Source Buoyancy Flux Research Articles

Turbulent ‘stopping plumes’ and plume pinch-off in uniform surroundings

Observations of turbulent convection in the environment are of variously sustained plume-like flows or intermittent thermal-like flows. At different times of the day the prevailing conditions may change and consequently the observed flow regimes may change. Understanding the link between these flows is of practical importance meteorologically, and here we focus our interest upon plume-like regimes that break up to form thermal-like regimes. It has been shown that when a plume rises from a boundary with low conductivity, such as arable land, the inability to maintain a rapid enough supply of buoyancy to the plume source can result in the turbulent base of the plume separating and rising away from the source. This plume ‘pinch-off’ marks the onset of the intermittent thermal-like behavior. The dynamics of turbulent plumes in a uniform environment are explored in order to investigate the phenomenon of plume pinch-off. The special case of a turbulent plume having its source completely removed, a ‘stopping plume’, is considered in particular. The effects of forcing a plume to pinch-off, by rapidly reducing the source buoyancy flux to zero, are shown experimentally. We release saline solution into a tank filled with fresh water generating downward propagating steady turbulent plumes. By rapidly closing the plume nozzle, the plumes are forced to pinch-off. The plumes are then observed to detach from the source and descend into the ambient. The unsteady buoyant region produced after pinch-off, cannot be described by the power-law behavior of either classical plumes or thermals, and so the terminology ‘stopping plume’ (analogous to a ‘starting plume’) is adopted for this type of flow. The propagation of the stopping plume is shown to be approximately linearly dependent on time, and we speculate therefore that the closure of the nozzle introduces some vorticity into the ambient, that may roll up to form a vortex ring dominating the dynamics of the base of a stopping plume.

Buoyant convection from a discrete source in a leaky porous medium

AbstractThe application of turbulent plume theory in describing the dynamics of emptying filling boxes, control volumes connected to an infinite exterior through a series of openings along the upper and lower boundaries, has yielded novel strategies for the natural ventilation of buildings. Making the plume laminar and having it fall through a porous medium yields a problem of fundamental significance in its own right, insights from which may be applied, for example, in minimizing the contamination of drinking water by geologically sequestered $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathrm{CO}}_2$ or the chemicals leached from waste piles. After reviewing the theory appropriate to rectilinear and axisymmetric plumes in porous media, we demonstrate how the model equations may be adapted to the case of an emptying filling box. In this circumstance, the long-time solution consists of two ambient layers, each of which has a uniform density. The lower and upper layers comprise fluid that is respectively discharged by the plume and advected into the box through the upper opening. Our theory provides an estimate for both the height and thickness of the associated interface in terms of, for example, the source volume and buoyancy fluxes, the outlet area and permeability, and the depth-average solute dispersion coefficient, which is itself a function of the far-field horizontal flow speed. Complementary laboratory experiments are provided for the case of a line source plume and show very good agreement with model predictions. Our measurements also indicate that the permeability, $k_f$, of the lower opening (or fissure) decreases with the density of the fluid being discharged, a fact that has been overlooked in some previous studies, wherein $k_f$ is assumed to depend only on the fissure geometry.

Radial intrusions from turbulent plumes in uniform stratification

Laboratory experiments investigate the radial spread of an intrusion created by a turbulent forced plume in uniformly stratified ambient fluid. The flow evolution is determined as it depends upon the ambient buoyancy frequency, N, and the source momentum and buoyancy fluxes, M0 and F0, respectively. The plume reaches its maximum vertical extent, Zm, collapses back upon itself as a fountain and then spreads radially outwards at its neutral buoyancy depth, Zs, where the intrusion has the same density as the ambient. Through theory and experiments we determine that Zs = f(σ)Hp, in which Hp = M03/4F0−1/2, σ = (M0N/F0)2, and f(σ) ∝ σ−3/8 for σ ≲ 50 and f(σ) ∝ σ−1/4 for σ ≳ 50. In the inertia-buoyancy regime the intrusion front advances in time approximately as Rf ∝ t3/4, consistent with models assuming a constant buoyancy flux into the intrusion. Where the intrusion first forms, at radius R1, its thickness h1 is approximately constant in time. The thickness of the intrusion as a whole, h(r, t), adopts a self-similar shape of the form h/h1 ≃ [(Rf − r)/(Rf − R1)]p, with p ≃ 0.55 ± 0.03. The comparison of these results to large volcanic plumes penetrating into and spreading in the stratosphere is discussed.

