R. Stephen J. Sparks

Axisymmetric collapses of granular columns

Experimental observations of the collapse of initially vertical columns of small grains are presented. The experiments were performed mainly with dry grains of salt or sand, with some additional experiments using couscous, sugar or rice. Some of the experimental flows were analysed using high-speed video. There are three different flow regimes, dependent on the value of the aspect ratio a = hi/ri ,w herehi and ri are the initial height and radius of the granular column respectively. The differing forms of flow behaviour are described for each regime. In all cases a central, conically sided region of angle approximately 59 ◦ , corresponding to an aspect ratio of 1.7, remains undisturbed throughout the motion. The main experimental results for the final extent of the deposit and the time for emplacement are systematically collapsed in a quantitative way independent of any friction coefficients. Along with the kinematic data for the rate of spread of the front of the collapsing column, this is interpreted as indicating that frictional effects between individual grains in the bulk of the moving flow only play a role in the last instant of the flow, as it comes to an abrupt halt. For a< 1.7, the measured final runout radius, r∞, is related to the initial radius by r∞ = ri(1 + 1.24a); while for 1.7 <a the corresponding relationship is r∞ = ri(1 + 1.6a 1/2 ). The time, t∞, taken for the grains to reach r∞ is given by t∞ =3 (hi/g) 1/2 =3 (ri/g) 1/2 a 1/2 ,w hereg is the gravitational acceleration. The insights and conclusions gained from these experiments can be applied to a wide range of industrial and natural flows of concentrated particles. For example, the observation of the rapid deposition of the grains can help explain details of the emplacement of pyroclastic flows resulting from the explosive eruption of volcanoes.

Entrainment into two-dimensional and axisymmetric turbulent gravity currents

Entrainment of ambient fluid into both two-dimensional and axisymmetric gravity currents is investigated experimentally using a novel neutralization technique. The technique involves the titrative neutralization of an alkaline gravity current which intrudes into and entrains an acidic ambient, and is visualized using a pH indicator solution. Using this technique, we can determine quantitative results for the amount of dilution in the head of the current. The head of the current is able to entrain ambient fluid both by shear instabilities on the current/ambient interface and by over-riding (relatively light) ambient fluid. Guided by our experimental observations, we present two slightly different theoretical models to determine the entrainment into the head of the current as a function of distance from the source for the instantaneous release of a constant volume of fluid in a two-dimensional geometry. By dimensional analysis, we determine from both models that the dimensionless entrainment or dilution ratio, E , defined as the ratio of the volumes of ambient and original fluid in the head, is independent of the initial reduced gravity of the current; and this result is confirmed by our experiments in Boussinesq situations. Our theoretical evaluation of E in terms of the initial cross-sectional area of the current agrees very well with our experimental measurements on the incorporation of an entrainment coefficient α, evaluated experimentally to be 0.063 ± 0.003. We also obtain experimental results for constant-volume gravity currents moving over horizontal surfaces of varying roughness. A particularly surprising result from all the experiments, which is reflected in the theoretical models, is that the head remains essentially unmixed – the entrainment is negligible – in the slumping phase. Thus the heads of gravity currents with identical initial cross-sectional areas but different initial aspect ratios (lock lengths) will begin to be diluted by ambient fluid at different positions and hence propagate at different rates. A range of similar results is determined, both theoretically and experimentally, for the instantaneous release of a fixed volume of (heavy) fluid in an axisymmetric geometry. By contrast, the results of our experiments with gravity currents fed by a constant flux exhibit markedly different entrainment dynamics due to the continual replenishment of the fluid in the head by the constant input of undiluted fluid from the tail.

