Plume Motion Research Articles

Natural convection in thermal plumes emerging from a single heat source

We report numerical simulations of confined natural convection from a single heat source, leading to the evolution of thermal plumes in two and three dimensions. Thermal plumes are driven through a single heat source mounted flush at the bottom of a slender cavity where vertical and top walls are isothermal heat sinks. Velocity and temperature fields were obtained for two Prandtl numbers, P=0.025,0.71 at three different values of the Rayleigh number, R=104,5×104,105 and for different box aspect ratios. Two kind of flow solutions were found: (i) Steady states corresponding to stable thermal plumes characterized by a well defined flow circulation inside the cavity and (ii) periodic states where both the flow and thermal fields oscillate in time. Unsteadiness of fluid and thermal flows is favored by choosing low Prandtl number fluids, working at high Rayleigh numbers inside high aspect ratio cavities. Instabilities are characterized by a periodic and propagative motion of the thermal plume in both transverse and vertical direction. It can be attributed to destabilizing shear stresses between ascending and descending fluid layers.

Provenance of plumes in global convection models

AbstractIn global convection models constrained by plume motions and subduction history over the last 230 Myr, plumes emerge preferentially from the edges of thermochemical structures that resemble present‐day large low shear velocity provinces (LLSVPs) beneath Africa and the Pacific Ocean. It has been argued that large igneous provinces (LIPs) erupting since 200 Ma may originate from plumes that emerged from the edges of the LLSVPs and numerical models have been devised to validate this hypothesis. Although qualitative assessments that are broadly in agreement with this hypothesis have been derived from numerical models, a quantitative assessment has been lacking. We present a novel plume detection scheme and derive Monte Carlo‐based statistical correlations of model plume eruption sites and reconstructed LIP eruption sites. We show that models with a chemically anomalous lower mantle are highly correlated to reconstructed LIP eruption sites, whereas the confidence level obtained for a model with purely thermal plumes falls just short of 95%. A network of embayments separated by steep ridges form in the deep lower mantle in models with a chemically anomalous lower mantle. Plumes become anchored to the peaks of the chemical ridges and the network of ridges acts as a floating anchor, adjusting to slab push forces through time. The network of ridges imposes a characteristic separation between conduits that can extend into the interior of the thermochemical structures. This may explain the observed clustering of reconstructed LIP eruption sites that mostly but not exclusively occur around the present‐day LLSVPs.

ECVT imaging of 3D spiral bubble plume structures in gas‐liquid bubble columns

AbstractElectrical Capacitance Volume Tomography (ECVT) is a 3D, real‐time imaging technique that is recently developed to image the multiphase flow behaviour in columns of regular or irregular geometries. In this study, the ECVT measurements are conducted to obtain phase holdups and flow structures in bubble columns of a straight‐cylinder shape and a tapered‐cylinder shape with porous and orifice gas distributors. The phase holdups obtained by the ECVT in a straight‐cylinder bubble column with porous gas distributor are verified by other measurement techniques and correlation equations reported in the literature. The flow regimes of the bubble columns are also characterized by the ECVT. Particularly, a dynamic 3D flow structure, which is uniquely represented by the spiral motion of the bubble plumes occurring within the heterogeneous regime of the gas‐liquid flow in a straight‐cylinder shape bubble column with perforated distributor, is captured for the first time instantaneously over the entire flow field with the ECVT. Other flow behaviour such as the converging flow pattern of the gas bubbles in a tapered‐cylinder shape bubble column is also revealed by the ECVT.

CFD Analysis of the Influence of Meteorological Conditions on Motion of Ammonia

The article presents the results of a numerical CFD model of gas ammonia plume motion and dispersion after an accidental release from a real ice stadium situated in an urban area. The CFD analysis was performed using the ANSYS Fluent 14.0 for two seasons and eight wind directions. Sixteen tasks emerged, the results of which can define the influence of meteorological conditions (wind direction, wind speed, temperature, etc.) and surrounding buildings on the motion and dispersion of pollutant plume. The simulation was performed with real local meteorological data. The numerical model had been verified by tasks performed in a low-speed wind tunnel. The results show that the influence of meteorological conditions, especially the influence of calendar seasons, on the pollutant plume propagation can be very pronounced. Principles and conclusions drawn from this and similar analyses may have great benefits for emergency planning in complex urban areas.

