Experiments on mixing in pyroclastic density currents generated from short-lived volcanic explosions

Earth and Planetary Science Letters 467 (2017) 138–148

Contents lists available at ScienceDirect

Earth and Planetary Science Letters www.elsevier.com/locate/epsl

Experiments on mixing in pyroclastic density currents generated from short-lived volcanic explosions Diana Sher, Andrew W. Woods ∗ BP Institute, University of Cambridge, England CB3 OEZ, UK

a r t i c l e

i n f o

Article history: Received 1 September 2016 Received in revised form 3 March 2017 Accepted 4 March 2017 Available online xxxx Editor: T.A. Mather Keywords: pyroclastic density current mixing sedimentation

a b s t r a c t During short lived volcanic eruptions, dilute, turbulent pyroclastic density currents are often observed to spread laterally from a collapsing fountain. These flows entrain and heat air while also sedimenting particles. Both processes lead to a reduction in the bulk density and since these flows often become vertically stratified, the upper part of the flow may then exhibit a reversal in buoyancy and lift off. The relative importance of entrainment and sedimentation in controlling the lift-off and the associated runout distance of short-lived flows is not well-understood. We report a series of novel analogue laboratory experiments in which a suspension of dense particles and salt powder is released into a flume filled with CO2 -laden water. A strong circulation develops in the head of the current: as current fluid reaches the front of the flow, it rises and mixes with ambient fluid which is displaced upwards over the advancing head. As the salt powder in the current mixes with the ambient fluid, small CO2 bubbles are released, decreasing the bulk density below the ambient and the mixture then rises off the current. As it advances, progressively more of the material in the flow circulates through the head, becomes buoyant and rises from the flow. Within a distance of order 9–12 times the initial size of the flow, all the original fluid has cycled through the head of the flow, mixed with ambient and lifted off. This suggests that dilute turbulent pyroclastic density currents produced by short-lived explosions, of initial length-scale L, will only propagate distances of order 9–12L. Currents with larger particles sediment more of their particles before the flow has fully mixed with the ambient, and this leads to a reduction in the mass which lifts off from the flow. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Pyroclastic density currents are one of the most dangerous type of volcanic phenomena known to humankind. They involve highly complex fluid dynamic processes which remain poorly understood and which are closely related to the dynamics of submarine turbidity currents. Indeed, the research challenges they pose overlap with scientists working in a number of fields including wider volcanology, hazard sciences, decision making, geophysics, fluid mechanics, engineering, sedimentology and the hydrocarbon industry. During many short-lived volcanic explosions, pyroclastic density currents composed of fragmented magma and fine ash form, either following collapse of a fountain or following partial failure and fragmentation of a dome. There is a spectrum of such flows, ranging from fully dilute and fully turbulent surge-type flows to granular–fluid pyroclastic density currents, which involve a range of gas–particle transport processes ranging from concentrated and

*

Corresponding author. E-mail address: [email protected] (A.W. Woods).

http://dx.doi.org/10.1016/j.epsl.2017.03.009 0012-821X/© 2017 Elsevier B.V. All rights reserved.

non-turbulent transport to fully dilute turbulent flow. The evolution of the flows is complex, and often the flows become segregated into a dilute and highly turbulent surge-type flow together with a dense basal flow which behaves more as an avalanche (Fisher, 1979; Calder et al., 1999; Dade and Huppert, 1996; Ogburn et al., 2014). This study explores the dynamics of pyroclastic density currents produced by a short-lived eruption, in which, following eruption, a dense particle laden suspension feeds the flow. One of the earliest recorded examples of a devastating pyroclastic density current developed during the eruption of Mt Pelee, Martinique, 1902. Important examples have also been described during the eruption of Soufriere Hills Volcano, Montserrat (Druitt et al., 2002; Ogburn et al., 2014), Lascar volcano, Chile (Calder et al., 2000), Colima volcano (Sulpizio et al., 2014), Galeras Volcano, Columbia (Stix et al., 1997), as well as Merapi volcano in Indonesia (Gertisser et al., 2012). Dilute pyroclastic density currents represent an important hazard in terms of their propagation distance and speed, with flows travelling distances in the range of a few km from the volcano with speeds of several tens of metres per second while pyroclastic density currents produced from directed blasts may travel larger distances in the range

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

139

Fig. 1. Evolution of the concentration of a saline gravity current as it advances along a flume. The colour scale indicates the mass of salt in the fluid per unit mass of liquid (g/kg) as a function of position in the current, with the initial saline fluid behind the lock gate having a value 50 g/kg.