Sediment-laden gravity currents with reversing buoyancy

There are many natural occurrences of sediment-laden gravity currents in which the density of the interstitial fluid is less than that of the ambient fluid, although the bulk density of the current is greater. Such currents are driven by the excess density of suspended particles. However, after sufficient particles have sedimented, the current will become buoyant, cease its lateral motion and ascend to form a plume. Examples of such currents include brackish underflows in deltas, turbidity currents and pyroclastic flows. Experimental studies are described which show that, due to sedimentation, sediment-laden gravity currents decelerate more rapidly than saline currents of the same density. There is little difference in the experiments between a sediment-laden current with neutrally buoyant interstitial fluid and one with buoyant interstial fluid until sufficient sediment has been lost to cause the latter kind of current to lift-off. A marked deceleration is then observed and a plume is generated, with lift-off occurring along the length of the current. The resulting buoyant plume then generates a gravity current below the upper surface of the fluid in the tank. The deposit from a current with buoyant fluid shows a fairly abrupt decrease in thickness beyond the lift-off distance and has a flatter profile than that from a simple sediment current. A theoretical model is presented, which is based on the two-layer shallow-water equations and incorporates a model of the sedimentation in which particles are assumed to be uniformly suspended by the turbulence of the current. The model shows good agreement with the observed lengths of the experimental currents as a function of time and predicts the lift-off distance reasonably well. These processes have implications for the behaviour of turbidity currents, the interpretation of turbidites, mixing processes in the oceans and the lift-off of pyroclastic flows.

Sedimentation from turbulent jets and plumes

Theoretical models are developed for the sedimentation from the margins of a particle-laden, axisymmetric, turbulent, buoyant plume, in a still environment and for an axisymmetric turbulent momentum jet. The models assume that the mass of each individual size fraction of sediment carried in a parcel of fluid decreases exponentially with time. For relatively coarse particles, the fallout models predict that the sediment deposition beyond a distance r on the ground expressed in log units should decay linearly with distance away from the vent for the momentum jet and should decrease with r1/3 for the buoyant plume. The exponential decay constant J is proportional to the terminal fall velocity Vt of the particles in both cases and inversely proportional to the square root of the initial momentum flux M0 for the jet fallout (Jj ∝ VtMo−1/2) and to the third power of the initial buoyancy flux Fo for the plume fallout (Jp ∝ VtFo−1/3). Smaller particles are affected by reentrainment caused by the turbulent eddies sweeping ambient fluid back into the plume or jet and thus reincorporating some particles that were released from the flow at greater heights. This is taken into account by introducing a reentrainment coefficient, ϕ, into the theoretical models with the assumption that the coefficient has a constant value for a plume of given strength. In new experiments, fallout occurs from the margins of particle-laden, fresh water, buoyant jets, and plumes in a tank of salty water, and sedimentation is measured on the tank floor. Two experiments were weakly affected by reentrainment and show excellent agreement with the simple theory. For smaller particles and increasingly buoyant plumes and strong jets, particle reentrainment is important. The experimental data are fitted by the new reentrainment theory, confirming that values of the reentrainment coefficient are approximately constant for a given flow. A settling number, β, is defined as the ratio of the characteristic velocity of the jet or plume to the particle settling velocity. For β ≥ 1, reentrainment seems to reach an equilibrium state for which the reentrainment coefficient is a constant of value 0.1 for jets and 0.4 for plumes, irrespective of flow strength or particle size. The plume experiments indicate that the value of the reentrainment coefficient is strongly dependent on plume strength and particle size for β slightly less than 1. The general principles of sedimentation from turbulent plumes and jets are applied to the fallout of pumice from volcanic eruption columns and of metalliferous particles from black smokers on the ocean floor. For volcanic eruptions, the results provide an explanation for the near vent overthickening of tephra fall deposits and imply that lithic and pumice fragments from small lapilli up to at least 1 m diameter blocks are efficiently reentrained into eruption columns. The size of particles reentrained in hydrothermal plumes is predicted to vary from less than 100 μm in weakly buoyant plumes up to over 1000 μm in megaplumes.