An upper bound on the growth rate of peak toxic load fluctuations

The nonlinearity of the acute inhalation toxicity of many harmful gases released into the turbulent atmosphere suggests that the statistical characteristics of large fluctuations in concentration over a fixed exposure duration are important in assessing the hazard from releases of these materials. In this paper, the rate of growth of peak toxic load fluctuations as a function of the exposure duration te is derived theoretically and validated experimentally with atmospheric plume concentration fluctuation data measured with a fast-response detector. The rate of growth of the peak toxic load fluctuations is found to increase as te for te tc and as (te logte) 1/2 for te tc ,w heretc is a characteristic plume time scale that is identified experimentally to coincide (approximately or better) with the time scale associated with the peak of the concentration power spectrum corresponding to the beginning (or, lowfrequency end) of the inertial-convective subrange of turbulent plume motions.

Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery.The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.

Numerical simulations of air entrainment in a plunging jet of liquid

Air entrainment upon impact of a jet of liquid is a phenomenon present in wide variety of applications. We performed a series of two-dimensional simulations consisting in three different conditions of jet impingement and compared the results to experimental data. This study was first dedicated to the establishment of the numerical configuration and the setting of the injection parameters of the jet. We studied the dynamics of air entrainment by the jets impacting on the surface of the water in a tank, from the creation of the aerated cavities to the motion of the bubble plumes resulting from their deterioration of the cavities. The results concerned time-dependent and transient phenomena. To validate the simulations, we made several comparisons with experimental data, considering three angles of jet impact. Finally, we compared two numerical models for the free-surface description, using the most prevalent method in the literature and an original free-surface tracking method recently developed in our numerical tool. We showed that the formation of air cavities was similar for each condition and each numerical model, in agreement with the experimental results. Moreover, it was observed that the air entrainment had a different behavior depending on the conditions of jet impact.

Suspended matter mean distribution and seasonal cycle in the Río de La Plata estuary and the adjacent shelf from ocean color satellite (MODIS) and in-situ observations

The Río de la Plata is one of the largest and most turbid estuaries of the world, carrying a total of 160 million tonsy−1 of suspended sediments. The knowledge of their spatial distribution and their scales of variability is fundamental for management and scientific reasons, but has been limited by the scarcity of observations. During 2009 and 2010, in-situ data (CTD and turbidity profiles, and water and bottom sediment samples) were collected at 26 sites during six repeated cruises and from three fixed instruments deployed in the frame of the FREPLATA/FFEM experiment. In this paper we complement the analysis of this in-situ data base with 10 years of daily intermediate resolution (1km) MODIS-Aqua observations processed for surface suspended matter using the IFREMER algorithm for coastal turbid waters. The aim of this work is to provide a comprehensive characterization of the annual mean suspended matter concentration distribution, to study its variability on seasonal time scale and to identify the involved physical mechanisms. The comparison between the statistics of the direct and remote sensed data is satisfactory, showing a good agreement in the magnitude and spatial distribution of the mean suspended sediments concentration, its standard deviation, so as the seasonal variability. Our data show that all along the year the concentration of surface suspended matter maximizes along the southern coast of the upper and intermediate estuary and at the tips of Samborombón Bay. This fact is linked in part with the higher solid discharge of the Paraná River – flowing along the southern coast – compared to the Uruguay River which flows following the northern coast. The former receives most of the sediments load to the Río de la Plata from the Bermejo River. The observed mean pattern is also related to the stronger tidal currents along the southern coast of the estuary and at the tips of Samborombón Bay, which act re-suspending sediments near the bottom. Then, wind waves during storms enhance vertical mixing, increasing the surface concentration. The concentration of suspended sediments rapidly falls seawards the Barra del Indio shoal, in the area of the salt wedge. In the outer estuary, suspended matter concentration is also strongly associated to the wind-forced motion of the freshwater plume. Suspended matter concentration exhibits a maximum in winter and a minimum in summer, that cannot be fully explained in terms of the seasonal cycle of the solid discharge of the tributaries, but seems to be related to a raise in the frequency of the storms in winter, increasing the frequency of strong winds and higher wind waves, and the associated re-suspension and mixing.