1–10 km (Coombs et al., 2010; Cole et al., 2014; Lube et al., 2015; Komorowski et al., 2013; Cronin et al., 2013). The topography can have a dominant impact on the flow evolution causing the dilute part of the flow to decouple from the denser basal part of the flow (Ogburn et al., 2014), and the dilute component may then advance independently from the basal flow. As air is mixed into the pyroclastic density current, the air heats up and its density decreases, thereby lowering the bulk density of the overall mixture (Wilson and Walker, 1982; Woods and Bursik, 1994). When operating in combination with sedimentation, the upper parts of the flow may become buoyant and lift off, forming an ash plume (cf. Woods and Wohletz, 1991; Woods and Kienle, 1994; Clarke et al., 2002). Owing to the importance of these flows, and the complexity of the interaction between the dense lower part of the flow and the overlying dilute flow, numerous models have been developed to account for the dynamics, using numerical and experimental modelling approaches. Reviews of both experimental and theoretical models of pyroclastic density currents (Sulpizio et al., 2014; Dufek, 2016) summarise the range of behaviour from dense avalanching flows to more dilute suspension flows. Of particular importance is the vertical stratification which often emerges in numerical models which suggest that there is a basal zone of high particle concentration overlain by a more dilute ash flow (Todesco et al., 2002; Takahashi and Tsujimoto, 2000; Clarke et al., 2002; Ishimine, 2005; Calder et al., 1997; Valentine and Wohletz, 1989). However, the detailed dynamics is complex and many of the models rely on detailed parameterisations of turbulence and particle transport in a multi-phase flow. Andrews and Manga (2012) carried out experiments using heated fine powder in an air based flume measuring the sedimentation pattern to estimate the fraction of the particle load which lifts off. Larger scale experiments have also been carried out in which particle suspensions in air have been released from a central source (Dellino et al., 2007, 2008) or a large flume (Lube et al., 2015) and spread over 10’s metres. Some different, but complementary small-scale analogue laboratory experiments have been carried out to examine the evolution of the density of pyroclastic density currents using particle laden currents of fresh water migrating through a flume filled with saline solution. As the particles sediment, the residual fluid becomes buoy-

ant and lifts off (cf. Sparks et al., 1993; Woods and Bursik, 1994; Bonnecaze et al., 1993). In another class of experiments, currents composed of methanol and ethylene glycol (MEG) mixed with water have been released into a water filled flume to examine the role of mixing on the dynamics of pyroclastic density currents. The density of a MEG–water mixture may initially be smaller than water, but on mixing with water, it becomes relatively dense, and so by running such an experimental system upside down, the generation of buoyancy through mixing can be modelled. Huppert et al. (1986) and Woods and Bursik (1994) carried out such MEG–water experiments, with the current propagating along a sloping boundary, demonstrating the importance of mixing in the head and the increase in the rate of entrainment as the angle of slope increases. Since these water-bath studies, there has been considerable progress in understanding the entrainment of ambient fluid into gravity currents (Sher and Woods, 2015; Samasiri and Woods, 2015). A strong circulation within the head means that all the current fluid eventually reaches the front of the flow where it rises up over the continuing head. Here it mixes with a fraction of the ambient fluid, originally ahead of the current, and which is displaced up over the head. The mixed fluid is then left behind the continuing head of the flow, forming a dilute wake. In Fig. 1, we present a series of images to illustrate the evolving width-averaged buoyancy within a saline gravity current as it migrates along a 3 m long flume. The buoyancy, shown in false colour, is obtained by using a uniform light source on the rear face of the tank, and calibrating the light intensity as a function of the salinity of the current, so that the width-averaged concentration of salt can be measured at each point along the flume using a high resolution digital image (Sher and Woods, 2015). The figure illustrates that after travelling about 10 lock lengths, all the original fluid in the current has mixed with ambient fluid and, subsequently, the concentration of salt everywhere in the flow is less than 0.4 of the original concentration. The speed of the current, u, in this initial phase of the flow is approximately constant and given by

