Understanding the longevity of volcanic ash‐clouds generated by powerful explosive eruptions is a long standing problem for assessing volcanic hazards and the nature and time scale of volcanic ...forcings on climate change. It is well known that the lateral spreading and longevity of these clouds is influenced by stratospheric winds, particle settling and turbulent diffusion. Observations of the recent 2010 Eyjafjallajökull and 2011 Grimsvötn umbrella clouds, as well as the structure of atmospheric aerosol clouds from the 1991 Mt Pinatubo event, suggest that an additional key process governing the cloud dynamics is the production of internal layering. Here, we use analog experiments on turbulent particle‐laden umbrella clouds to show that this layering occurs where natural convection driven by particle sedimentation and the differential diffusion of primarily heat and fine particles give rise to a large scale instability. Where umbrella clouds are particularly enriched in fine ash, this “particle diffusive convection” strongly influences the cloud longevity. More generally, cloud residence time will depend on fluxes due to both individual settling and diffusive convection. We develop a new sedimentation model that includes both sedimentation processes, and which is found to capture real‐time measurements of the rate of change of particle concentration in the 1982 El Chichon, 1991 Mt Pinatubo and 1992 Mt Spurr ash‐clouds. A key result is that these combined sedimentation processes enhance the fallout of fine particles relative to expectations from individual settling suggesting that particle aggregation is not the only mechanism required to explain volcanic umbrella longevity.
Key PointsNew theory for layer formation in volcanic ash‐cloudsParticle diffusive convection affects the cloud residence timeA new sedimentation model captures real-time measurements of historical events
Predictions for the heights and downwind trajectories of volcanic plumes using integral models are critical for the assessment of risks and climate impacts of explosive eruptions but are strongly ...influenced by parameterizations for turbulent entrainment. We compare four popular parameterizations using small scale laboratory experiments spanning the large range of dynamical regimes in which volcanic eruptions occur. We reduce uncertainties on the wind entrainment coefficient β which quantifies the contribution of wind‐driven radial velocity shear to entrainment and is a major source of uncertainty for predicting plume height. We show that models better predict plume trajectories if (i) β is constant or increases with the plume buoyancy to momentum flux ratio and (ii) the superposition of the axial and radial velocity shear contributions to the turbulent entrainment is quadratic rather than linear. Our results have important implications for predicting the heights and likelihood of collapse of volcanic columns.
Plain Language Summary
One‐dimensional models of volcanic plumes can predict whether a volcanic column will collapse and produce devastating pyroclastic flows or rise as a buoyant plume. In this case, 1‐D models can predict the height at which the volcanic plume will inject gases and ash, which is critical to make predictions for the climate impact of an eruption, as well as to assess ash fallout hazard. In these models, the mixing between the plume and the ambient atmosphere is parameterized. Uncertainties on this parameterization are very large and undermine all model predictions, such as the height a volcanic plume. In this study, we use small‐scale laboratory experiments to improve constraints on the most used parameterizations for mixing between a volcanic plume and the atmosphere. The experimental data set used spans the large range of dynamical regimes in which explosive volcanic eruptions occur. Our result significantly reduce uncertainties for predicting (i) under which conditions an eruptive column will collapse and produce pyroclastic flows and (ii) what eruption magnitude is required for a volcanic plume to reach the stratosphere (the higher part of the atmosphere) and significantly reduce Earth's surface temperature.
Key Points
Turbulent entrainment parameterizations in 1‐D volcanic plume models govern predictions for plume height and the likelihood of collapse
We test parameterizations using experiments spanning the full range of conditions for natural eruptions
We improve constraints on entrainment parameterizations for the four models most commonly used to model volcanic plumes
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.
This study compares and evaluates one-dimensional (1D) and three-dimensional (3D) numerical models of volcanic eruption columns in a set of different inter-comparison exercises. The exercises were ...designed as a blind test in which a set of common input parameters was given for two reference eruptions, representing a strong and a weak eruption column under different meteorological conditions. Comparing the results of the different models allows us to evaluate their capabilities and target areas for future improvement. Despite their different formulations, the 1D and 3D models provide reasonably consistent predictions of some of the key global descriptors of the volcanic plumes. Variability in plume height, estimated from the standard deviation of model predictions, is within ~20% for the weak plume and ~10% for the strong plume. Predictions of neutral buoyancy level are also in reasonably good agreement among the different models, with a standard deviation ranging from 9 to 19% (the latter for the weak plume in a windy atmosphere). Overall, these discrepancies are in the range of observational uncertainty of column height. However, there are important differences amongst models in terms of local properties along the plume axis, particularly for the strong plume. Our analysis suggests that the simplified treatment of entrainment in 1D models is adequate to resolve the general behaviour of the weak plume. However, it is inadequate to capture complex features of the strong plume, such as large vortices, partial column collapse, or gravitational fountaining that strongly enhance entrainment in the lower atmosphere. We conclude that there is a need to more accurately quantify entrainment rates, improve the representation of plume radius, and incorporate the effects of column instability in future versions of 1D volcanic plume models.
