Plume Rise Height Research Articles

Dynamic characteristics of two-vent submarine hydrothermal plumes: A case study of Longqi hydrothermal field

Submarine hydrothermal plumes play an important role in the process of material and energy exchange in the deep sea. Due to the influence of complex environmental factors (multiple vents, deep-sea stratified environment) and the limitation of observation capabilities, the dynamic characteristics of submarine hydrothermal plumes have not been fully understood, and it is urgent to study the diffusion and evolution process of submarine hydrothermal plumes by the computational fluid dynamics (CFD) model. In this paper, a CFD model was established to effectively simulate the diffusion and evolution process of two-vent submarine hydrothermal plumes under the deep-sea stratified environment, obtained the three-dimensional plume flow field structure of two-vent submarine hydrothermal plumes, and obtained the spatial distribution of dynamic characteristics parameters such as velocity, turbulent viscosity, turbulent kinetic energy and turbulence dissipation rate of two-vent submarine hydrothermal plumes. The equations for calculating the maximum plume rise height and the neutrally buoyant plume height of a two-vent submarine hydrothermal plume were deduced and established. In addition, a comparative analysis of the single-vent submarine hydrothermal plume revealed the mechanism of the influence of the key characteristics of the two-vent submarine hydrothermal plumes such as the maximum plume rise height. It was applied to analyze the dynamic characteristics of the plume occurred in Longqi hydrothermal field in the southwest Indian Ocean, and the results were verified by the field observation data. The spatial distribution of mass concentration of hydrothermal plume particles was further analyzed, and the difference of mass concentration in different hydrothermal plume structures was compared to study the exchange mechanism of material and energy between submarine hydrothermal plume and surrounding seawater. The results are of guiding significance for the tracing of submarine hydrothermal vents, the study of marine material exchange and energy transport processes, and the exploration and environmental evaluation of submarine polymetallic sulfide resources.

A One‐Dimensional Volcanic Plume Model for Predicting Ash Aggregation

AbstractDuring explosive volcanic eruptions, volcanic ash is ejected into the atmosphere, impacting aircraft safety and downwind communities. These volcanic clouds tend to be dominated by fine ash (<63 μm in diameter), permitting transport over hundreds to thousands of kilometers. However, field observations show that much of this fine ash aggregates into clusters or pellets with faster settling velocities than individual particles. Models of ash transport and deposition require an understanding of aggregation processes, which depend on factors like moisture content and local particle collision rates. In this study, we develop a Plume Model for Aggregate Prediction, a one‐dimensional (1D) volcanic plume model that predicts the plume rise height, concentration of water phases, and size distribution of resulting ash aggregates from a set of eruption source parameters. The plume model uses a control volume approach to solve mass, momentum, and energy equations along the direction of the plume axis. The aggregation equation is solved using a fixed pivot technique and incorporates a sticking efficiency model developed from analog laboratory experiments of particle aggregation within a novel turbulence tower. When applied to the 2009 eruption of Redoubt Volcano, Alaska, the 1D model predicts that the majority of the plume is over‐saturated with water, leading to a high rate of aggregation. Although the mean grain size of the computed Redoubt aggregates is larger than the measured deposits, with a peak at 1 mm rather than 500 μm, the present results provide a quantitative estimate for the magnitude of aggregation in an eruption.

Two Decades of Monitoring Hydrothermal Plumes at the Brothers Submarine Volcano, Kermadec Arc, New Zealand

