensitive infrared camera, and the near-surface horizontal velocity field was measured using particle image velocimetry. The experimental results were explained using a model based on similarity solutions with variable turbulent viscosity. While classical Schlichting’s solution with constant turbulent viscosity predicts complete similarity for transverse velocity/temperature distributions only in a plane that coincides with the flow axis, the present solution predicts similarity in an arbitrary plane parallel to the flow axis, which was confirmed using data collected at the surface. Comparisons of present data with available previous results also showed general agreement.     

Monitoring and estimating the flow conditions and fish presence probability under various flow conditions at reach scale using genetic algorithms and kriging methods

The combination of current velocity and water depth influences stream flow conditions, and fish activities prefer particular flow conditions. This study develops a novel optimal flow classification method for identifying types of stream flow based on the current velocity and the water depth using a genetic algorithm. It is applied to the Datuan stream in northern Taiwan. Fish were sampled and their habitat investigated at the study site during the spring, summer, fall and winter of 2008-2009. The current velocity, water depth and maps of the presence probability of fish were estimated by ordinary and indicator kriging. The optimal classification results were compared with the classification results obtained using the Froude number and empirical methods. The flow classification results demonstrate that the proposed optimal flow classification method that considers depth-velocity and optimally identified criteria for classifying flow types, yields a current velocity and water depth of 0.32 (m/s) and 0.29 (m), respectively, and classifies the flow conditions in the study area as pool, run, riffle and slack. The variography results of the current velocity and the water depth data reveal that seasonal flows are not spatially stationary among seasons in the study area. Kriging methods and a two-dimensional hydrodynamic model (River 2D) with empirical and optimal flow classification methods are more effective than the Froude number method in classifying flow conditions in the study area. The flow condition classifications and probability maps were generated by River 2D, ordinary kriging and indicator kriging, to quantify the flow conditions preferred by Sicyopterus japonicus in the study area. However, the proposed optimal classification method with kriging and River 2D is an effective alternative method for mapping flow conditions and determining the relationship between flow and the presence probability of target fish in support of stream restoration.     

Stratified flow interactions with a suspended canopy

Field observations of the interactions between a stratified flow and a canopy suspended from the free surface above a solid boundary are described and analysed. Data were recorded in and around the canopy formed by a large long-line mussel farm. The canopy causes a partial blockage of the water flow, reducing velocities in the upper water column. Deceleration of the approaching flow results in a deepening of isopycnals upstream of the canopy. Energy considerations show that the potential for an approaching stratified flow to be diverted beneath a porous canopy is indicated by a densimetric Froude number. Strong stratification or low-velocities inhibit vertical diversion beneath the canopy, instead favouring a horizontal diversion around the sides. The effect on vertical mixing is also considered with a shear layer generated beneath the canopy and turbulence generated from drag within the canopy. In the observations, stratification is shown to be of sufficient strength to limit the effectiveness of the first mixing process, while the turbulence within the canopy is likely to enhance vertical exchange. Velocity and temperature microstructure measurements are used to investigate the effect of the canopy on turbulent dissipation and show that dissipation is enhanced within the canopy.     

Vertical dense jet in flowing current

The discharge of brackish water, as a dense jet in a natural water body, by the osmotic power plants, undergoes complex mixing processes and has significant environmental impacts. This paper focuses on the mixing processes that develop when a dense round jet outfall perpendicularly enters a shallow flowing current. Extensive experimental measurements of both the salinity and the velocity flow fields were conducted to investigate the hydrodynamic jet behavior within the ambient current. Experiments were carried out in a closed circuit flume at the Coastal Engineering Laboratory (LIC) of the Technical University of Bari (Italy). The salinity concentration and velocity fields were analyzed, providing a more thorough knowledge about the main features of the jet behavior within the ambient flow, such as the jet penetration, spreading, dilution, terminal rise height and its impact point with the flume lower boundary. In this study, special attention is given to understand and confirm the conjecture, not yet experimentally demonstrated, of the development and orientation of the jet vortex structures. Results show that the dense jet is almost characterized by two distinct phases: a rapid ascent phase and a gradually descent phase. The measured flow velocity fields definitely confirm the formation of the counter-rotating vortices pair, within the jet cross-section, during both the ascent and descent phases. Nevertheless, the experimental results show that the counter-rotating vortices pair of both phases (ascent and descent) are of opposite rotational direction.     