u = 0.9( go h)1/2

(1)

where go is the reduced gravity defined in terms of the density difference between the ambient fluid, ρa , and the original lock gate fluid, ρc , go = g (ρc − ρa )/ρa , and h is the depth of the head. By comparison of the rate of change of volume of the current based

140

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

Table 1 Table of typical properties. Property

Pyroclastic density current

Experiment

Speed Height Buoyancy Particle size Reynolds number Stokes number Rouse number

10–90 m/s 10–100 m 0.1–1.0 m/s2 10−3 –10−1 m 106 –107 0.1–100 0.5–1.6

0.05–0.15 m/s 0.05–0.15 m 0.1–1.0 m/s2 10−4 –10−2 m 103 –104 0.1–10 0.1–1.6

on the light attenuation data, Sher and Woods (2015) estimated that a fraction of about 0.6 ± 0.1 of the ambient fluid originally ahead of the current and displaced by the current is entrained into the current. This parameterisation is based on observations that the main phase of mixing occurs in the head region of the flow, where the ambient fluid rises up over the current and mixes through a shear-type instability on the rear part of the head. The purpose of this paper is to explore the mixing into the head of a pyroclastic density current, produced by a short-lived volcanic explosion, through a new series of experiments in which we simulate the generation of buoyancy through the mixing at the head of a two dimensional gravity current. In our analogue experiments, a dense aqueous salt solution containing a suspension of salt powder is released into a flume filled with CO2 -laden ambient fluid. As the salt powder mixes with the CO2 laden fluid, small bubbles of gas are generated, causing the density of the mixture to fall below that of the ambient fluid and leading to lift off. We contrast this process with the lift-off which occurs through particle sedimentation when an initially dense particle-laden current of fresh water migrates through a saline ambient (cf. Sparks et al., 1993). We then discuss the implications of our experiments on the evolution of pyroclastic density currents produced by a short-lived eruption. 1.1. Scaling between the experiments and pyroclastic density currents There has been some discussion about the difference between small-scale aqueous experiments and particle–air experiments in terms of providing a representative analogue model for the flow processes in a pyroclastic density current (Burgisser et al., 2005; Andrews and Manga, 2012). Our purpose is not to simulate a pyroclastic density current, but to study the mixing in the head of the flow and the resulting generation of buoyancy, and to contrast that with the effects of sedimentation of particles from the flow. From these experiments, we can then draw some principles about the controls on the dynamics of pyroclastic density currents. In this spirit, we aim to ensure that the dynamical balances in our experiments are equivalent to those in a pyroclastic density current (Table 1). This requires that (i) the flow is turbulent, with Reynolds