Abstract Brothers volcano is arguably the most well-studied submarine arc volcano on Earth. Between 1996, when massive sulfides were first recovered by dredging, and 2018, when International Ocean Discovery Program (IODP) Expedition 376 recovered cores from as deep as 453 m below the sea floor at two chemically distinct hydrothermal upflow zones, over 60 conductivity-temperature-depth (CTD) vertical casts and tow-yo operations mapped hydrothermal plumes over and around the edifice by employing hydrothermal tracer-specific sensors. These surveys started in 1999 and were completed during nine separate expeditions at one- to three-year intervals, except for a six-year gap between 2011 and 2017. Hydrothermal plume distributions over this two-decade period show variability in the intensity and vertical rise height of plumes from the four main vent fields (Upper Cone, Lower Cone, NW Caldera, and Upper Caldera, with the latter not discovered until 2017). Upper Cone plumes were more intense than all other sites in 1999, 2002, 2007, and 2009, then significantly diminished from 2011 to 2018. The Lower Cone plume was the most intense in 2004, then the NW Caldera site became the dominant source of hydrothermal particles from 2011 to 2018. Despite the gap of six years between 2011 and 2017, hydrothermal output appears to have increased within the caldera sometime after the 2009 survey while simultaneously decreasing in intensity at the cone sites. This supports other evidence of linkages between the cone and caldera sites in the deep hydrothermal circulation system, and may be related to the predicted deepening of hydrothermal circulation, infiltration of seawater to facilitate “mining” of magmatic brines, and modulation of subseafloor mineralization processes associated with a modeled, pulsed injection of magmatic gasses. The surveys also revealed ways in which the highly variable regional hydrographic environment impacts the flux of hydrothermal products to the surrounding ocean. Plumes from sources located above the caldera rim disperse hydrothermal components without hindrance, but particles and heat from sources within the caldera become trapped and are dispersed episodically by caldera-flushing events. While on site for 18 days in 2018, repeat CTD casts into the deepest part of the caldera, which was isolated from the surrounding ocean, showed a progressive increase in temperature, representing a net heat flux of 79 MW from conductive and advective sources deeper than 1,570 m.

Numerical modeling of hydrodynamic processes of deep-sea hydrothermal plumes: A case study on Daxi hydrothermal field, Carlsberg Ridge

A RANS-based computational fluid dynamic model is developed to simulate the propagation and turbulent mixing of hydrothermal plumes in a stratified deep-sea environment and it is employed to study the Daxi hydrothermal field (DHF), Carlsberg Ridge in the Indian Ocean. Based on the results of in-situ measurements of the hydrothermal plume in the DHF, the parameter sensitivity is analyzed to evaluate the effects of the volume flux released from the vent orifice and the ambient buoyancy frequency on the plume dynamics. The results reveal the three-layer velocity field and obtain several important scalings, including the maximum plume rise height and neutrally buoyant plume height. Thus, it can be concluded that the classical entrainment assumption is applicable only to the plume stem below 0.6 times of the maximum plume rise height, and above that level, the structure of the flow field tends to be complicated due to the lateral spreading in the neutrally buoyant layer and circulation in the plume cap region. In addition, the simulation results show that both turbulent kinetic energy and turbulence dissipation rate attain their maximum values near the vent. However, the maximum turbulent viscosity is observed in the plume cap region, indicating strong turbulent mixing in that region. A quantitative analysis of the hydrothermal plumes in the DHF is performed by the proposed model and verified by the in-situ measurements, and the results suggest that the discrete heat flux of the DHF is about 39.38 MW. The proposed model can provide useful information for tracing the submarine hydrothermal vents, studying the matter and energy cycling in the ocean basin, and the exploration of submarine polymetallic sulfides resources and environmental assessment.

Convective instability-induced mixing and its parameterization using large eddy simulation

A large eddy simulation (LES) model is applied to study convective instability processes driven by hydrothermal exhalations. The process of convective mixing induced by a bottom heating source is examined in a stratified and rotating frame. The control case of numerical experiment is configured with the horizontal and vertical resolution 5 m located at 35°S. Its results show that the three-dimensional structure of the hydrothermal plume displays an umbrella shape. A strong clockwise vortex above the vent is present and the axis of the vortex is tilted with organized precession. A series of numerical experiments are conducted to test the sensitivity of three characteristic parameters (eddy viscosity (K), maximum plume rise height (Zmax) and the intensity of the vortex (Ivortex)) to three variables: heat flux from the vent (HF), rotation rate (f) and background stratification (N). Based on the sensitivity experiments, parameterizations of eddy viscosity and maximum plume rise height with respect to HF, f and N are obtained.

Anomalous Pacific‐Antarctic Ridge Volcanism Precedes Glacial Termination 2

AbstractWe present results from a well‐dated sediment core on the Pacific‐Antarctic Ridge (PAR) that document a ∼15 cm thick layer of basaltic ash shards that precedes the penultimate deglaciation (Termination 2). The glasses have MORB composition consistent with an axial source and their morphologies are typical of pyroclastic deposits created by submarine volcanism. The ash layer was deposited ∼7 km from the PAR axis, a distance that implies buoyant plumes lofted debris high into the water column with subsequent fallout to the core location. We infer plume rise height using grain settling velocities, the water depth at the core site, and deep ocean current speeds from ARGO floats. Rise heights of 1.5 km or less require unrealistically large current speeds to transport grains to the core site. Instead, the data are consistent with a plume rise height of at least 2 km, implying that T2 was an interval of anomalous volcanism along this segment of the PAR. The timing and duration of the ash deposit is consistent with glacial‐interglacial modulation of ridge magmatism. Volcaniclastic records from additional locations will be necessary to assess whether the PAR record is a rare find or it is representative of mid‐ocean ridge volcanism during glacial terminations.