Limited latitudinal mantle plume motion for the Louisville hotspot

Hotspots that form above upwelling plumes of hot material from the deep mantle typically leave narrow trails of volcanic seamounts as a tectonic plate moves over their location. These seamount trails are excellent recorders of Earth’s deep processes and allow us to untangle ancient mantle plume motions. During ascent it is likely that mantle plumes are pushed away from their vertical upwelling trajectories by mantle convection forces. It has been proposed that a large-scale lateral displacement, termed the mantle wind, existed in the Pacific between about 80 and 50 million years ago, and shifted the Hawaiian mantle plume southwards by about 15° of latitude. Here we use 40Ar/39Ar age dating and palaeomagnetic inclination data from four seamounts associated with the Louisville hotspot in the South Pacific Ocean to show that this hotspot has been relatively stable in terms of its location. Specifically, the Louisville hotspot—the southern hemisphere counterpart of Hawai’i—has remained within 3–5° of its present-day latitude of about 51° S between 70 and 50 million years ago. Although we cannot exclude a more significant southward motion before that time, we suggest that the Louisville and Hawaiian hotspots are moving independently, and not as part of a large-scale mantle wind in the Pacific.

Mushy-layer dynamics in micro and hyper gravity

We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions.

Lagrangian acceleration measurements in convective thermal turbulence

AbstractWe report the first experimental study of Lagrangian acceleration in turbulent Rayleigh–Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance $\langle {a}^{2} \rangle $ was obtained for various values of the three control parameters: the Rayleigh number $\mathit{Ra}$ ($6\ensuremath{\times} 1{0}^{8} \leq \mathit{Ra}\leq 1\ensuremath{\times} 1{0}^{11} $), the Prandtl number $\mathit{Pr}$ ($\mathit{Pr}= 4. 4, 5. 5$ and 6.1) and the system size $L~(L= 19. 2\text{~and~} 48. 6~\mathrm{cm} )$. These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that $\langle {a}^{2} \rangle $ in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg–Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant ${a}_{0} $ of the acceleration variance in the micro-scale Reynolds number range $20\leq {R}_{\lambda } \leq 120$, which fills a gap in this constant in the lower ${R}_{\lambda } $ end from the experimental side, and provides possible constraints for its high ${R}_{\lambda } $ behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different $\mathit{Ra}$. It is found that the zero crossing time of acceleration correlation functions is at $\tau \approx 2. 2{\tau }_{\eta } $ (${\tau }_{\eta } $ is the Kolmogorov time scale) over the range of $\mathit{Ra}({R}_{\lambda } )$ spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time ${\tau }_{1/ e} = (1. 12\pm 0. 05){\tau }_{\eta } $, which is larger than $(0. 73\ensuremath{\sim} 0. 80){\tau }_{\eta } $ found experimentally for other types of turbulent flows with larger ${R}_{\lambda } $.

New40Ar/39Ar age progression for the Louisville hot spot trail and implications for inter-hot spot motion