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.     

Flow structure and turbulence characteristics downstream of a spanwise suspended linear array

Laboratory experiments are conducted to quantify the mean flow structure and turbulence properties downstream of a spanwise suspended linear array in a uniform ambient water flow using Particle Tracking Velocimetry. Eighteen experimental scenarios, with four depth ratios (array depth to water column depth) of 0.35, 0.52, 0.78, and 0.95 and bulk Reynolds number (length scale is the array depth) from 11,600 to 68,170, are investigated. Three sub-layers form downstream of the array: (1) an internal wake zone, where the time-averaged velocity decreases with increasing distance downstream, (2) a shear layer which increases in vertical extent with increasing distance downstream of the array, and the rate of the increase is independent of the bulk Reynolds number or the depth ratio, and (3) an external wake layer with enhanced velocity under the array. The location of the shear layer is dependent on the depth ratio. The spatially averaged and normalized TKE of the wake has a short production region, followed by a decay region which is comparable to grid turbulence decay and is dependent on the depth ratio. The results suggest that the shear layer increases the transfer of horizontal momentum into the internal wake zone from the fluid outside of the array and that the turbulence in the internal wake zone can be modeled similarly to that of grid turbulence.     

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).     

The Thermal Discharges From Nuclear Power Plants in Taiwan

The increasing use of sea water for industrial cooling presents a real threat to the ecological environment in the ocean. in Taiwan where many electric power plants along the coast take sea water for cooling, people are concerned seriously about nuclear power plants. There are three nuclear power plants in Taiwan. Each plant has two units for generating power. the first two are located along the northern coast of Taiwan. the third is located in Kenting National Park along the coast of southernmost Taiwan. the plants take sea water for cooling, and discharge their heated effluents to the ocean surface from the coast. the thermal effluents have variable effects on the ecological environment near the plants. Fishermen living near the power plants complain that the heated water affects the inshore fishery catch. in addition, the thermal water from the second plant is easily accumulated near the coastal zone to influence the nearby swimming area in the summer-time. the thermal water from the third plant bleaches or kills some corals in shallow water near the outlet, and this conflicts with the interests of Kenting National Park.     

The Thermal Discharges From Nuclear Power Plants in Taiwan

The increasing use of sea water for industrial cooling presents a real threat to the ecological environment in the ocean. in Taiwan where many electric power plants along the coast take sea water for cooling, people are concerned seriously about nuclear power plants. There are three nuclear power plants in Taiwan. Each plant has two units for generating power. the first two are located along the northern coast of Taiwan. the third is located in Kenting National Park along the coast of southernmost Taiwan. the plants take sea water for cooling, and discharge their heated effluents to the ocean surface from the coast. the thermal effluents have variable effects on the ecological environment near the plants. Fishermen living near the power plants complain that the heated water affects the inshore fishery catch. in addition, the thermal water from the second plant is easily accumulated near the coastal zone to influence the nearby swimming area in the summer-time. the thermal water from the third plant bleaches or kills some corals in shallow water near the outlet, and this conflicts with the interests of Kenting National Park.     

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.     

Experimental investigation of meandering jets in shallow reservoirs

Meandering flows in rectangular shallow reservoirs were experimentally investigated. The characteristic frequency, the longitudinal wave length and the mean lateral extension of the meandering jet were extracted from the first paired modes, obtained by a proper orthogonal decomposition of the surface velocity field measured by large scale PIV. The depth-normalised characteristic lengths and the Strouhal number were then compared to the main dimensionless numbers characterizing the experiments: Froude number, friction number and reservoir shape factor. The normalised wave length and mean lateral extension of the meandering jet are neither correlated with the Froude number nor with the reservoir shape factor; but a clear relationship is found with the friction number. Similarly, the Strouhal number is found proportional to a negative power of the friction number. In contrast, the Froude number and the reservoir shape factor enable to predict the occurrence of a meandering flow pattern: meandering jets occur for Froude number greater than 0.21 and for a shape factor smaller than 6.2.     

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.     