Multi-level emulation of a volcanic ash transport and dispersion model to quantify sensitivity to uncertain parameters

Abstract. Following the disruption to European airspace caused by the eruption of Eyjafjallajökull in 2010 there has been a move towards producing quantitative predictions of volcanic ash concentration using volcanic ash transport and dispersion simulators. However, there is no formal framework for determining the uncertainties of these predictions and performing many simulations using these complex models is computationally expensive. In this paper a Bayesian linear emulation approach is applied to the Numerical Atmospheric-dispersion Modelling Environment (NAME) to better understand the influence of source and internal model parameters on the simulator output. Emulation is a statistical method for predicting the output of a computer simulator at new parameter choices without actually running the simulator. A multi-level emulation approach is applied using two configurations of NAME with different numbers of model particles. Information from many evaluations of the computationally faster configuration is combined with results from relatively few evaluations of the slower, more accurate, configuration. This approach is effective when it is not possible to run the accurate simulator many times and when there is also little prior knowledge about the influence of parameters. The approach is applied to the mean ash column loading in 75 geographical regions on 14 May 2010. Through this analysis it has been found that the parameters that contribute the most to the output uncertainty are initial plume rise height, mass eruption rate, free tropospheric turbulence levels and precipitation threshold for wet deposition. This information can be used to inform future model development and observational campaigns and routine monitoring. The analysis presented here suggests the need for further observational and theoretical research into parameterisation of atmospheric turbulence. Furthermore it can also be used to inform the most important parameter perturbations for a small operational ensemble of simulations. The use of an emulator also identifies the input and internal parameters that do not contribute significantly to simulator uncertainty. Finally, the analysis highlights that the faster, less accurate, configuration of NAME can, on its own, provide useful information for the problem of predicting average column load over large areas.

Detection of diffuse seafloor venting using a structured light laser sensor: 2. Evaluation of detection sensitivity and limitations

Algorithms to detect diffuse hydrothermal vent fluids using the structured light laser sensor have proven to be successful. However, potential limitations due to survey parameters, including altitude and vehicle heading, have not been explored and are the focus of this study. Data from 12 surveys conducted over a single hydrothermal vent at three different altitudes (2.7 m, 4.2 m, and 6.2 m) and four different headings are analyzed. Increasing survey altitude decreases the resolution and intensity of the imaged laser line; therefore, range‐dependent processing considerations to maintain detection sensitivity are presented. Analysis of these surveys suggests minimal degradation of vent detection capabilities from survey altitudes up to 6 m. Additionally, as the shape and location of the detected distortion patterns vary with survey heading and altitude they are presented as potential indications of plume shape and rise height. The effects of range and survey heading are important for future applications of this sensor which may include surveying from higher, faster flying autonomous underwater vehicles.

Natural convection induced by radiation in a water filled square cavity: Experimental observations

This investigation is motivated by interest in the mixing caused by the absorption of solar radiation in the near-shore regions of lakes. In the daytime, incoming solar radiation is absorbed by the water following Beer’s law. In the near-shore region where the water depth is less than the penetration depth of solar radiation, the residual radiation reaches the bottom and is absorbed and re-emitted back into the water body as a bottom heat flux, resulting in an adverse temperature gradient which may become unstable. In this laboratory-scale experimental study, this situation is modelled with a water-filled, open top tank with a black bottom subjected to radiative heating from a halogen theatre spotlight. Concurrent shadowgraph and Particle Image Velocimetry (PIV) are utilised for simultaneous visualisation of the temperature field and flow measurements. Initially, there is no motion and two distinct thermal boundary layers simultaneously grow from the water surface and from the bottom boundary. The bottom boundary layer becomes unstable at a certain thickness, and rising plumes are formed. The plumes transfer heat and cause circulation and vertical mixing in the water body. Subsequently the plumes disappear as the bottom boundary layer is dismantled, the bottom boundary layer is re-established, and the plumes re-formed. This paper will focus on characterising the first and the second stages. Accordingly, the onset of convection, plume rise height, and plume rise velocity are investigated through analysis of the PIV and shadowgraph images and compared with previously published scaling.