On the entrainment coefficient in a forced plume: quantitative effects of source parameters

Abstract. The behavior of a forced plume is mainly controlled by the source buoyancy and momentum fluxes and the efficiency of turbulent mixing between the plume and the ambient fluid (stratified or not). The interaction between the plume and the ambient fluid controls the plume dynamics and is usually represented by the entrainment coefficient αE. Commonly used one-dimensional models incorporating a constant entrainment coefficient are fundamental and very useful for predictions in geophysical flows and industrial situations. Nevertheless, if the basic geometry of the flow changes, or the type of source or the environmental fluid conditions (e.g., level of turbulence, shear, ambient stratification, presence of internal waves), new models allowing for variable entrainment are necessary. The presented paper is an experimental study based on a set of turbulent plume experiments in a calm unstratified ambient fluid under different source conditions (represented by different buoyancy and momentum fluxes). The main result is that the entrainment coefficient is not a constant and clearly varies in time within the same plume independently of the buoyancy and the source position. This paper also analyzes the influence of the source conditions on the mentioned time evolution. The measured entrainment coefficient αE has considerable variability. It ranges between 0.26 and 0.9 for variable Atwood number experiments and between 0.16 and 0.55 for variable source position experiments. As is observed, values are greater than the traditional standard value of Morton et al. (1956) for plumes and jets, which is about 0.13.

A turbulent convection model with an observational context for a deep-sea hydrothermal plume in a time-variable cross flow

[1] A turbulent convection model for a hydrothermal fluid discharging into a tidally modulated, stratified cross flow is used to investigate time-variable conditions in plumes, such as the one rising from Dante, a sulfide mound at ∼2175 m depth on the Endeavour segment of the Juan de Fuca Ridge. That plume is the consequence of the coalescence of 10 or more small, individual plumes from chimneys discharging hot, salt-diminished fluid into the near-bottom ocean. At Dante, the discharge encounters ambient horizontal currents with speeds oscillating from near zero to a maximum of ∼7 cm s−1, speeds which can bend a plume more than 45° from the vertical. Model results are compatible with field measurements of the plume footprint size and vertical velocity both 20 m above the source when earlier estimates for Dante's heat flux of ∼50 MW drive the convection. The small-scale short period variability of velocities and properties distributions observed in the field is mimicked in model results. Plumes pool above a source during periods of weak cross flows but stream away from the source, with more diluted concentrations and lower rise heights, at other times. Plume distributions, at identical cross-flow speeds, differ whether the flow is accelerating or decelerating. Small changes in background hydrographic profiles create differences in rise heights comparable to those caused by large changes in source buoyancy flux. If put into an entrainment context, results suggest an entrainment coefficient (αEFF) that varies from ∼0.11 to ∼0.025 with increasing height (2–76 m) above the source.

Theoretical modeling of unsteady buoyancy-driven natural ventilation

A modified theoretical model is developed to examine the unsteady natural ventilation produced by a localized inner heat source at the floor of a room. The model is validated by using experimental results in the literature. The main difference between this model and previous models is that the buoyant layer is regarded as composed of a middle layer and a near-ceiling layer rather than being well-mixed. This model is therefore named the three-layer model and then used to investigate the unsteady process. Three characteristic times are defined to predict the time taken for the stratification interface to reach three particular positions during the transient process. When the dimensionless effective vent area is smaller, the steady-state depths of the near-ceiling layer and the middle layer are smaller and larger, respectively. The dimensionless buoyancies of the near-ceiling layer and the middle layer increase gradually over time while the plume buoyancy at the lower interface increases rapidly to its maximum and then decreases slowly. The temperature difference between the near-ceiling layer and the middle layer is small, but it is not negligible comparing to the temperature difference between the middle layer and the lower layer. The variations of the layer buoyancy and ventilation flow rate with time are both dependent on the source buoyancy flux, the floor area, the effective vent area and the enclosure height.

