Andrew W. Woods

Rheological and Physiological Consequences of Conversion of the Maternal Spiral Arteries for Uteroplacental Blood Flow during Human Pregnancy

Physiological conversion of the maternal spiral arteries is key to a successful human pregnancy. It involves loss of smooth muscle and the elastic lamina from the vessel wall as far as the inner third of the myometrium, and is associated with a 5–10-fold dilation at the vessel mouth. Failure of conversion accompanies common complications of pregnancy, such as early-onset preeclampsia and fetal growth restriction. Here, we model the effects of terminal dilation on inflow of blood into the placental intervillous space at term, using dimensions in the literature derived from three-dimensional reconstructions. We observe that dilation slows the rate of flow from 2 to 3 m/s in the non-dilated part of an artery of 0.4–0.5 mm diameter to approximately 10 cm/s at the 2.5 mm diameter mouth, depending on the exact radius and viscosity. This rate predicts a transit time through the intervillous space of approximately 25 s, which matches observed times closely. The model shows that in the absence of conversion blood will enter the intervillous space as a turbulent jet at rates of 1–2 m/s. We speculate that the high momentum will damage villous architecture, rupturing anchoring villi and creating echogenic cystic lesions as evidenced by ultrasound. The retention of smooth muscle will also increase the risk of spontaneous vasoconstriction and ischaemia–reperfusion injury, generating oxidative stress. Dilation has a surprisingly modest impact on total blood flow, and so we suggest the placental pathology associated with deficient conversion is dominated by rheological consequences rather than chronic hypoxia.

The fluid dynamics and thermodynamics of eruption columns

A new model for Plinian eruption columns is derived from first principles and investigated numerically. The dynamics particular to the momentum-driven basal ‘gas-thrust region’ and the upper buoyancy-driven convective region are treated separately. The thermal interactions in the column are modelled by the steady-flow-energy equation. The main results of the present paper are that: (1) the basal gas-thrust region model predicts a very rapid initial expansion of the material on leaving the vent; (2) the gas-thrust region height decreases with initial temperature, inital gas content of the erupted material and initial velocity, but increases with vent radius; (3) the total column height increases with initial temperature, initial velocity and vent radius, but decreases with initial gas content; (4) column collapse occurs for initial velocities of the order of 100 m/s; the precise value increases as the initial gas content in the erupted material decreases; (5) for large vent radii or low initial gas content of the erupted material, the velocity in the column can increase with height once in the buoyancy-driven region instead of decaying to zero monotonically; (6) the interaction of the potential energy with the enthalpy is found to be the dominant thermal interaction in the upper part of the column. Previous models of eruption columns involve inconsistencies and simplifications; these are shown to lead to significant differences in the results in comparison to the present model.

The accretion of oceanic crust by episodic sill intrusion

Seismic refraction data from mature oceanic regions show remarkable consistency in crustal thickness between sites, yet the characteristics of different spreading centers show great variation. This leads to the paradox that the similarity in mature oceanic crust suggests that the igneous processes in crustal accretion are the same across a range of spreading rates but that the differences in the spreading centers themselves imply the opposite. We have developed a simple two dimensional model for crustal accretion at oceanic spreading centers by the episodic addition of sills at a high level within the crust, as implied by recent geophysical studies of spreading centers. Using our model, we have calculated velocity and temperature fields in the crust, including the effects of hydrothermal cooling. We show that oscillations in the temperature field due to episodicities of 200–20000 years have an effect localized to the region within 50–500 m of the intrusion. By assuming that all latent heat and excess specific heat introduced by the injection of sills is convected away by hydrothermal circulation, we estimate that the maximum heat transfer associated with hydrothermal cooling in the upper crust is of the order of 10 times greater than the conductive flux. We have calculated seismic velocities associated with the model temperature field in the crust, and we show that these are consistent with results from both seismic refraction and reflection experiments. The model may be applied to both fast and slow spreading ridges, and it accounts for the apparent increases in both the mean crustal temperature and the frequency of presence of melt with increasing spreading rate, hence resolving the paradox. We also show that the implications of this model are consistent with geological observations of layering in ophiolites.