[1] In this study we present 42 new 40Ar/39Ar incremental heating age determinations that contribute to an updated age progression for the Louisville seamount trail. Louisville is the South Pacific counterpart to the Hawaiian-Emperor seamount trail, both trails representing intraplate volcanism over the same time interval (∼80 Ma to present) and being examples of primary hot spot lineaments. Our data provide evidence for an age-progressive trend from 71 to 21 Ma. Assuming fixed hot spots, this makes possible a direct comparison to the Hawaiian-Emperor age progression and the most recent absolute plate motion (APM) model (WK08G) of Wessel and Kroenke (2008). We observe that for the Louisville seamount trail the measured ages are systematically older relative to both the WK08G model predictions and Hawaiian seamount ages, with offsets ranging up to 6 Myr. Taking into account the uncertainty about the duration of eruption and magmatic succession at individual Louisville volcanoes, these age offsets should be considered minimum estimates, as our sampling probably tended to recover the youngest lava flows. These large deviations point to either a contribution of inter–hot spot motion between the Louisville and Hawaiian hot spots or to a more easterly location of the Louisville hot spot than the one inferred in the WK08G model. Both scenarios are investigated in this paper, whereby the more eastern hot spot location (52.0°S, 134.5°W versus 52.4°S, 137.2°W) reduces the average age offset, but still results in a relatively large maximum offset of 3.7 Myr. When comparing the new ages to the APM models (S04P, S04G) by Steinberger et al. (2004) that attempt to compensate for the motion of hot spots in the Pacific (Hawaii) or globally (Hawaii, Louisville, Reunion and Walvis), the measured and predicted ages are more in agreement, showing only a maximum offset of 2.3 Myr with respect to the S04G model. At face value these more advanced APM models, which consider both plate and hot spot motions, therefore provide a better fit to the new Louisville age data. The fit is particularly good for seamounts younger than 50 Ma, a period for which there is little predicted motion for the Louisville hot spot and little inter–hot spot motion with Hawaii. However, discrepancies in the Louisville age-distance record prior to 50 Ma indicate there is an extra source of inter–hot spot motion between Louisville and the other Pacific hot spots that was not corrected for in the global S04G model. Finally, based on six new 40Ar/39Ar age dates, the 169°W bend in the Louisville seamount trail seems to have formed at least 3 Myr before the formation of the Hawaiian-Emperor bend. The timing of the most acute parts of both bends thus appears to be asynchronous, which would require other processes (e.g., plume motions) than a global plate motion change between 50 and 47 Ma to explain these two observations.

CO2 migration in saline aquifers. Part 2. Capillary and solubility trapping

AbstractThe large-scale injection of carbon dioxide (CO2) into saline aquifers is a promising tool for reducing atmospheric CO2 emissions to mitigate climate change. An accurate assessment of the post-injection migration and trapping of the buoyant plume of CO2 is essential for estimates of storage capacity and security, but these physical processes are not fully understood. In Part 1 of this series, we presented a complete solution to a theoretical model for the migration and capillary trapping of a plume of CO2 in a confined, sloping aquifer with a natural groundwater through-flow. Here, we incorporate solubility trapping, where CO2 from the buoyant plume dissolves into the ambient brine via convective mixing. We develop semi-analytical solutions to the model in two limiting cases: when the water beneath the plume saturates with dissolved CO2 very slowly or very quickly (‘instantaneously’) relative to plume motion. We show that solubility trapping can greatly slow the speed at which the plume advances, and we derive an explicit analytical expression for the position of the nose of the plume as a function of time. We then study the competition between capillary and solubility trapping, and the impact of solubility trapping on the storage efficiency, a macroscopic measure of plume migration. We show that solubility trapping can increase the storage efficiency by several-fold, even when the fraction of CO2 trapped by solubility trapping is small.

Verification of large-scale rapid transport in the lower thermosphere: Tracking the exhaust plume of STS-107 from launch to the Antarctic

[1] New analysis of the Doppler shift of O2 airglow spectra recorded by the TIMED Doppler Interferometer (TIDI) and the High Resolution Doppler Imager (HRDI) have provided conclusive evidence that the shuttle main engine exhaust plume generated in the lower thermosphere by the launch of STS-107 and imaged by the Global Ultraviolet Imager (GUVI) instrument on TIMED was transported to the Antarctic in ∼80 h, supporting a key inference from the initial study by Stevens et al. (2005). These new results were aided by improved knowledge of the effects of instrumental and satellite artifacts imposed on the Doppler spectra. STS-107 launched on 16 January 2003, and the neutral wind near its launch trajectory and nearby volume was sampled within minutes by TIDI. These initial observations suggested that the northernmost end of the shuttle's exhaust plume would move northeast and that the southern end would move southeast, motions that were identified in imagery acquired during the next orbit of TIMED. The direction and magnitude of plume motion inferred from GUVI images obtained 12, 26, and 50 h after launch were again confirmed by TIDI and HRDI. The appearance of the plume over the Antarctic ∼80 h after launch, inferred from earlier work by the appearance of iron ablated from the shuttle's main engines, was consistent with neutral winds measured by the satellite Doppler instruments over the Antarctic. The transport of the plume from the coast of Florida to the Antarctic was aided by the favorable phase and strong amplitude of a 2 day planetary wave of wave number three in the southern hemisphere on 18 January 2003. The existence of the 2 day wave was deduced from zonally averaged and combined TIDI and HRDI neutral wind observations. We conclude that the existence of strong and sustained winds in the MLT, significantly greater than expected from empirical and theoretical models, is indisputable and provides compelling evidence supporting the global-scale nature of thermospheric winds with magnitude greater than 100 m/s observed by Larsen (2002) from 40 years of sounding rocket chemical release experiments.