The role of rooted emergent vegetation on periodically thermal-driven flow over a sloping bottom

Thermal-driven flow is generated due to topographic or vegetation-shading effects. Asymptotic solutions by assuming a small bottom slope are derived to discuss effects of rooted emergent vegetation and interactions between emergent vegetation and sloping topography on thermal-driven flow during diurnal heating and cooling cycles. The results show that the zero-order horizontal velocity is significantly reduced by vegetative drag, and the time lag between the change of horizontal velocity and the reversal of pressure gradient is also shortened. The solutions reveal that the viscous effect is dominant in very shallow water, and the drag force becomes important as the water depth increases. The inertial term is only important at the very beginning stage of flow initiation. Different vegetation distributions can significantly change the temperature fields that then affect patterns of thermal-driven circulation and exchange flowrates. For the case of tall vegetation growth in shallow water, and when the deep water side is open, the effects of vegetation shading may interfere with the topographic effects and dramatically alter the flow patterns. The blockage of solar radiation due to vegetation shading can determine the patterns and magnitude of thermal-driven flow. By means of the derived asymptotic horizontal velocity, exchange flow rates can be estimated, which are in good agreement with previous studies. The limitation and valid ranges of asymptotic solutions are finally discussed.     

Laboratory studies defining flow regimes for negatively buoyant surface discharges into crossflow

Surface discharges of negatively buoyant jets into moving ambient water create a range of complex flow patterns. These complexities arise through the interplay between the discharge’s initial fluxes and the motion of the ambient current. In this study a series of laboratory experiments were conducted for negatively buoyant surface discharges into crossflow to investigate flow patterns under different discharge and ambient conditions. The results compared with simulations of the CORMIX model, an expert system for ocean outfall design. In CORMIX, the simulation module DHYDRO for dense discharges has been used. Finally the flow different patterns were arranged in a dimensionless diagram to propose a modified flow classification system with new criteria.     

Dredged Material Disposal at the Edge of the Florida Current

A field data collection project was undertaken to investigate the short-term fate of dredged material discharged in the designated Miami Ocean Dredged Material Disposal Site (ODMDS) before dredging of the Miami River and the Miami Harbor Turning Basin begins. the designated ODMDS is located in relatively deep water for discharge sites with a typical bottom depth of 150 metres and is also located in the western boundary region of the Gulf Stream current off Miami. Acoustical backscattering, current, particulate, temperature and salinity data were gathered over a three day period from April 24, 1990 through April 26, 1990. the major generic features of shallow-water discharge plumes were observed to be present: (a) the presence of a rapid convective descending plume portion; (b) impact of that plume portion with the ocean bottom and concomitant generation of a bottom surge; (c) rapid horizontal width growth of the descending plume through entrainment; and (d) retention of a residual plume portion within the water column. A well-mixed upper water column layer extending to a depth of 40 to 60 metres below the surface of the ocean permitted measurements of the plume entrainment coefficient free from bottom boundary, water column density gradient, and vertical current shear effects which are usually present in relatively shallow, e.g. less than 40 metres bottom depth, coastal ocean discharge studies. Entrainment coefficient estimates obtained in this study were between 0.5 to 0.7. the residual water plume material was tracked over one-half hour during each of eight discharge events and was transported in a north-northeast direction.     

Dredged Material Disposal at the Edge of the Florida Current

A field data collection project was undertaken to investigate the short-term fate of dredged material discharged in the designated Miami Ocean Dredged Material Disposal Site (ODMDS) before dredging of the Miami River and the Miami Harbor Turning Basin begins. the designated ODMDS is located in relatively deep water for discharge sites with a typical bottom depth of 150 metres and is also located in the western boundary region of the Gulf Stream current off Miami. Acoustical backscattering, current, particulate, temperature and salinity data were gathered over a three day period from April 24, 1990 through April 26, 1990. the major generic features of shallow-water discharge plumes were observed to be present: (a) the presence of a rapid convective descending plume portion; (b) impact of that plume portion with the ocean bottom and concomitant generation of a bottom surge; (c) rapid horizontal width growth of the descending plume through entrainment; and (d) retention of a residual plume portion within the water column. A well-mixed upper water column layer extending to a depth of 40 to 60 metres below the surface of the ocean permitted measurements of the plume entrainment coefficient free from bottom boundary, water column density gradient, and vertical current shear effects which are usually present in relatively shallow, e.g. less than 40 metres bottom depth, coastal ocean discharge studies. Entrainment coefficient estimates obtained in this study were between 0.5 to 0.7. the residual water plume material was tracked over one-half hour during each of eight discharge events and was transported in a north-northeast direction.