On the thermal evolution of the Earth's core

The Earths magnetic field is sustained by dynamo action in the fluid outer core. The energy sources available to the geodynamo are well established, but their relative importance remains uncertain. We focus on the issue of thermal versus compositional convection, which is inextricably coupled to the evolution of the core as the Earth cools. To investigate the effect of the various physical processes on this evolution, we develop models based on conservation of energy and the assumption that the core is well mixed by vigorous convection. We depart from previous numerical studies by developing an analytical model. The simple algebraic form of the solution affords insight into both the evolution of the core and the energy budget of the geodynamo. We also present a numerical model to compare with the quantitative predictions of our analytical model and find that the differences between the two are negligible. An important conclusion of this study is that thermal convection can contribute significantly to the geodynamo. In fact, a modest heat flux in excess of that conducted down the adiabatic gradient is sufficient to power the geodynamo, even in the absence of compositional convection and latent-heat release. The relative contributions of thermal and compositional convection to the dynamo are largely determined by the magnitude of the heat flux from the core and the inner-core radius. For a plausible current-day heat flux of Q = 3.0 × 1012 W and the current inner-core radius, we find that compositional convection is responsible for approximately two thirds of the ohmic dissipation in the core and thermal convection for the remaining one third. The proportion of ohmic dissipation produced by thermal convection increases to 45% with an increase in Q to 6.0 × 1012 W. In the early Earth, when the inner core was smaller and the heat flux probably greater than the present values, thermal convection would have been the dominant energy source for the dynamo. We also calculate the history of inner-core growth as a function of the heat flux. For example, the inner core would have grown to its present size in 2.8 × 109 years if the average heat flux was Q = 4.0 × 1012 W. The model does not require the heat flux to be constant.

The dynamics of explosive volcanic eruptions

Explosive volcanic eruptions involve the ejection of dense mixtures of ash and gas from a volcanic vent at high speed and pressure. This mixture is generated as liquid magma rises from a crustal magma chamber and decompresses, exsolving water vapor. As gas is exsolved, the mixture inflates, accelerates, and becomes foam-like. Once the liquid films around the bubbles are unable to spread as rapidly as the bubbles are expanding through decompression, the films rupture, and a fragmented mixture of ash and volatiles ascends to the volcanic vent. On eruption from the vent, the material decompresses, either into a volcanic crater or directly into the atmosphere. In the case of free decompression, the mixture typically has a high speed, while decompression in a crater can lead to either very low or very high eruption speeds. After decompression, the hot, dense mixture begins to entrain and heat ambient air, thereby lowering the mixture density, but it also decelerates under gravity. If the eruption velocity is sufficiently high, then the material can become buoyant and will generate a buoyant ash plume, called a Plinian eruption column, which rises above the vent. In contrast, if the eruption velocity is small or the mass flux is very large, then the material will typically collapse back toward the Earth and form a dense, laterally spreading flow. Buoyant eruption columns are able to transport the material high into the atmosphere, since they provide an efficient means of converting the initial thermal energy of the mixture into potential energy through entrainment and heating of ambient air. The height of rise of such eruption columns depends upon the eruption rate, the stratification of the atmosphere, the degree of thermal disequilibrium between the particles and the air, and the amount of water vapor in the atmosphere. Dense, hot ash flows, generated by collapsing fountains, transport ash and clasts laterally from the vent, sedimenting many of the larger clasts and entraining air en route. As a result, the density of the mixture may fall below that of the atmosphere, and the finer-grained solid material may thereby become buoyant and rise from the flow. The distance it travels increases with both the cloud mass and the mean particle size. The ensuing buoyant ash plume, called a coignimbrite eruption column, may have a source several kilometers from the original volcanic vent. Once the thermal energy of an eruption column has become exhausted, the ash intrudes laterally into the atmosphere. Ultimately, the cloud is swept downwind, where sedimentation of ash leads to fall deposits over hundreds of kilometers from the volcano.

Satellite observations and interpretation of the 1991 Mount Pinatubo eruption plumes

We demonstrate the use of hourly Geostationary Meteorological Satellite (GMS) and NOAA polar-orbiting advanced very high resolution radiometer (AVHRR) satellite images of the June 1991 Mount Pinatubo volcanic eruption plumes in providing details of the timing, changing eruptive style, and umbrella plume movement and dynamics. A chronology of explosive events, which culminated in a >9-hour-long climactic phase on June 15, has been determined from satellite data and favorably compared to ground-based and other ancillary information. Maximum eruption column altitudes of 40 km and column-top undercooling in excess of 55°C below the ambient atmosphere occurred during the climactic phase. Phases dominated by Plinian versus coignimbrite eruptive plumes can be distinguished on the images. Analysis of the spreading umbrella plume during the climactic phase suggests that over the first 4–5 hours the plume spread laterally as a gravitational intrusion before becoming advected in the ambient winds. We compare the rate of plume growth to a model of a radially symmetric, continuously fed intrusion to describe the motion. The rate of plume growth shows good agreement with this simple model for the first 4–5 hours. From column-top heights we determine eruption rates and obtain an independent estimate of the total volume of magma erupted from June 12–16 of ∼5.5 km3 dense rock equivalent (DRE), in good agreement with an independent estimate of the total eruptive volume made from deposits on land and submarine ash fall of up to 5.3 km3 DRE. We also show that secondary explosions in the Pinatubo ignimbrite deposits produced ash plumes reaching altitudes as high as 19 km in September 1991. This study indicates that realistic interpretation and monitoring of major eruption plumes can be accomplished by analysis of high temporal resolution satellite data.