Transient pollutant flushing of buoyancy-driven natural ventilation

The transient flushing of neutrally-buoyant pollutants from a naturally ventilated enclosure is investigated. A simplified transient model for buoyancy-driven natural ventilation produced by a point source of heat is presented to describe the ventilation development from the plume generation to its steady state. The instantaneous thermal stratification interface height and ventilation flow rate and the time taken for the flow to reach the steady state are then examined by the transient model. The results indicate that the decrease of the thermal stratification interface height with dimensionless time, the steady-state interface height and the dimensionless time taken for the flow to reach the steady state are only determined by the dimensionless effective area of the vents. The ventilation flow rate can be increased by decreasing the enclosure floor area or increasing the effective vent area, enclosure height or source buoyancy flux. Accordingly, for rooms with smaller floor area, larger effective vent area or larger source buoyancy flux, ventilation airflow provides more effective flushing of neutrally-buoyant pollutant. Nevertheless, increasing the enclosure height is only beneficial to flush the pollutant from the lower layer rapidly and is disadvantageous to reduce the pollutant concentration of the upper layer.

Laboratory experiments on two coalescing axisymmetric turbulent plumes in a rotating fluid

We investigate the early-time coalescence of two co-flowing axisymmetric turbulent plumes and the later-time flow of the induced vortices in a rotating, homogeneous fluid using laboratory experiments. The experiments demonstrate the critical importance of the rotation period Tf=2π/f, where f is the Coriolis parameter of the background rotation. We find that if the plumes’ sources are sufficiently “close” for the plumes to merge initially at an “early time” tm≲tr=3Tf/4, the experimentally observed merging height zme agrees well with the non-rotating theoretical relationship of zmt≈(0.44/α)x0<zr=5.5F01/4f-3/4, where α is the entrainment “constant” of the turbulent plumes, x0 is the separation distance between the two plume sources, F0 is the source buoyancy flux of each plume, and zr is the distance that the plume rises in the time tr before rotational effects become significant. Therefore, rotation does not affect the initial time to merger or the initial merger height of such “close” plumes. For “late” times t>tr, however, the flow dynamics are substantially more complicated, as the flow becomes significantly affected by rotation. The propagation and entrainment of the plumes becomes strongly affected by the vortices induced by the entrainment flow in a rotating environment. Also, the plume fluid itself starts to interact with these vortices. If the plumes have already initially merged by the time t=tr, a single vortex (initially located at the midpoint of the line connecting the two plume sources) develops, which both advects and modifies the geometry of the merging plumes. Coupled with the various suppressing effects of rotation on the radial plume entrainment, the “apparent” observed height of merger can vary substantially from its initial value. Conversely, for more widely separated “distant” plumes, where x0>xc=(25α/2)F01/4f-3/4, the plumes do not merge before the critical time tr when rotation becomes significant in the flow dynamics and two vortices are observed, each located over a plume source. The combined effect of these vortices with the associated suppression of entrainment by rotation thus significantly further delays the merger of the two plumes, which apparently becomes possible only through the merger of the induced vortices.

The role of diffusion on the interface thickness in a ventilated filling box

We examine the role of diffusivity, whether molecular or turbulent, on the steady-state stratification in a ventilated filling box. The buoyancy-driven displacement ventilation model of Linden et al. (J. Fluid Mech., vol. 212, 1990, p. 309) predicts the formation of a two-layer stratification when a single plume is introduced into an enclosure with vents at the top and bottom. The model assumes that diffusion plays no role in the development of the ambient buoyancy stratification: diffusion is a slow process and the entrainment of ambient fluid into the plume from the diffuse interface will act to thin the interface resulting in a near discontinuity of density between the upper and lower layers. This prediction has been corroborated by small-scale salt bath experiments; however, full-scale measurements in ventilated rooms and complementary numerical simulations suggest an interface that is not sharp but rather smeared out over a finite thickness. For a given plume buoyancy flux, as the cross-sectional area of the enclosure increases the volume of fluid that must be entrained by the plume to maintain a sharp interface also increases. Therefore the balance between the diffusive thickening of the interface and plume-driven thinning favours a thicker interface. Conversely, the interface thickness decreases with increasing source buoyancy flux, although the dependence is relatively weak. Our analysis presents two models for predicting the interface thickness as a function of the enclosure height, base area, composite vent area, plume buoyancy flux and buoyancy diffusivity. Model results are compared with interface thickness measurements based on previously reported data. Positive qualitative and quantitative agreement is observed.

