Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes.

Turbulent buoyant plumes moving through density stratified environments transport large volumes of fluid vertically. Eventually, the fluid reaches its neutral buoyancy level at which it intrudes into the environment. For single-phase plume, the well-known theory of Morton, Taylor and Turner (Morton BR, Taylor GI, Turner JS. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. A 234, 1-23. (doi:10.1098/rspa.1956.0011)) describes the height of the intrusion with great accuracy. However, in multiphase plumes, such as descending particle plumes formed from the surface vessel during deep-sea mining operations, or ascending volcanic plumes, consisting of hot gas and dense ash particles, the sedimentation of particles can change the buoyancy of the fluid very significantly. Even if the plume speed far exceeds the sedimentation speed, the ultimate intrusion height of the fluid may be significantly affected by particle sedimentation. We explore this process, illustrating the phenomena with a series of analogue experiments and some simple modelling, and we discuss the applications in helping to quantify some environmental impacts of deep-sea mining and in helping to assess the eruption conditions leading to the formation of large laterally spreading ash clouds in the atmosphere. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Some fluid mechanical constraints on crystallization and recharge within sills.

The injection of hot magma into a sill can lead to heating and melting of the walls and roof of the reservoir while the injected magma cools and crystallizes. If the crystals are relatively dense, they will try to sediment from the injected magma to form a cumulate layer. In this cumulate layer, the crystals form a porous framework which traps the melt as it is built up. As the melt within the sill continually cools and precipitates dense crystals, there will be a gradual reduction in the density of the remaining silicate liquid. As a result, the melt which is progressively trapped in the pore space of the cumulate layer will become stably stratified in density. Using an idealized model of the fluid mechanical and thermodynamical principles, we explore some of the controls on the thickness and density stratification of cumulate layers following replenishment of a sill-like magma chamber. We show the balance between jamming of the crystal laden melt to form a homogeneous layer and the formation of a stratified cumulate zone depends on the cooling time scale compared to the sedimentation time scale. A key finding is that the composition and stratification in a packed crystal-melt suspension and the associated cumulate layer formed by cooling an intrusion of hot melt injected into the crust may have considerable variability, depending on the properties of the overlying roof melt and the size and hence fall speed of crystals which form in the melt. This article is part of the Theo Murphy meeting issue 'Magma reservoir architecture and dynamics'.

Near-surface magma flow instability drives cyclic lava fountaining at Fagradalsfjall, Iceland.

Lava fountains are a common manifestation of basaltic volcanism. While magma degassing plays a clear key role in their generation, the controls on their duration and intermittency are only partially understood, not least due to the challenges of measuring the most abundant gases, H2O and CO2. The 2021 Fagradalsfjall eruption in Iceland included a six-week episode of uncommonly periodic lava fountaining, featuring ~ 100-400 m high fountains lasting a few minutes followed by repose intervals of comparable duration. Exceptional conditions on 5 May 2021 permitted close-range (~300 m), highly time-resolved (every ~ 2 s) spectroscopic measurement of emitted gases during 16 fountain-repose cycles. The observed proportions of major and minor gas molecular species (including H2O, CO2, SO2, HCl, HF and CO) reveal a stage of CO2 degassing in the upper crust during magma ascent, followed by further gas-liquid separation at very shallow depths (~100 m). We explain the pulsatory lava fountaining as the result of pressure cycles within a shallow magma-filled cavity. The degassing at Fagradalsfjall and our explanatory model throw light on the wide spectrum of terrestrial lava fountaining and the subsurface cavities associated with basaltic vents.

Dynamics of deep-submarine volcanic eruptions.

Deposits from explosive submarine eruptions have been found in the deep sea, 1-4 km below the surface, with both flow and fall deposits extending several km's over the seafloor. A model of a turbulent fountain suggests that after rising 10-20 m above the vent, the erupting particle-laden mixture entrains and mixes with sufficient seawater that it becomes denser than seawater. The momentum of the resulting negatively buoyant fountain is only sufficient to carry the material 50-200 m above the seafloor and much of the solid material then collapses to the seafloor; this will not produce the far-reaching fall deposits observed on the seabed. However, new laboratory experiments show that particle sedimentation at the top of the fountain enables some of the hot, buoyant water in the fountain to separate from the collapsing flow and continue rising as a buoyant plume until it forms a radially spreading intrusion higher in the water column. With eruption rates of 10[Formula: see text]-10[Formula: see text] [Formula: see text], we estimate that this warm water may rise a few 100's m above the fountain. Some of the finer grained pyroclasts can be carried upwards by this flow and as they spread out in the radial intrusion, they gradually sediment to form a fall deposit which may extend 1000's m from the source. Meanwhile, material collapsing from the dense fountain forms aqueous pyroclastic flows which may also spread 1000's m from the vent forming a flow deposit on the seabed. Quantification of the controls on the concurrent fall and flow deposits, and comparison with field observations, including from the 2012 eruption of Havre Volcano in the South Pacific, open the way to new understanding of submarine eruptions.

On the use of plume models to estimate the flux in volcanic gas plumes.