Unstable Process Identification in a Pure Thermal Plume under Forced Rotating Conditions

A pure thermal plume development arising from a finite-size rotating heat source was analyzed experimentally. Qualitative investigation through extensive visualization has brought into focus the existence of a threshold rotation frequency (i.e., a swirl number) above which stretching effects are strengthened, thereby forcing the ascending plume motion to spiral around the geometrical axis heat source. Nevertheless, above the threshold frequency (i.e., above the swirl number), unstable processes appear through flow field pulsation in close proximity to the heat source; the pulsations literally beat and drive the flow field vicinity. From a strictly quantitative point of view, the data underscore the fact that heat source rotation presents two opposed trends. Below the threshold frequency, the higher the frequency, the more the temperature level is concentrated on the plume axis. In contrast, at the strongest rotation frequencies studied, the opposite is observed. Above the threshold rotating frequency, the characteristic rotating time scale appears to be too short to interact with the characteristic plume time scale. As a consequence, rotation of the heat source enhances transition from laminar to turbulence.

Modeling glacial meltwater plume dynamics and sedimentation in high-latitude fjords

[1] A model, SedPlume, has been developed to simulate marine sediment deposited by glacial meltwater plumes emerging from tidewater glaciers. Turbid meltwater emerging from beneath a glacier into a fjord rises as a buoyant forced plume due to density contrasts with the ambient fjord water. SedPlume assumes that meltwater discharge flows at a constant rate for long enough periods that the plume reaches a steady state. Entrainment of ambient fluid into the turbulent plume is assumed to occur at a rate proportional to the local velocity of the plume. Plume motion is considered in two dimensions: one horizontal dimension (perpendicular to the glacier front) and the vertical dimension. An integral model is formulated for the conservation equations of volume, momentum, buoyancy, and sediment flux along the path of a turbulent plume injected into stably stratified ambient fluid. Sedimentation occurs from the plume when the radial component of the sediment fall velocity exceeds the entrainment velocity. When the plume reaches the surface, it is treated as a radially spreading surface gravity current, for which exact solutions exist for the sediment deposition rate. Flocculation of silt and clay particles is modeled using empirical measurements of particle settling velocities in fjords to adjust the settling velocity of fine-grained sediments. SedPlume has been applied to McBride Inlet, Alaska, a temperate glaciated fjord where the majority of sedimentation originates from meltwater sources. SedPlume produces rates and patterns of sedimentation in good agreement with observations, with calculated peak ice-proximal annual sedimentation rates of approximately 22 m yr−1.

3D-PTV Measuring of Ambient Fluid Velocities in a Bubble Plume

This experimental research concerns an air-bubble-jet flow in water. The authors try to conduct the measurements of the flow applying a three-dimensional particle-tracking-velocimetry (3D-PTV) technique, in order to show both air-bubble and liquid (water) velocities. As tracers, we regard air bubbles in bubble-velocity measurements, and we regard polyethylene particles suspended in the liquid in liquid-velocity measurements. Then, we visualise the three-dimensional motions of air bubbles and ambient liquid. As we record stereo images using two high-speed video cameras, we can get timely-consecutive information of air-bubble and ambient-liquid motions. As a result, we quantitatively reveal the three-dimensional instantaneous motion of an unsteady bubble-jet plume from a simple air nozzle.