Mixed convection in a ventilated enclosure

This paper presents analysis, visualizations and differential pressure measurements of the flow within a confined ventilated space resulting from a buoyant turbulent 2D plume originating at the bottom of the enclosure with initial source volume flux, Q 0 and buoyancy flux, B 0. The enclosure is ventilated through lower and upper openings of heights H E and H S separated by a vertical distance H. Simple analysis shows that flow regimes between the interior and the exterior of the enclosure depends on a densitometric Froude number Fr ¯ H = Q 0 2 / ( Δ ρ ¯ H / ρ ) gH ( C S A S ) 2 related to the source flow rate, the density inside the enclosure and the area of the upper opening. For Fr ¯ H < 2 , a displacement regime is observed with inflow at the lower opening and outflow at the higher opening. For Fr ¯ H > 2 , the regime is blocked with two outflows. When the enclosure is well mixed the value Fr ¯ H = 2 corresponds to the criteria given by Woods et al. (2003). Experiments show that the natural regime is observed for Fr ¯ H < 2 while the blocked regime appears when Fr ¯ H > 2.6 . There is an intermediate regime for 2 > Fr ¯ H > 2.6 . This last regime where inflow and outflow are both present through the lower opening is due to the non negligible size of this opening not taken into account in the analysis.

The effect of sudden source buoyancy flux increases on turbulent plumes

Building upon the recent experimentally verified modelling of turbulent plumes which are subject to decreases in their source strength (Scase et al., J. Fluid Mech., vol. 563, 2006b, p. 443), we consider the complementary case where the plume's source strength is increased. We consider the effect of increasing the source strength of an established plume and we also compare time-dependent plume model predictions for the behaviour of a starting plume to those of Turner (J. Fluid Mech., vol. 13, 1962, p. 356).Unlike the decreasing source strength problems considered previously, the relevant solution to the time-dependent plume equations is not a simple similarity solution. However, scaling laws are demonstrated which are shown to be applicable across a large number of orders of magnitude of source strength increase. It is shown that an established plume that is subjected to an increase in its source strength supports a self-similar ‘pulse’ structure propagating upwards. For a point source plume, in pure plume balance, subjected to an increase in the source buoyancy flux F0, the rise height of this pulse in terms of time t scales as t3/4 while the vertical extent of the pulse scales as t1/4. The volume of the pulse is shown to scale as t9/4. For plumes in pure plume balance that emanate from a distributed source it is shown that the same scaling laws apply far from the source, demonstrating an analogous convergence to pure plume balance as that which is well known in steady plumes. These scaling law predictions are compared to implicit large eddy simulations of the buoyancy increase problem and are shown to be in good agreement.We also compare the predictions of the time-dependent model to a starting plume in the limit where the source buoyancy flux is discontinuously increased from zero. The conventional model for a starting plume is well approximated by a rising turbulent, entraining, buoyant vortex ring which is fed from below by a ‘steady’ plume. However, the time-dependent plume equations have been defined for top-hat profiles assuming only horizontal entrainment. Therefore, this system cannot model either the internal dynamics of the starting plume's head or the extra entrainment of ambient fluid into the head due to the turbulent boundary of the vortex ring-like cap. We show that the lack of entrainment of ambient fluid through the head of the starting plume means that the time-dependent plume equations overestimate the rise height of a starting plume with time. However, by modifying the entrainment coefficient appropriately, we see that realistic predictions consistent with experiment can be attained.