number in excess of 3000 so that the inertia of the flow dominates the frictional stresses; (ii) the characteristic speed of the turbulent motions in the flow are greater than the fall speed of the particles, so that particles can be suspended and mixed up by the turbulence; and (iii) the Stokes number of the flow, which measures the ratio of the time for solid particles to respond to fluctuations in the velocity compared to the time scale of the fluctuations in the velocity, should be small, otherwise the particles will not follow the turbulent fluctuations. We generate our experimental flows by the release of a finite mass of fluid from behind a lock gate. This forms a gravity current type flow in which the speed of the front u ∼ ( g  h)1/2 where g  = g (ρc − ρa )/ρa is the buoyancy contrast between the current and the ambient fluid, and h is the depth of the flow. This leads to a Froude number, F r = u /( g  h)1/2 of order unity, and so for sufficient source volume, the Reynolds number of the flow exceeds 3000 (Simpson, 1997; Sher and Woods, 2015). The fall speed of the particles, v s , relative to the magnitude of the turbulent fluctuations in the velocity, known as the Rouse number, Ro, (cf. Stix, 2001; Choux and Druitt, 2002) can be estimated using the relation Ro = v s /ku ∗ with k = 0.4 and u ∗ = 0.4u /(ln( y /h∗ )) where h∗ is the vertical scale of the boundary layer at the base of the flow which is influenced by surface roughness, u the mean speed and y the height above the bed. Once the Rouse number increases beyond about 2.5, particles cannot be suspended by the turbulence. Fig. 2a illustrates the typical values of the Rouse number in a laboratory gravity current, with a speed in the range of 5–15 cm/s, and depth of order 5–10 cm, as a function of the particle size. It is seen that particles smaller than about 50–100 micron may be suspended by such flows, whereas with larger particles or slower flows, the particles will tend to sediment through the flow. By contrast, in pyroclastic density current with speed 50–90 m/s (Fig. 2b), particles of size smaller than about 2 cm have a Rouse number smaller than 2.5 at a point 10 m above the base of the flow. The Stokes number of the flow is given by St = T p / T f , where T p is the response time of particles to changes in the flow speed, which depends on the frictional force on the particles, and eddy circulation time, T f , is approximated by he /u ∗ , the length scale of eddies, he , divided by the friction speed u ∗ . We expect the largest eddies to scale with the depth of the flow, and depending on the boundary layer scale, in a current with speed 50–100 m/s, particles of size 0.1–1.0 cm have Stokes numbers in the range 0.1–100. This suggests that larger particles respond slowly to changes in the flow, while smaller particles respond more rapidly. Our laboratory experiments, with particles of size 10–100 micron, and currents of speed 5–15 cm/s, have Stokes numbers in the range 0.1–10. Based on these scalings, we propose that there is an overlap in the be-

Fig. 2. Variation of the Rouse number in (a) a laboratory current with speeds of 5, 10 and 15 cm/s, and (b) a pyroclastic density current with speeds 50, 70, and 90 m/s, as a function of the particle size.

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

141

Table 2 Table of experimental conditions in experiments 1–38. Exp. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

g 0

L (cm)

H (cm)

Particle size (μ)

Salt powder (g)

Particle mass (g)

(cm/s2 )

Ambient fluid

12 12 11 12 13 14 11 12 13 14 20 11 14 16 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

13 13 11 12 13 14 11 12 13 14 20 11 14 16 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

– – – – – – – – – – – – – – 18 18 18 18 18 18 30 30 30 53 53 53 63 63 63 75 75 75 106 106 106 106 106 106

39 39 30 36 42 49 30 36 42 49 100 30 49 64 72 72 0 72 72 0 72 72 0 72 72 0 72 72 0 72 72 0 72 72 0 72 72 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 169.2 169.2 325.2 84.6 84.6 238.3 84.6 84.6 238.3 84.6 84.6 238.3 169.2 169.2 325.5 169.2 169.2 325.5 169.2 169.2 325.5 84.6 84.6 238.3

121.5 121.5 34.8 34.8 34.8 34.8 65.7 65.7 65.7 65.7 65.7 121.5 121.5 121.5 78.4 78.4 115.6 39.2 39.2 78.4 39.2 39.2 78.4 39.2 39.2 78.4 78.4 78.4 115.6 78.4 78.4 115.6 78.4 78.4 115.6 39.2 39.2 78.4

lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution lemonade fresh water saline solution