Sensitivity analysis of a one-dimensional model of a volcanic plume with particle fallout and collapse behavior

We run a volcanic plume model with uncertain boundary conditions and entrainment related model parameters. Output variables tested for their sensitivity to the inputs are total rise height, and mass flux of particles into the umbrella cloud or downwind plume. Boundary or source conditions are vent radius, initial velocity, grain size mean and grain size standard deviation. Model parameters are entrainment rate, α, wind entrainment rate, β, and wind speed.Five sensitivity metrics were considered. Three of these are calculated for each given point in the input parameter space, by perturbing the input variable around fixed points. Two global sensitivity measures quantify the impact on the output of the input over its entire uncertain domain.We find that vent radius and initial speed have a much more profound effect on both outputs than does total grain size distribution. Plume rise height and particle mass flux are sensitive to the entrainment parameters, α and β, but these parameters are not of greater importance than the wind speed. This suggests that while efforts to better characterize entrainment parameters through laboratory experiments is important, similar efforts should be made to collect appropriate meteorological data for the region near the site of the eruption.

Uncertainty analysis of a model of wind-blown volcanic plumes.

Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and entrainment coefficients results in a large range of plausible values of the source mass flux. Our analysis shows that better constraints on entrainment coefficients for volcanic plumes and more precise observations of plume height are required to obtain tightly constrained estimates of the source mass flux.

Lithospheric controls on magma composition along Earth's longest continental hotspot track.

Hotspots are anomalous regions of volcanism at Earth's surface that show no obvious association with tectonic plate boundaries. Classic examples include the Hawaiian-Emperor chain and the Yellowstone-Snake River Plain province. The majority are believed to form as Earth's tectonic plates move over long-lived mantle plumes: buoyant upwellings that bring hot material from Earth's deep mantle to its surface. It has long been recognized that lithospheric thickness limits the rise height of plumes and, thereby, their minimum melting pressure. It should, therefore, have a controlling influence on the geochemistry of plume-related magmas, although unambiguous evidence of this has, so far, been lacking. Here we integrate observational constraints from surface geology, geochronology, plate-motion reconstructions, geochemistry and seismology to ascertain plume melting depths beneath Earth's longest continental hotspot track, a 2,000-kilometre-long track in eastern Australia that displays a record of volcanic activity between 33 and 9 million years ago, which we call the Cosgrove track. Our analyses highlight a strong correlation between lithospheric thickness and magma composition along this track, with: (1) standard basaltic compositions in regions where lithospheric thickness is less than 110 kilometres; (2) volcanic gaps in regions where lithospheric thickness exceeds 150 kilometres; and (3) low-volume, leucitite-bearing volcanism in regions of intermediate lithospheric thickness. Trace-element concentrations from samples along this track support the notion that these compositional variations result from different degrees of partial melting, which is controlled by the thickness of overlying lithosphere. Our results place the first observational constraints on the sub-continental melting depth of mantle plumes and provide direct evidence that lithospheric thickness has a dominant influence on the volume and chemical composition of plume-derived magmas.

Assessing eruption column height in ancient flood basalt eruptions

A buoyant plume model is used to explore the ability of flood basalt eruptions to inject climate-relevant gases into the stratosphere. An example from the 1986 Izu-Oshima basaltic fissure eruption validates the model's ability to reproduce the observed maximum plume heights of 12–16 km above sea level, sustained above fire-fountains. The model predicts maximum plume heights of 13–17 km for source widths of between 4–16 m when 32% (by mass) of the erupted magma is fragmented and involved in the buoyant plume (effective volatile content of 6 wt%). Assuming that the Miocene-age Roza eruption (part of the Columbia River Basalt Group) sustained fire-fountains of similar height to Izu-Oshima (1.6 km above the vent), we show that the Roza eruption could have sustained buoyant ash and gas plumes that extended into the stratosphere at ∼45°N. Assuming 5 km long active fissure segments and 9000 Mt of SO2 released during explosive phases over a 10–15 year duration, the ∼180km of known Roza fissure length could have supported ∼36 explosive events/phases, each with a duration of 3–4 days. Each 5 km fissure segment could have emitted 62 Mt of SO2 per day into the stratosphere while actively fountaining, the equivalent of about three 1991 Mount Pinatubo eruptions per day. Each fissure segment could have had one to several vents, which subsequently produced lava without significant fountaining for a longer period within the decades-long eruption. Sensitivity of plume rise height to ancient atmospheric conditions is explored. Although eruptions in the Deccan Traps (∼66Ma) may have generated buoyant plumes that rose to altitudes in excess of 18 km, they may not have reached the stratosphere because the tropopause was substantially higher in the late Cretaceous. Our results indicate that some flood basalt eruptions, such as Roza, were capable of repeatedly injecting large masses of SO2 into the stratosphere. Thus sustained flood basalt eruptions could have influenced climate on time scales of decades to centuries but the location (i.e., latitude) of the province and relevant paleoclimate is important and must be considered.