Transient ventilation dynamics following a change in strength of a point source of heat

We investigate the transient ventilation flow within a confined ventilated space, with high- and low-level openings, when the strength of a low-level point source of heat is changed instantaneously. The steady-flow regime in the space involves a turbulent buoyant plume, which rises from the point source to a well-mixed warm upper layer. The steady-state height of the interface between this layer and the lower layer of exterior fluid is independent of the heat flux, but the upper layer becomes progressively warmer with heat flux. New analogue laboratory experiments of the transient adjustment between steady states identify that if the heat flux is increased, the continuing plume propagates to the top of the room forming a new, warmer layer. This layer gradually deepens, and as the turbulent plume entrains fluid from the original warm layer, the original layer is gradually depleted and disappears, and a new steady state is established. In contrast, if the source buoyancy flux is decreased, the continuing plume is cooler than the original plume, so that on reaching the interface it is of intermediate density between the original warm layer and the external fluid. The plume supplies a new intermediate layer, which gradually deepens with the continuing flow. In turn, the original upper layer becomes depleted, both as a result of being vented through the upper opening of the space, but also due to some penetrative entrainment of this layer by the plume, as the plume overshoots the interface before falling back to supply the new intermediate layer. We develop quantitative models which are in good accord with our experimental data, by combining classical plume theory with models of the penetrative entrainment for the case of a decrease in heating. Typically, we find that the effect of penetrative entrainment on the density of the intruding layer is relatively weak, provided the change in source strength is sufficiently large. However, penetrative entrainment measurably increases the rate at which the depth of the draining layer decreases. We conclude with a discussion of the importance of these results for the control of naturally ventilated spaces.

On the rise of turbulent plumes: Quantitative effects of variable entrainment for submarine hydrothermal vents, terrestrial and extra terrestrial explosive volcanism

The maximum height reached by a turbulent plume rising in a stratified environment is a key tool to estimate the flux released at its source, particularly for large‐scale flows because flux can often be very hard to measure directly. This height is known to be mainly controlled by the stratification of the ambient fluid, source buoyancy flux, and the efficiency of turbulent mixing between the plume and the external fluid. The latter effect has been only superficially explored in spite of its fundamental control on the dynamics. Here we show that commonly used one‐dimensional models incorporating a constant entrainment coefficient do not provide satisfying predictions. We propose a new model allowing for variable entrainment which gives excellent predictions of maximum heights reached by laboratory plumes in stratified environments. We then apply our formalism to natural plumes produced by explosive volcanic eruptions under terrestrial, paleo‐Martian, and Venusian conditions and by submarine hydrothermal activity at mid‐ocean ridges. Source mass discharge rates deduced from maximum volcanic column heights for terrestrial eruptions are found to be greater than those estimated with the commonly used constant entrainment parameterization by a factor of 2. In the paleo‐Martian atmosphere, existing models overestimate plume heights by 14–27%. In the current atmosphere of Venus, the maximum height reached by a volcanic plume is also found to be smaller than previously estimated for large eruption rates. The source heat flux released by the TAG field (Atlantic Ocean) deduced from several submarine hydrothermal plumes is found greater by a factor 3 with our model.

Time-dependent plumes and jets with decreasing source strengths

The classical bulk model for isolated jets and plumes due to Morton, Taylor &amp; Turner (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1) is generalized to allow for time-dependence in the various fluxes driving the flow. This new system models the spatio-temporal evolution of jets in a homogeneous ambient fluid and Boussinesq and non-Boussinesq plumes in stratified and unstratified ambient fluids.Separable time-dependent similarity solutions for plumes and jets are found in an unstratified ambient fluid, and proved to be linearly stable to perturbations propagating at the velocity of the ascending plume fluid. These similarity solutions are characterized by having time-independent plume or jet radii, with appreciably smaller spreading angles ( is the conventional entrainment coefficient. These new similarity solutions are closely related to the similarity solutions identified by Batchelor (Q. J. R. Met. Soc., vol. 80, 1954, p. 339) in a statically unstable ambient, in particular those associated with a linear increase in ambient density with height.If the source buoyancy flux (for a rising plume) or source momentum flux (for a rising jet) is decreased generically from an initial to a final value, numerical solutions of the governing equations exhibit three qualitatively different regions of behaviour. The upper region, furthest from the source, remains largely unaffected by the change in buoyancy flux or momentum flux at the source. The lower region, closest to the source, is an effectively steady plume or jet based on the final (lower) buoyancy flux or momentum flux. The transitional region, in which the plume or jet adjusts between the states in the lower and upper regions, appears to converge very closely to the newly identified stable similarity solutions. Significantly, the predicted narrowing of the plume or jet is observed. The size of the narrowing region can be determined from the source conditions of the plume or jet. Minimum narrowing widths are considered with a view to predicting pinch-off into rising thermals or puffs.