haviour of particles in our experiments and in pyroclastic density currents. We also note that in our experiments, the generation of buoyancy is associated with the production of bubbles rather than the heating of the air as occurs in a pyroclastic density current. In order that the flows behave in an analogous fashion, we require that the rise speed of the bubbles is smaller than the flow speed. The bubbles produced by nucleation are expected to be of comparable size to the particles, with a rise speed of order 0.05–0.2 cm/s, while the experimental flow speeds are of order 0.1 m/s, leading to bubble Rouse numbers of order 0.01–0.1 and a bubble Stokes number 1. The time for bubbles to nucleate scales as d2 / D where d is the bubble size and D the gas diffusion coefficient in the water. This has value of order 0.1–1.0 s for bubbles of size 10–30 μm. This is short compared to the time-scale for the flow to travel a distance of order 10 lock lengths, which is of order 10–20 s, and so the buoyancy associated with the bubbles is generated rapidly after mixing of the ambient fluid with the current in an analogous fashion to the heat transfer in a pyroclastic density current.

L s / Lm

2.3 – 2.3 – – – 1.7 – 1.7 1.1 – 1.1 1.2 – 1.2 0.8 – 0.8 0.7 – 0.7 0.6 – 0.6

In our experiments, we used a range of different silicon carbide particles, as shown in Table 2, with sizes ranging from 18–106 microns. In order to generate buoyancy through mixing, salt powder, with a grain size of order 100 microns and settling speed of order 0.1 cm/s was added to the fluid in the lock. Exploratory experiments using different masses of salt powder were carried out, and we found that a constant mass fraction equal 2.5 wt% of the mass of the source fluid was effective in generating the small bubbles which led to a reversal of the buoyancy, while remaining sufficiently dilute that the rheology of the source fluid was not significantly affected. The salt powder was added to the fluid behind the lock gate immediately prior to opening the gate in order to minimise any dissolution during the 10–20 s duration of the experiment. In the experiments using a suspension of silicon carbide particles, the fluid behind the lock gate was stirred thoroughly prior to opening the lock gate and a repeatable technique was developed to generate the flows. Unfortunately in these experiments, with the high concentration of particles, so much light is absorbed by the particles that the light attenuation technique cannot resolve differences in concentration.

2. Experiments 2.1. Buoyancy generation through mixing We carried out a series of gravity current experiments in a flume which was 10 cm wide, 3 m long and which had a depth of 50 cm. In each experiment, the main flume tank was filled with ambient fluid, and the current fluid was then placed behind a lock gate. The experimental tank was backlit with a uniform matrix LED light panel (W and Co Displays and Signs) and a Casio EX-FH25 camera was used to record the evolution of the flow.

We first carried out experiments in which buoyancy is generated by mixing. The main tank was filled with a 50:50 mixture of lemonade, with density 1.001 ± 0.001, and fresh water. The fluid behind the lock gate consisted of a salt solution and 2.5 wt% salt powder as listed in Table 2 (experiments 1–14) so that the initial flow was dense relative to the ambient fluid. Experiments were

142

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

Fig. 3. A. Evolution of an initially dense salt and salt powder gravity current propagating through a flume filled with lemonade; B. Illustration of the time-dependent mixing of ambient fluid (green) into the head of the flow (red) and the subsequent lift off of mixed buoyant fluid from the rear of the head. C. Schematic illustrating the process of mixing and lift off. (For interpretation of the colours in this figure, the reader is referred to the web version of this article.)

carried out using a range of different source volumes and a range of different initial salt concentrations of the source fluid, but with a fixed mass fraction of salt powder. This enabled us to test how the mixing and buoyancy generation depends on current size and on the initial density of the flow. The results of Sher and Woods (2015) for salt currents suggest that the mixing and hence run-out distance should increase with the initial size of the flow; also, with a greater initial salt concentration, we may expect a greater runout distance as more mixing may be required to reverse the initial buoyancy of the flow (Table 2). In a typical experiment, as the advancing current (red) displaces the ambient fluid (clear) up over the head of the flow, some of the lemonade in the ambient mixes with the salt powder in the current (Fig. 3A). The salt powder provides nucleii for heterogeneous nucleation of small bubbles of CO2 in the mixture. The salt powder has dimensions of order 10–100 microns, and so the bubbles produced by nucleation are expected to be of comparable size with a rise speed of order 0.05–0.2 cm/s. This is consistent with observations and much smaller than the typical flow speed, so the Rouse number is of order 0.01–0.1 and the Stokes number has value 1. Therefore the bubbles move with the flow and as the bubbly zone which develops just behind the head becomes buoyant, it lifts off from the current as a continuous stream. The parcels of buoyant, bubble laden fluid appear to rise with speed of order 1–10 cm/s