How volcanoes work: a 25 year perspective

Over the past 25 years, our understanding of the physical processes that drive volcanic eruptions has increased enormously thanks to major advances in computational and analytical facilities, instrumentation, and collection of comprehensive observational, geophysical, geochemical, and petrological data sets associated with recent volcanic activity. Much of this work has been motivated by the recognition that human exposure to volcanic hazard is increasing with both expanding populations and increasing reliance on infrastructure (as illustrated by the disruption to air traffic caused by the 2010 eruption of Eyjafjallajokull volcano in Iceland). Reducing vulnerability to volcanic eruptions requires a thorough understanding of the processes that govern eruptive activity. Here, we provide an overview of our current understanding of how volcanoes work. We focus particularly on the physical processes that modulate magma accumulation in the upper crust, transport magma to the surface, and control eruptive activity.

Convection and crystallization in magma cooled from above

Calculations are presented for the cooling from above of melts in the Di-An system in which the kinetics of crystallization are incorporated and play a dominant role. The results indicate that even with no initial superheat whatsoever, convection plays an important role in the cooling of magma chambers and allows substantial internal cooling, crystallization and differentiation. The calculations show, in agreement with observations, that in magma bodies hundreds of meters thick, crystallization occurs predominantly in the interior or at the floor, even though heat is lost only from the roof. The ratio of the final thickness of the layer formed at the floor to that formed at the roof increases as the overall size of the chamber increases, owing to the effects of convection.

Uturuncu volcano, Bolivia: Volcanic unrest due to mid-crustal magma intrusion

Uturuncu volcano, SW Bolivia, is a dormant stratovolcano (∼85 km3) dominated by dacitic lava domes and flows. 39Ar/40Ar ages show that the volcano was active between 890 ka and 271 ka, with the lavas becoming younger and less extensive at higher elevations. There are current signs of unrest. Between 1992 and 2006 geodetic satellite measurements record an ongoing 70 km deformation field with a central uplift rate of 1 to 2 cm/yr. Deformation indicates volume changes of 400 × 108 m3 over 14 years, an average of ∼1 m3/s (10−2 km3/yr). The deformation is attributed to magma intrusion into the Altiplano-Puna regional crustal magma body. Deformation models indicate a source at depths of 17 to 30 km beneath current local relief. In a reconnaissance survey, persistent seismic activity (mean of 2.6 earthquakes per hour with a maximum of 14 per hour) was recorded at about 4 km depth below the center of the uplift, 4 km SW of the volcanos summit. The seismic events have a normal b value (∼1.04) and activity is attributed to brittle deformation in the elastic crust above the active deep magma intrusion. The porphyritic dacite lavas (64−68% SiO2) have a plagioclase-orthopyroxene-biotite-magnetite-ilmenite assemblage and commonly contain juvenile silicic andesite inclusions, cognate norite nodules and crustal xenoliths. Temperature estimates are in the range 805 to 872°C for the dacites and about 980°C for the silicic andesites. The dacite magmas formed by fractional crystallization of andesite forming norite cumulates and involving partial melting of crust. Compositions and zoning patterns of orthopyroxene and plagioclase phenocrysts indicate that compositional variation in the dacites is caused by magma mixing with the silicic andesite. Reversely zoned orthopyroxene phenocrysts in the andesitic end-member are explained by changing oxidation states during crystallization. Fe3+/Fe2+ ratios from orthopyroxene crystals and Fe3+ in plagioclase provide evidence for a relatively reduced melt that subsequently ascended, degassed and became more oxidized as a consequence of degassing. The geophysical and petrological observations suggest that dacite magma is being intruded into the Altiplano-Puna regional crustal magma body at 17 km or more depth, consistent with deformation models. In the Late Pleistocene dacitic and andesitic magmas ascended from the regional crustal magma body to a shallow magma system at a few kilometers depth where they crystallized and mingled together. The current unrest, together with geophysical anomalies and 270 ka of dormancy, indicate that the magmatic system is in a prolonged period of intrusion. Such circumstances might eventually lead to eruption of large volumes of intruded magma with potential for caldera formation.