Boussinesq plumes and jets with decreasing source strengths in stratified environments

Solutions to the equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1) describing turbulent plumes and jets rising in uniformly stratified environments are identified for the first time. The evolution of plumes and jets with sources whose driving flux decreases with time is considered in a stratified environment. Numerical calculations indicate that as the source buoyancy flux, for a Boussinesq plume (or source momentum flux, for a Boussinesq jet), is decreased, a transitional narrowing region with characteristic spreading angle tan -1 (2α/3) is formed, where α is the well-known entrainment coefficient. The plume or jet dynamics are modelled well by a separable solution to the governing equations which predicts stalling in the plume at a critical stall time t s = π/N and stalling in the jet at a critical stall time t s = π/(2N), where N is the buoyancy frequency of the ambient background stratification. This stall time is independent of the driving source conditions, a prediction which is verified by numerical solution of the underlying evolution equations.

Sedimentation from Buoyant Jets

An integral model is developed to describe sedimentation from a turbulent, buoyant jet injected at an angle into a stationary, uniform ambient fluid. Entrainment is modeled using the standard entrainment assumption and sediment is assumed to fall from the jet where the outward component of the fall velocity normal to the jet boundary exceeds the inward entrainment velocity. When appropriately scaled by source momentum and buoyancy fluxes, turbulent, buoyant jets may be described in terms of a single parameter: the angle θ0 between the flow and the horizontal at the virtual origin (which is close to the actual source for large initial densimetric Froude numbers). Including sedimentation in the model introduces a further parameter ws , which is the ratio of the fall speed of the sedimenting particles to a typical entrainment velocity (and so wS is a nondimensional fall speed). An important result is that this ratio is independent of the source speed, so that the proportion of the sediment load deposited nea...

New experimental techniques for validation of marine discharge models

A new three-dimensional Laser-Induced Fluorescence (3DLIF) system was applied to study the mixing of a produced water outfall discharge typical of that used in offshore production operations. The outfall consists of a pipeline terminating in a multiport diffuser discharging into water about 12 m deep. Scaled laboratory experiments were done using conditions based on measured oceanographic conditions near the site. The current was perpendicular to the diffuser, and the receiving water was linearly stratified. The model was undistorted and the jet densimetric Froude number was the same as in the prototype. This scaling results in correct modeling of the source volume, momentum, and buoyancy fluxes, and equality of other line source dimensionless parameters. The experiments were conducted in a constant refractive-index environment which enabled detailed three-dimensional concentration measurements in the near field mixing zone to be obtained despite the density variations in the flow field. The mixing processes were found to be complex. The jets discharging upstream were quickly swept downstream, where they began merging with the downstream jets. Lateral mixing caused the concentration profiles to quickly become laterally homogeneous. Initially, dilution increased rapidly with distance from the diffuser, but farther away the rate of increase of dilution slowed as the turbulence became affected by the ambient density stratification. The dilution eventually becomes approximately constant; the location where this occurs defines the end of the near field, where mixing is primarily due to turbulence and other processes induced by the discharge itself. The end of the near field is marked by collapse of the self-induced turbulence under the influence of the ambient stratification. The results were compared to predictions of commonly used mathematical models of marine mixing zones: RSB, UM3, and CORMIX. The best predictions of the near field dilution and the length of the near field were by RSB. UM3 gave good predictions of the near field dilution, but CORMIX overestimated the dilution and rise height substantially. It is believed that this overestimation by CORMIX is due to its approximation of the diffuser as a row of vertically discharging jets of equivalent total momentum flux; this is clearly a poor approximation to the diffuser conditions modeled here. 3DLIF is an exciting new technique that can give unprecedented insight into the complex hydrodynamics and processes occurring in buoyancy-modified mixing zones and to improvement of near field mathematical models. Experiments on other discharge configurations are continuing.