and with length scale of 5–10 cm. The loss of this buoyant fluid from the rear of the head reduces the mass in the remaining current, and on reaching a distance of about 9–12 lock lengths from the source, the dense gravity driven flow has essentially dissipated. As in the experiments of Sher and Woods (2015), much of the mixing seems to occur on the upper surface of the head of the flow, as the current displaces ambient fluid up and over the advancing nose of the flow. As a result, the bubbly fluid is generated in the rear part of the head of the flow, and then rises upwards off the flow, as seen in the photographs. The time-scale of bubble formation, of order 0.1–1.0 s, is comparable to or shorter than the turn-over time of the fluid in the head of the current, and so does not delay the generation of the buoyancy. In Fig. 3B we present a series of images from a second experiment in which a region of ambient fluid ahead of the current was dyed green, while again the current fluid was dyed red. As the current head reaches the green dye, it is seen that the green ambient fluid rises up over the current and mixes. The ensuing generation of bubbles at the rear of the head produces a cloud of buoyant mixed red and green fluid which rises up from the rear of the head. This visualisation helps to demonstrate the importance of the mixing in the generation of buoyancy (see also video in supplementary material).

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

143

Fig. 4. Distance travelled by the front of the flow as a function of time for expts 3–14, Table 2, corresponding to currents of aqueous salt solution with a suspension of salt powder propagating through a flume filled with a lemonade–fresh water mixture. The currents have different initial volume and different initial mass of dissolved salt, but the same mass of salt powder per unit mass of fluid. The data is plotted in a non-dimensional form. The dotted, dashed and solid lines correspond to experiments with three different initial salinities, 5 (dashed), 10 (solid) and 20 (dotted) wt%, while the different curves within each salinity set correspond to different initial volumes of the fluid, as shown in Table 2. With the same initial salinity in the current, the data suggest that the dimensionless run out distance is similar.

We carried out a systematic series of experiments in which we changed either the volume or the salinity of the aqueous solution behind the lock gate, as shown in Table 2. In these experiments, the mass of salt powder per unit volume of salt solution behind the lock gate was fixed at 2.5 wt%. In Fig. 4, we present data showing the distance reached by the head of the flow as a function of time for the experiments 3–14 listed in Table 2. In each case, the lengths are scaled with the size of the lock, L, and the time is scaled with the characteristic time ( L / go )1/2 , where go the initial buoyancy of the fluid behind the lock relative to the ambient fluid. Data are shown for three values of the initial salinity, leading to different go (dashed – salinity of 5 wt%, solid – 10 wt% and dotted – 20 wt% lines), and for a range of lock sizes. For each value of go , the data follow a similar dimensionless curve, independent of the size of the flow. Different lock sizes in the range of 120–400 cm2 are represented by the different colours. This is expected, since the evolution of the flow is only expected to depend on the characteristic length scale, L, and time scale, ( L / go )1/2 . With a larger dissolved salt content, corresponding to a larger go , the currents are denser, and so on mixing with the lemonade and generating bubbles of CO2 , a smaller fraction of the flow becomes buoyant. This leads to a more gradual generation of buoyant fluid which rises from the current and so the current travels a greater total distance before the original volume of fluid in the current becomes mixed with the ambient fluid. Indeed, Fig. 4 shows a systematic increase in run-out length from about (9 ± 1) L to (14 ± 1) L as the initial dissolved salt content of the solution increases. The initial speed of all the currents follow a similar scaling as given by eqn. (1). However, as the mixing develops and fluid liftsoff from the flow, there is a small but systematic decrease in the speed which may be seen as the slight decrease in the slope of the curves with distance. The currents with smaller initial salt content wane most rapidly since these undergo a faster reversal in buoyancy with mixing and bubble generation. 2.2. Buoyancy generation through mixing in a sedimenting current In a further series of experiments, we replaced the salt dissolved in the solution behind the lock gate with a comparable mass of silicon carbide particles, and the suspension of particles and salt powder were released into a flume tank again filled with