Modified ensemble Kalman filter for nuclear accident atmospheric dispersion: Prediction improved and source estimated

Atmospheric dispersion models play an important role in nuclear power plant accident management. A reliable estimation of radioactive material distribution in short range (about 50km) is in urgent need for population sheltering and evacuation planning. However, the meteorological data and the source term which greatly influence the accuracy of the atmospheric dispersion models are usually poorly known at the early phase of the emergency. In this study, a modified ensemble Kalman filter data assimilation method in conjunction with a Lagrangian puff-model is proposed to simultaneously improve the model prediction and reconstruct the source terms for short range atmospheric dispersion using the off-site environmental monitoring data. Four main uncertainty parameters are considered: source release rate, plume rise height, wind speed and wind direction. Twin experiments show that the method effectively improves the predicted concentration distribution, and the temporal profiles of source release rate and plume rise height are also successfully reconstructed. Moreover, the time lag in the response of ensemble Kalman filter is shortened. The method proposed here can be a useful tool not only in the nuclear power plant accident emergency management but also in other similar situation where hazardous material is released into the atmosphere.

Influence of Gas-Gas Heater on Wet Flue Gas Desulfuration

Material balance calculation was adopted to a wet flue gas desulfurization (WFGD) system for exploring impacts of gas-gas heater (GGH). Effects of GGH on flue and water consumption were analyzed. Results showed that inlet flue temperature of desulfurization tower reduced by 3.4 °C at 100% load after installation of GGH. Exhausted gas temperature of system increased by 34.9°C. The heat release of original flue in desulfurization tower reduced by 43.72%. Plume rise height was significantly improved. Water evaporation in desulfurization tower declined by 42.07%.Amount of addendum water reduced by 39.06%, and water vapor carried by flue decreased by 19.78% at the outlet of WFGD. Therefore, operation condition of flue emission is improved and water consumption decreases with GGH.

Physical controls on mixing and transport within rising submarine hydrothermal plumes: A numerical simulation study

A computational fluid dynamics (CFD) model was developed to simulate the turbulent flow and species transport of deep-sea high temperature hydrothermal plumes. The model solves numerically the density weighted unsteady Reynolds-averaged Navier–Stokes equations and energy equation and the species transport equation. Turbulent entrainment and mixing is modeled by a k–ε turbulence closure model. The CFD model explicitly considers realistic vent chimney geometry, vent exit fluid temperature and velocity, and background stratification. The model uses field measurements as model inputs and has been validated by field data. These measurements and data, including vent temperature and plume physical structure, were made in the ABE hydrothermal field of the Eastern Lau Spreading Center. A parametric sensitivity study based on this CFD model was conducted to determine the relative importance of vent exit velocity, background stratification, and chimney height on the mixing of vent fluid and seawater. The CFD model was also used to derive several important scalings that are relevant to understanding plume impact on the ocean. These scalings include maximum plume rise height, neutrally buoyant plume height, maximum plume induced turbulent diffusivity, and total plume vertically transported water mass flux. These scaling relationships can be used for constructing simplified 1-dimensional models of geochemistry and microbial activity in hydrothermal plumes. Simulation results show that the classical entrainment assumptions, typically invoked to describe hydrothermal plume transport, only apply up to the vertical level of ~0.6 times the maximum plume rise height. Below that level, the entrainment coefficient remains relatively constant (~0.15). Above that level, the plume flow consists of a pronounced lateral spreading flow, two branches of inward flow immediately above and below the lateral spreading, and recirculation flanking the plume cap region. Both turbulent kinetic energy and turbulence dissipation rate reach their maximum near the vent; however, turbulent viscosity attains its maximum near the plume top, indicating strong turbulent mixing in that region. The parametric study shows that near vent physical conditions, including chimney height and fluid exit velocity, influence plume mixing from the vent orifice to a distance of ~10 times the vent orifice diameter. Thus, physical parameters place a strong kinetic constraint on the chemical reactions occurring in the initial particle-forming zone of hydrothermal plumes.