Thermal stratification produced by plumes and jets in enclosed spaces

The airflow and thermal stratification produced by a localised heat source located at floor level in a closed room is of considerable practical interest and is commonly referred to as a ‘filling box’. In rooms with low aspect ratios H/ R≲1 (room height H to characteristic horizontal dimension R) the thermal plume spreads laterally on reaching the ceiling and a descending horizontal ‘front’ forms separating a stably stratified, warm upper region from cooler air below. The stratification is well predicted for H/ R≲1 by the original filling box model of Baines and Turner (J. Fluid. Mech. 37 (1968) 51). This model represents a somewhat idealised situation of a plume rising from a point source of buoyancy alone—in particular the momentum flux at the source is zero. In practical situations, real sources of heating and cooling in a ventilation system often include initial fluxes of both buoyancy and momentum, e.g. where a heating system vents warm air into a space. This paper describes laboratory experiments to determine the dependence of the ‘front’ formation and stratification on the source momentum and buoyancy fluxes of a single source, and on the location and relative strengths of two sources from which momentum and buoyancy fluxes were supplied separately. For a single source with a non-zero input of momentum, the rate of descent of the front is more rapid than for the case of zero source momentum flux and increases with increasing momentum input. Increasing the source momentum flux effectively increases the height of the enclosure, and leads to enhanced overturning motions and finally to complete mixing for highly momentum-driven flows. Stratified flows may be maintained by reducing the aspect ratio of the enclosure. At these low aspect ratios different long-time behaviour is observed depending on the nature of the heat input. A constant heat flux always produces a stratified interior at large times. On the other hand, a constant temperature supply ultimately produces a well-mixed space at the supply temperature. For separate sources of momentum and buoyancy, the developing stratification is shown to be strongly dependent on the separation of the sources and their relative strengths. Even at small separation distances the stratification initially exhibits horizontal inhomogeneity with localised regions of warm fluid (from the buoyancy source) and cool fluid. This inhomogeneity is less pronounced as the strength of one source is increased relative to the other. Regardless of the strengths of the sources, a constant buoyancy flux source dominates after sufficiently large times, although the strength of the momentum source determines whether the enclosure is initially well mixed (strong momentum source) or stably stratified (weak momentum source).

Characteristics of Radial Jets and Mixing under Buoyant Conditions

This paper reports on measurements of radial jets using a laser-doppler anemometer and compares the mixing efficiency of a single radial jet with that of a single round jet under buoyant conditions based on experimental data. Dimensional analysis yields two parameters for the calculation of initial dilutions of jets and buoyant plumes. It is noticed that initial dilution of radial jets is much higher than that of round jets having the same source discharge, source buoyancy flux, outlet velocity and area because of intensive entrainment of the radial jet in the zone near the discharge point. Theoretical analysis indicates that the central velocity of the radial jet decays with jet path at a rate of −n ( n > 1), the value of which is proportional to the relative turbulence intensity and hence is related to the geometry of the radial jet. Experimental results show that in most situations, the value of n is approximately 1.5. Measurements also show that the ratio of half-width to distance from the virtual origin of the radial jet is given by b w /r0= 0.101 which is close to that of round jets. However velocity profiles of the radial jet are not completely similar, although the entrainment coefficient is basically a constant of 0.102. These results can help to predict correctly the flow field of the radial jet and its initial dilution.

A model for Meddy formation

A particular feature of “Meddies” is that the water within them has stable gradients of salinity and temperature. In this paper a model for a dense turbulent plume falling in a stationary, linearly-stratified environment is described. The density of the plume is assumed to be a linear function of two components, while the ambient density gradient is due to a gradient in only one of these components (labelled component one). The ratio of the contributions to the source buoyancy flux of the two components within the plume is identified as the important parameter for this type of flow. After deriving the steady equations for the plume, a simplified model for the filling process which creates the Meddy is described, which shows how a layer of fluid may be formed with stable gradients in both components in the lower part of the intrusion. The intrusion is shown to be less stratified than the surrounding fluid, with relatively weak gradients in component one (identified with temperature in the Meddy) that vary from unstable at the top to stable at the bottom of the intrusion and a fairly constant (stable) gradient in the second component (salinity for a Meddy). If the stable gradients in a Meddy are due solely to the filling process then, during formation, the top of the Meddy must become cooler than the surrounding water at the same level. The observed stable temperature gradient in Meddies is likely to be due to mixing processes after their formation, whereas the stable salanity gradient is mainly due to the filling process during formation.