Dynamics of the Mackenzie River plume on the inner Beaufort shelf during an open water period in summer

The oceanographic conditions of the Mackenzie River plume in the Arctic Ocean were examined during a 12-day period in August 2007. Field observations in the river channel and the delta region (2–6 m depth), ship-based observations on the shelf and satellite observations of sea surface temperatures indicate that movements of plume density fronts cause changes in water temperatures of over 10 C over a few days. We used a 1D model to compare the strength of stratification versus surface wind stress, and a 3D numerical model to simulate the plume motions under forcing from the river flows, local wind and water level variations from tides and wind-driven surge. The results indicate that the coastal region is stratified with a ∼2 m thick surface plume even in water depths of 3–4 m, resulting in strong vertical variation of horizontal currents. Moderate easterly winds of 5–10 m/s are sufficient to induce offshore transport of the surface plume and onshore transport of the deeper shelf water, leading to large fluctuations in temperature and salinity in the coastal region. This study examined a period of offshore transport and mean water level set-down, and indicates the rapid response of the plume to wind over the shallow delta.

Initial expansion of the Columbia River tidal plume: Theory and remote sensing observations

Analysis of the Columbia River tidal plume using Lagrangian frontal equations provides a concise description of the evolution of frontal depth H, velocity U, reduced gravity g′, and frontal internal Froude number FR. Because the estuary mouth is narrow, the initial radial plume motion is supercritical (FR > 1) for up to 12 hours. Understanding this supercritical phase is vital, because plume properties change rapidly, with strong ecosystem impacts. To analyze this expansion, analytical and numerical models (the latter with three mixing formulations) were tested. Model results are compared to synthetic aperture radar images to verify that the predicted frontal properties are realistic. Lagrangian theory provides especially simple constraints (independent of the mixing model) on spatial variations in FR and Ug′H. For parameters representative of the Columbia River plume, the plume spreads 10–35 km and thins to 25–60% of its initial depth before becoming subcritical. After liftoff, FR increases as the front accelerates and thins, it then decreases to unity; g′ decreases, but more slowly than H and U. H, controlled by a balance between spreading and mixing, first decreases then increases. The strength of vertical mixing and the mixing efficiency EF (ratio of buoyancy flux to dissipation) both play a significant role in determining plume properties, and it is important to include both the horizontal gradient in g′ and surface slope component of the pressure gradient. A model with an Ellison‐Turner type entrainment scheme predicts the plume trajectory better than one that assumes a constant interfacial gradient Richardson number.

Turbulent plumes with heterogeneous chemical reaction on the surface of small buoyant droplets

A model is developed for a turbulent plume with heterogeneous chemical reaction rising in an unbounded environment. The chemical reaction, which may generate or deplete buoyancy in the plume, occurs at the interface between two phases, a continuous phase and a dispersed one. We study the case in which a buoyant reactant is released at the source and forms the dispersed phase, consisting of very small bubbles, droplets or particles. Once in contact with the ambient fluid, a first-order irreversible reaction takes place at the surface of the, for example, droplets. The behaviour of this plume in a uniform and stratified environment is examined. We show that the dynamics of a pure plume with such heterogeneous reaction is completely determined by the ratio of the environmental buoyancy frequency N and a frequency parameter associated with the chemical reaction, G. The group G is a measure of the ability of the reaction to generate buoyancy in the plume. In a uniform environment, the sign of parameter G fully determines the plume motion. When the reaction generates buoyancy (positive G) the motion is unbounded, whilst when reaction depletes buoyancy (negative G) the plume reaches a level of neutral buoyancy. A relation for this neutral buoyancy level as a function of the initial buoyancy flux of the plume and G is calculated. Our theoretical predictions compared well with experimental results using a plume of calcium carbonate particles descending in an acidic aqueous solution. In a stratified environment, the motion of the plume is always bounded, irrespective of the magnitude of G, and we determine the level of maximum buoyancy flux, as well as those of zero buoyancy and zero momentum as a function of N/G. Finally, our model is applied to study the dynamics of a localized release of carbon dioxide in the ocean.