a 50:50 mixture of fresh water and lemonade. As above, the mixing of the salt powder into the lemonade produces bubbles which leads to buoyancy reversal and lift-off just behind the head. In Fig. 5a, we present a series of photographs which illustrate the time evolution of one such particle laden current. It is similar to the flow observed in Fig. 3. The mixing with ambient fluid leads to the continuous production of a low density mixture which rises from behind the head of the current and eventually leads to termination of the flow. In these currents, the sedimentation of silicon carbide particles also reduces the density of the mixture. If the time for sedimentation is smaller than the time for mixing, much of the sediment will settle from the current rather than being lifted up by the flow, whereas with slow sedimentation we expect a substantial part of the sediment load to rise from the flow in the buoyant mixed fluid. The mixing distance, L m ∼ 10L o and the distance required for particles to sediment from the flow, L s ∼ uL o / v s where u is the characteristic speed of the flow, u = ( go L o )1/2 , and v s the fall speed of the particles. Therefore, the ratio of the sedimentation time to the mixing time may be expressed as

R ∗ = L s / L m = u /10v s

(2)

In our experiments, this had values in the range 0.6 to 2.3. In the discussion section we consider the implication of these results for pyroclastic density currents. With small particles of size 18 micron, the fall speed, v s , has value 3 mm/s, and the sedimentation length is of order 20L o , which far exceeds the mixing length, and so there is relatively little sedimentation prior to lift off. In contrast, with the larger particles of size 106 micron, the sedimentation distance is about 6L o and so there is much more sedimentation prior to lift off. In Fig. 5c, we illustrate the variation of the maximum run out distance of the flow as a function of R ∗ (open symbols). As the ratio R ∗ increases, the sedimentation rate decreases, and so there is a small increase in run-out distance required to generate buoyancy (cf. Fig. 4). However, the dominant process controlling the run-out distance is the mixing (cf. section 2.1). 2.3. Buoyancy generation through sedimentation To place the results on buoyancy generation by mixing in context, we have carried out a further series of experiments in which

144

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

Fig. 5. Series of images of (a) a particle laden current, with particles of size 106 micron, in fresh water with a suspension of salt powder migrating through a tank filled with lemonade, and a series of images (b) of a particle laden current with particles of 106 micron, in fresh water with a suspension of salt powder, migrating through purely saline solution. (c) Run-out distance as a function of R ∗ (= L s / L m ) for 14 different currents. Seven currents advancing through an ambient containing lemonade with the source fluid consisting of a mixture of particles and salt powder (open symbols), and seven currents propagate through an ambient of the saline solution with the source fluid consisting of fresh water mixed with particles (solid symbols). The details of each experiment, indicated by the number next to the symbols in the figure, are listed in Table 2.

the ambient fluid was saline solution, and the current was initially composed of fresh water laden with particles. The initial particle load was chosen so that the density of the fluid behind the lock was in excess of that of the saline solution, and in each case, the buoyancy of the current relative to the ambient was set equal to the buoyancy of one of the experiments presented in section 2.2. As a result, R ∗ has the same value (Table 2). As these currents advance along the flume, they sediment particles, and the remaining mixture eventually becomes buoyant because the fluid in the lock gate was fresh (cf. Sparks et al., 1993). At this point the current ceases to migrate along the flume as may be seen in the series of photographs of the evolution of one of these currents (Fig. 5b). The run out distances of these currents as a function of R ∗ (eqn. (2)) are shown in Fig. 5c with the solid symbols. It is seen that for R ∗ larger than unity, the run-out distance increases beyond the range 9–12 L o , as the lift-off is now limited by the sedimentation. Indeed with small particles, the current travels more than 20L o before lifting off. For values of R ∗ smaller than unity, the current only travels a distance of order (5–8) L o before the particles have sedimented and lift off occurs. This is considerably smaller than the case of mixing-generated buoyancy.