•We present the main results of an eruptive column model inter-comparison exercise.•Simulations with standard inputs for strong and weak eruptive plumes were performed.•We compare results of empirical, one-dimensional, and three-dimensional models.•Results allowed for evaluating model capabilities and areas for model improvement.
The maximum height of an explosive volcanic column, H, depends on the 1/4th power of the eruptive mass flux, Q, and on the 3/4th power of the stratification of the atmosphere, N. Expressed as scaling ...laws, this relationship has made H a widely used proxy to estimate Q. Two additional effects are usually included to produce more accurate and robust estimates of Q based on H: particle sedimentation from the volcanic column, which depends on the total grain-size distribution (TGSD) and the atmospheric crosswind. Both coarse TGSD and strong crosswind have been shown to decrease strongly the maximum column height, and TGSD, which also controls the effective gas content in the column, influences the stability of the column. However, the impact of TGSD and of crosswind on the dynamics of the volcanic column are commonly considered independently. We propose here a steady-state 1D model of an explosive volcanic column rising in a windy atmosphere that explicitly accounts for particle sedimentation and wind together. We consider three typical wind profiles: uniform, linear, and complex, with the same maximum wind velocity of 15ms−1. Subject to a uniform wind profile, the calculations show that the maximum height of the plume strongly decreases for any TGSD. The effect of TGSD on maximum height is smaller for uniform and complex wind profiles than for a linear profile or without wind. The largest differences of maximum heights arising from different wind profiles are observed for the largest source mass fluxes (>107kgs−1) for a given TGSD. Compared to no wind conditions, the field of column collapse is reduced for any wind profile and TGSD at the vent, an effect that is the strongest for small mass fluxes and coarse TGSD. Provided that the maximum plume height and the wind profile are known from real-time observations, the model predicts the mass discharge rate feeding the eruption for a given TGSD. We apply our model to a set of eight historical volcanic eruptions for which all the required information is known. Taking into account the measured wind profile and the actual TGSD at the vent substantially improves (by ≈30%) the agreement between the mass discharge rate calculated from the model based on plume height and the field observation of deposit mass divided by eruption duration, relative to a model taking into account TGSD only. This study contributes to the improvement of the characterization of volcanic source term required as input to larger scale models of ash and aerosol dispersion.
•We detail a model of volcanic plumes that includes wind effect and particle fallout.•We validate the model against a specially assembled data set of Plinian eruptions.•We show that the atmospheric wind profile strongly affects the rise of the column.•Predictions of eruptive mass flux from plume height are significantly improved.
Turbulent fountains are of major interest for many natural phenomena and industrial applications, and can be considered as one of the canonical examples of turbulent flows. They have been the object ...of extensive experimental and theoretical studies that yielded scaling laws describing the behaviour of the fountains as a function of source conditions (namely their Reynolds and Froude numbers). However, although such scaling laws provide a clear understanding of the basic dynamics of the turbulent fountains, they usually rely on more or less ad hoc dimensionless proportionality constants that are scarcely tested against theoretical predictions. In this paper, we use a systematic comparison between the initial and steady-state heights of a turbulent fountain predicted by classical top-hat models and those obtained in experiments. This shows scaling agreement between predictions and observations, but systematic discrepancies regarding the proportionality constant. For the initial rise of turbulent fountains, we show that quantitative agreement between top-hat models and experiments can be achieved by taking into account two factors: (i) the reduction of entrainment by negative buoyancy (as quantified by the Froude number), and (ii) the fact that turbulence is not fully developed at the source at intermediate Reynolds number. For the steady-state rise of turbulent fountains, a new model (‘confined top-hat’) is developed to take into account the coupling between the up-flow and the down-flow in the steady-state fountain. The model introduces three parameters, calculated from integrals of experimental profiles, that highlight the dynamics of turbulent entrainment between the up-flow and the down-flow, as well as the change of buoyancy flux with height in the up-flow. The confined top-hat model for turbulent fountains achieves good agreement between theoretical predictions and experimental results. In particular, it predicts a systematic increase of the ratio between the initial and steady-state heights of turbulent fountains as a function of their source Froude number, an observation that was not handled properly in previous models.