Using simple plume models to refine the source mass flux of volcanic eruptions according to atmospheric conditions

A simple three-dimensional volcanic plume model that incorporates the effects of moisture and ambient wind is presented and used iteratively to refine the source mass flux, obtained from an empirical relationship between the plume rise height and source mass flux, according to the prevailing atmospheric conditions. It is applied to the eruption of Eyjafjallajökull in May 2010 using realistic atmospheric profiles appropriate to the time of the eruption. It is shown that the ambient wind has the largest effect on the refined source mass flux with moisture playing a secondary though still important role. It is also shown that significant differences in the values of the revised source mass fluxes can arise when the realistic atmospheric profiles are approximated by idealised profiles. The revised source mass flux is used to initialise a long-range dispersion model of ash in the atmosphere.

Assessing Coastal Plumes in a Region of Multiple Discharges: The U.S.−Mexico Border

The San Diego/Tijuana border region has several environmental challenges with regard to assessing water quality impacts resulting from local coastal ocean discharges for which transport is not hindered by political boundaries. While an understanding of the fate and transport of these discharged plumes has a broad audience, the spatial and temporal scales of the physical processes present numerous challenges in conducting assessment with any fidelity. To address these needs, a data-driven model of the transport of both shoreline and offshore discharges is developed and operated in a hindcast mode for a four-year period to analyze regional connectivity between the discharges and the receiving of waters and the coastline. The plume exposure hindcast model is driven by surface current data generated by a network of high-frequency radars. Observations provided by both boat-based CTD measurements and fixed oceanographic moorings are used with the Roberts-Snyder-Baumgartner model to predict the plume rise height. The surface transport model outputs are compared with shoreline samples of fecal indicator bacteria (FIB), and the skill of the model to assess low water quality is evaluated using receiver operating characteristic (ROC) analysis.

Dissolution of Direct Ocean Carbon Sequestration Plumes Using an Integral Model Approach

We present the results of a double-plume integral model for a positively buoyant multiphase plume of liquid carbon dioxide injected at mid-depths (500–2000m) in the ocean. In addition to the relevant plume physics, the model accounts for dissolution of the carbon dioxide droplets, the effect on dissolution of clathrate hydrate films, and the increase in seawater density due to enrichment by dissolved carbon dioxide. Due to the creation of negative buoyancy in the entrained fluid through dissolution of carbon dioxide, the near-field mixing exhibits a complex set of energetic descending outer plume structures that do not converge to a steady state. The unsteady near field is shown to be inherent in the plume physics, resulting in enhanced distribution of the dissolved carbon dioxide over the plume height and formation of multiple, unsteady intrusion layers. Despite the complex plume near field, we demonstrate that the height of maximum plume rise has a steady solution. A general empirical design equation for the maximum height of plume rise is presented from the model results, dependent on the initial droplet diameter and buoyancy flux, the strength of the ambient stratification, and the linear mass transfer reduction factor due to hydrate formation. A sensitivity analysis of the design equation highlights the droplet diameter as the most important design variable and demonstrates that current uncertainty in the value of the mass transfer reduction factor results in uncertainty of the plume rise height within a factor of three.

Linear bubble plume model for hypolimnetic oxygenation: Full‐scale validation and sensitivity analysis

An existing linear bubble plume model was improved, and data collected from a full‐scale diffuser installed in Spring Hollow Reservoir, Virginia, were used to validate the model. The depth of maximum plume rise was simulated well for two of the three diffuser tests. Temperature predictions deviated from measured profiles near the maximum plume rise height, but predicted dissolved oxygen profiles compared very well with observations. A sensitivity analysis was performed. The gas flow rate had the greatest effect on predicted plume rise height and induced water flow rate, both of which were directly proportional to gas flow rate. Oxygen transfer within the hypolimnion was independent of all parameters except initial bubble radius and was inversely proportional for radii greater than approximately 1 mm. The results of this work suggest that plume dynamics and oxygen transfer can successfully be predicted for linear bubble plumes using the discrete‐bubble approach.