Many of the standard volcanic gas flux measurement approaches involve absorption spectroscopy in combination with wind speed measurements. Here, we present a new method using video images of volcanic plumes to measure the speed of convective structures combined with classical plume theory to estimate volcanic fluxes. We apply the method to a nearly vertical gas plume at Villarrica Volcano, Chile, and a wind-blown gas plume at Mount Etna, Italy. Our estimates of the gas fluxes are consistent in magnitude with previous reported fluxes obtained by spectroscopy and electrochemical sensors for these volcanoes. Compared to conventional gas flux measurement techniques focusing on SO2, our new model also has the potential to be used for sulfur-poor plumes in hydrothermal systems because it estimates the H2O flux.

The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.

The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.

The control of magma crystallinity on the fluctuations in gas composition at open vent basaltic volcanoes.

Basaltic open vent volcanoes are major global sources of volcanic gases. Many of these volcanoes outgas via intermittent Strombolian-type explosions separated by periods of passive degassing. The gas emitted during the explosions has high molar CO2/SO2 and SO2/HCl ratios, while during the passive degassing these ratios are lower. We present new laboratory experiments in a model volcanic conduit, which suggest that these differences in gas geochemistry are a consequence of gas migration through crystal-rich magma. We show that gas may flow along channels through the particle-laden liquid and, at a critical depth, the gas may displace an overlying crystal-rich plug en masse, producing a growing slug of gas. Owing to the friction on the walls of the conduit, this plug becomes progressively sheared and weakened until gas enriched in the least soluble volatiles breaks through, causing an explosion at the surface. When the gas slug bursts, liquid is drawn up in its wake, which exsolves the more soluble volatile components, which then vent passively at the surface until the next explosive slug-bursting event.

Evidence for a universal saturation profile for radial viscous fingers.

Complex fingering patterns develop when a low viscosity fluid is injected from a point source into the narrow space between two parallel plates initially saturated with a more viscous, immiscible fluid. We combine historical and new experiments with (a) a constant injection rate; (b) a constant source pressure; and (c) a linearly increasing injection rate, together with numerical simulations based on a model of diffusion limited aggregation (DLA), to show that for viscosity ratios in the range 300-10,000, (i) the finger pattern has a fractal dimension of approximately 1.7 and (ii) the azimuthally-averaged fraction of the area occupied by the fingers, S(r,t), is organised into three regions: an inner region of fixed radius, r < rb, which is fully saturated with injection fluid, S = 1; a frozen finger region, rb < r < rf (t), in which the saturation is independent of time, S(r) = (r/rb)-0.3; and an outer growing finger region, rf(t) < r < 1.44 rf(t), in which the saturation decreases linearly to zero from the value (rf/rb)-0.3 at rf(t). For a given injected volume per unit thickness of the cell, V ≫ πrb2, we find rf = 0.4rb (V/rb2)1/1.7. This apparent universality of the saturation profile of non-linear fingers in terms of the inner region radius, rb, and the injected volume V, demonstrates extraordinary order in such a complex and fractal instability. Furthermore, control strategies designed to suppress viscous fingering through variations in the injection rate, based on linear stability theory, are less effective once the instability becomes fully nonlinear.

Topographic viscous fingering: fluid-fluid displacement in a channel of non-uniform gap width.

We consider the displacement of one fluid by a second immiscible fluid through a long, thin permeable channel whose thickness and permeability decrease away from the axis of the channel. We build a model that illustrates how the shape of the fluid-fluid interface evolves in time. We find that if the injected fluid is of the same viscosity as the original fluid, then the cross-channel variations in permeability and thickness tend to focus the flow along the centre of the channel. If the viscosity of the injected fluid is smaller than the original fluid, then this flow focusing intensifies, leading to very poor sweep of the original fluid in the system, with the injected fluid bypassing much of the channel. We also show that if the viscosity ratio of the injected fluid to the original fluid is sufficiently large, then a blunt nose may develop at the leading edge of the injected fluid, whereas the remainder of the fluid-fluid interface becomes stretched out along the edges of the channel. This leads to a much more efficient sweep of the original fluid from the channel. We generalize the model to illustrate how buoyancy forces and capillary pressure affect the evolution of the system and compare our model predictions with some simple laboratory experiments. This partial stabilization of a fluid interface in a channel of non-uniform width represents a generalization of the classical Saffman-Taylor instability, and our nonlinear solutions for the evolution of the interface highlight the importance of cross-channel variations in permeability and thickness in modelling flow in channelled reservoirs.This article is part of the themed issue 'Energy and the subsurface'.

The role of volatiles in magma chamber dynamics.

Many andesitic volcanoes exhibit effusive eruption activity, with magma volumes as large as 10(7)-10(9) m(3) erupted at rates of 1-10 m(3) x s(-1) over periods of years or decades. During such eruptions, many complex cycles in eruption rates have been observed, with periods ranging from hours to years. Longer-term trends have also been observed, and are thought to be associated with the continuing recharge of magma from deep in the crust and with waning of overpressure in the magma reservoir. Here we present a model which incorporates effects due to compressibility of gas in magma. We show that the eruption duration and volume of erupted magma may increase by up to two orders of magnitude if the stored internal energy associated with dissolved volatiles can be released into the magma chamber. This mechanism would be favoured in shallow chambers or volatile-rich magmas and the cooling of magma by country rock may enhance this release of energy, leading to substantial increases in eruption rate and duration.