On the variations of flow rate in non-explosive lava eruptions

Abstract A physical model is developed to determine factors which influence the dynamics of non-explosive lava eruptions. In the model, magma rises in a laminar regime from an overpressured chamber surrounded by elastic rock and erupts at the surface, where the accumulation of lava may alter the vent pressure. In a flow rate versus volume diagram, an eruption follows a path which is sensitive to relative changes in flow variables such as viscosity, conduit dimensions and thickness of lava over the vent. The path does not depend on the unknown elastic properties of the country rock or the chamber dimensions. With appropriate volcanological data, an observed flow rate versus volume path can be interpreted. The approach is applied to three well-documented eruptions. In each case the eruption rate was partially influenced by decreasing chamber pressure. The 1988–1990 eruption of Lonquimay (Chile) exhibits an early phase of conduit shrinkage which lasted about 100 days, probably due to magma solidification against country rock. The 1979 eruption of La Soufriere de Saint Vincent (West Indies) was initially affected by lava dome growth and later passed through a phase possibly caused by constriction of the conduit. The 1943–1952 eruption of Paricutin (Mexico) was affected by changes of lava level in the cinder cone and magma properties. In these three eruptions, the pre-eruptive chamber overpressures were similar (10–20 MPa) even though the erupted volumes differed by as much as two orders of magnitude.

Extreme natural hazards: population growth, globalization and environmental change

Mankind is becoming ever more susceptible to natural disasters, largely as a consequence of population growth and globalization. It is likely that in the future, we will experience several disasters per year that kill more than 10 000 people. A calamity with a million casualties is just a matter of time. This situation is mainly a consequence of increased vulnerability. Climate change may also be affecting the frequency of extreme weather events as well as the vulnerability of coastal areas due to sea-level rise. Disastrous outcomes can only increase unless better ways are found to mitigate the effects through improved forecasting and warning, together with more community preparedness and resilience. There are particular difficulties with extreme events, which can affect several countries, while the largest events can have global consequences. The hazards of supervolcanic eruptions and asteroid impacts could cause global disaster with threats to civilization and deaths of billions of people. Although these are very rare events, they will happen and require consideration. More frequent and smaller events in the wrong place at the wrong time could have very large human, environmental and economic effects. A sustained effort is needed to identify places at risk and take steps to apply science before the events occur.

Distribution of volcanoes in active margins

We report a comprehensive study of the distribution of volcanoes in 16 active plate margins, corresponding to a total of 479 volcanic systems. The active volcanic arcs are found to have a ribbon geometry with an average length / width ratio of around 10. The shape of the volcanic arc is compared to the shape of the associated trench by projecting one onto the other. The projection direction agrees with the direction of plate convergence, which shows that plate motion is the main factor constraining magma generation on the lithospheric scale. There is no characteristic spacing between volcanoes. In each arc, the distribution of volcano spacing is best represented by a Gamma distribution which corresponds to randomly generated points in the same geometrical conditions. In order to explain how such distributions may be generated, we have investigated in the laboratory the gravitational instability of a layer of buoyant liquid which is fed at a constant rate at the bottom of denser fluid. Different dynamic regimes are reached for different values of the viscosity ratio between the two fluids. For low viscosity contrasts, there is only one initial instability event, with buoyant plumes organized in a periodic pattern. These plumes are fed continuously by the source, even at large times. For high viscosity contrasts, which is relevant to the geological problem, plumes are produced intermittently by individual instability events. They take the form of “cavity” plumes fed by narrow tails. Once the plumes have reached the surface, they continue to be fed from below by material rising through their shrinking tail. In successive instability events, plume generation is not repeated at the same locations which leads to a complex plan-form. With time, and hence with increasing number of instability events, the cumulative distribution of plume spacing changes from periodic to random. Material from a single plume is able to sustain volcanic eruptions for a period longer than the time between two instability events, and hence the distribution of active volcanic centers reflects the cumulative distribution of several instability events. This is consistent with the observed distributions.