The longevity of submarine plumes generated at sea-floor hydrothermal systems constrains the hydrothermal input of chemical species into the deep-ocean. Decades of observations of episodic “event ...plumes” suggest that a key process governing the dynamics of an hydrothermal cloud spreading out laterally from a buoyant rising plume is the production of internal layering. Here, we use analog experiments on turbulent, hot particle-laden plumes and clouds to show that this layering occurs where particle diffusive convection driven by the differential diffusion of heat and small mineral precipitates gives rise to a large scale double diffusive instability. Where hydrothermal clouds are enriched in fine minerals, this “particle diffusive convection” can extend the longevity of an event plume to 2 yr after its emplacement. The very long residence time imposed by diffusive convective effects enables complete dissolution of fine sulfide and sulfate minerals. We develop a new theoretical model that includes both sedimentation and dissolution processes to quantify the potential amount of iron produced by the dissolution of iron-sulfide minerals settling through the cloud by diffusive convection. A key prediction is that the concentration of dissolved iron in hydrothermal clouds can reach up to 19±3 nM, which represents about 5% of the global hydrothermal discharge. If these results are representative of all hydrothermal vent fields, hydrothermal systems could provide 75% of the global budget of dissolved iron in the deep-ocean. Regionally, this flux is expected to scale in magnitude with mid-ocean ridge heat flow, consistent with observations and global ocean models.
•We present laboratory experiments simulating hydrothermal submarine plumes.•Sedimentation from submarine clouds is driven by particle diffusive convection.•This process can extend the longevity of event plumes to 2 yr.•Complete dissolution of fine sulfide minerals occurs prior to their sedimentation.•Hydrothermal clouds could provide 75% of the global dissolved iron in the deep-ocean.
Explosive volcanic eruptions commonly undergo a transition from stable plume to collapsing fountain with associated destructive pyroclastic density currents. A major goal in physical volcanology is ...to predict quantitatively the limit between the flow regimes as a function of the source and environmental conditions. Atmospheric winds influence the dynamics and stability of the column causing bending and enhancing turbulent air entrainment. However, the predictions made with 1‐D models of volcanic plumes accounting for the presence of wind strongly depend on the wind entrainment coefficient β, a parameter whose value varies in the literature. Here we present a new theoretical model to identify an analytical criterion for column collapse in windy conditions. We then present new laboratory experiments on turbulent jets with reversing buoyancy rising in a crossflow in order to better constrain β. Our results show that a single value of
β=0.5 can be used to describe the behavior of laboratory jets with arbitrary buoyancy. The results allow us to parameterize our 1‐D model of volcanic plumes PPM and to show the crucial importance of wind gradient and profile on volcanic column dynamics through the use of the 1991 Mt. Hudson eruption as a case study. Finally, we propose a new transition diagram between the stable plume and collapsing fountain regimes, as a function of wind speed and mass discharge rate only, which can be used for the rapid assessment of major hazards during an explosive eruption.
Key Points
We quantify the wind entrainment coefficient using laboratory experiments of jets with a reversing buoyancy
We show the crucial importance of wind gradient and profile on volcanic column dynamics
We use the Mt. Hudson eruption in 1991 to test our 1‐D model and show that strong winds prevented the volcanic plume to collapse
Explosive volcanic jets present an unusual dynamic situation of reversing buoyancy. Their initially negative buoyancy with respect to ambient fluid first opposes the motion, but can change sign to ...drive a convective plume if a sufficient amount of entrainment occurs. The key unknown is the entrainment behaviour for the initial flow regime in which buoyancy acts against the momentum jet. To describe and constrain this regime, we present an experimental study of entrainment into turbulent jets of negative and reversing buoyancy. Using an original technique based on the influence of the injection radius on the threshold between buoyant convection and partial collapse, we show that entrainment is significantly reduced by negative buoyancy. We develop a new theoretical parameterization of entrainment as a function of the local (negative) Richardson number that (i) predicts the observed reduction of entrainment and (ii) introduces a similarity drift in the velocity and buoyancy profiles as a function of distance from source. This similarity drift allows us to reconcile the different estimates found in the literature for entrainment in plumes.
The description of entrainment in turbulent free jets is at the heart of physical models of some major flows in environmental science, from volcanic plumes to the dispersal of pollutant wastes. The ...classical approach relies on the assumption of complete self-similarity in the flows, which allows a simple parameterization of the dynamical variables in terms of constant scaling factors, but this hypothesis remains under debate. We use in this paper an original parameterization of entrainment and an extensive review of published experimental data to interpret the discrepancy between laboratory results in terms of the systematic evolution of the dynamic similarity of the flow as a function of downstream distance from the source. We show that both jets and plumes show a variety of local states of partial self-similarity in accordance with the theoretical analysis of George (1989), but that their global evolution tends to complete self-similarity via a universal route. Plumes reach this asymptotic regime faster than jets which suggests that buoyancy plays a role in more efficiently exciting large-scale modes of turbulence.
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