The role of volatiles in magma chamber dynamics

Many andesitic volcanoes exhibit effusive eruption activity, with magma volumes as large as 107–109 m3 erupted at rates of 1–10 m3 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.

Moist convection and the injection of volcanic ash into the atmosphere

If unsaturated water vapor is carried upward by a volcanic eruption column, it may eventually become saturated owing to the decrease in temperature of the column as it expands through decompression and transfers heat to entrained air. Heat released as a result of the subsequent condensation of water vapor causes the air within the column to expand. We show that this increases the buoyancy and therefore the total height of rise of the column. The increase in height is significant in relatively small sub-Plinian and Strombolian eruptions in which mass eruption rates lie in the range 103 to 106 kg/s. In such eruptions, the latent heat released as the entrained water vapor condenses may provide the main source of heat which drives the ash and clasts upward. The height of rise then becomes relatively insensitive to the mass flux erupted at the vent and depends primarily upon the vapor loading of the atmosphere. In a moist atmosphere, ash may rise several kilomtres higher than in an eruption of comparable strength in a dry environment. Moist convection leads to much wider ash dispersal, particularly from very small eruptions. Subsequently, rain flushing of ash from umbrella clouds may result from the water which forms through the condensation of entrained vapor; the ash provides natural condensation nuclei for some of this entrained vapor, whose mass may be much greater than that of the ash. In small columns ( 107 kg/s), the latent heat released by condensation of vapor is relatively small in comparison with the thermal energy provided by the hot clasts and therefore moisture has no significant effect upon the eruption column dynamics; furthermore, the mass of water vapor originating from the erupted volatiles is usually comparable to, or greater than, that entrained from the ambient air. Our model also shows that, if the erupting mixture becomes buoyant, then the eruption columns associated with phreatomagmatic eruptions ascend nearly as high as Plinian columns with the same mass eruption rate. This is because the water which is vaporized by the hot ash at the source, condenses higher in the column and thereby restores its latent heat to the ascending ash.

On buoyancy-driven natural ventilation of a room with a heated floor

The natural ventilation of a room, both with a heated floor and connected to a cold exterior through two openings, is investigated by combining quantitative models with analogue laboratory experiments. The heated floor generates an areal source of buoyancy while the openings allow displacement ventilation to operate. When combined, these produce a steady state in which the air in the room is well-mixed, and the heat provided by the floor equals the heat lost by displacement. We develop a quantitative model describing this process, in which the advective heat transfer through the openings is balanced with the heat flux supplied at the floor. This model is successfully tested with observations from small-scale analogue laboratory experiments. We compare our results with the steady-state flow associated with a point source of buoyancy: for a given applied heat flux, an areal source produces heated air of lower temperature but a greater volume flux of air circulates through the room. We generalize the model to account for the effects of (i) a cooled roof as well as a heated floor, and (ii) an external wind or temperature gradient. In the former case, the direction of the flow through the openings depends on the temperature of the exterior air relative to an averaged roof and floor temperature. In the latter case, the flow is either buoyancy dominated or wind dominated depending on the strength of the pressure associated with the wind. Furthermore, there is an intermediate multiple-solution regime in which either flow regime may develop.

The decompression of volcanic jets in a crater during explosive volcanic eruptions

During explosive volcanic eruptions, fragmented silicic magma and volatiles exit the vent with pressures typically in the range 10–100 atm and at the speed of sound of the mixture. We show that for magmatic volatile contents no in the range 0.03 < no < 0.06 this has the approximate value (0.95 ± 0.05)(noRT)12, where R is the gas constant and T is the eruption temperature. This speed is nearly independent of the vent pressure and vent radius. By assuming there is negligible mixing with the air, we have modelled the decompression of such jets following eruption from the vent. For free decompression into the atmosphere the velocity of the decompressed jet has the approximate value (1.85 ± 0.05)(noRT)12; this is nearly independent of the eruption rate. For decompression into a crater the process is more complex. At low eruption rates with low vent pressure, the material becomes underpressured as it rises in the crater. A shock then forms in the crater. This recompresses the magma-volatile mixture, which then issues from the crater as a relatively slow subsonic jet at atmospheric pressure. As the eruption rate increases, such shocks move towards the top of the crater, and ultimately cannot form in the crater. Instead, the material issues from the crater as a high-speed supersonic jet. The upward thrust provided by the crater walls on this high-pressure jet then increases the upward velocity above that of a freely decompressing jet. The presence of a crater may therfore cause collapse in relatively small eruptions, whereas it may promote formation of buoyant eruption columns at higher eruption rates. If a crater grows through erosion during an eruption, column collapse will typically ensue even if the mass flux remains steady.