3. Discussion The experimental measurements have some striking implications for the dynamics of dilute pyroclasic density currents arising from short-lived explosions. In observing the evolution of a pyroclastic density current, there may be a spectrum of phenomena: however, two situations can be envisaged which lead to formation of a dilute pyroclastic density current. First, a small explosion may generate a small eruption cloud which mixes with some air, and then collapses and spreads out over the ground (Clarke et al., 2002; Cole et al., 2014) and secondly, an explosive dome collapse event from a pressurised dome may produce a dilute, expanded cloud which then flows over the ground driven by the density contrast with the ambient air (e.g. Woods et al., 2002; Loughlin et al., 2002). As these flows then evolve along the ground, sedimentation may lead to formation of a dense pyroclastic flow at the base (cf. Druitt et al., 2002), while the front of the dilute pyroclastic density current continues to mix with air displaced by the cloud, resulting in lift off near the front of the flow (Fig. 6a). Sedimentation and mixing both act to limit the extent of the dilute cloud from such short-lived explosions. This picture is also consistent with the observations of the flow fronts formed during the eruptions at Mt

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

145

Fig. 6. (a) Schematic illustrating the process of column collapse, entrainment and formation of a dense pyroclastic density current, and the subsequent mixing of air displaced by the head of the flow and sedimentation of coarser grained particles. (b) Pyroclastic density current on 8 January 2010 at Soufriere Hills Volcano, Montserrat (reproduced from Cole et al., 2014, Fig. 5.5b).

Unzen as described by Fujii and Nakada (1999) and, in Fig. 5.5b of Cole et al. (2014) (reproduced here as Fig. 6b), we see a flow formed during an eruption of Soufriere Hills Volcano in which material is lofting upwards just behind the head of the flow.

In order to assess the mass of air required to reduce the buoyancy of the flow and generate lift off, we assume that the density of the ash–air mixture is given by the relation



nR T m

 −1

3.1. Lift-off through mixing Our experiments suggest that all the material is likely to circulate through the head of the flow over a length scale of about 9–12 times the initial scale of the flow. As the material circulates through the head of the flow, our experiments suggest it will mix with a fraction of order 0.6–0.7 of the air displaced by the flow. If this mixing, combined with any sedimentation, reduces the density of the mixed fluid below that of the surrounding air, then the material will be elutriated from the flow, gradually causing the current to wane, and the results from our experiments relating to the run-out distance (Fig. 5c) may be adopted to provide a guide as to the run-out distance of the dilute flow.

where ρs is the density of the ash, n the gas mass fraction in the flow, R the gas constant, T m is the mixture temperature and P the pressure. This model is based on the simplification that the flow is well-mixed, but provides a useful reference for the impact of the mixing on the flow evolution. To calculate the mixture temperature, T m , we assume that on exiting the vent, there is an initial mixing phase, for example associated with a collapsing fountain or a lateral blast (Clarke et al., 2002; Cole et al., 1998). If a fraction f of the clasts are sufficiently small for thermal equilibration during this initial mixing phase, then conservation of thermal energy requires

P

+

1−n

ρ=

ρs

(3)

146

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

Fig. 7. Model of the speed (dashed) and density (solid) of a dilute pyroclastic density current propagating in a 300 m wide valley, with a mass flux of 108 kg as a function of the mass of gas mixed into the flow during the collapsing fountain stage of the flow. Curves are given for the case in which a different fraction of the solid material is in good thermal equilibrium with the air, ranging from 1.0 to 0.25 as shown on the different curves. When the solid lines meet the horizontal dot-dashed line, the flow becomes buoyant.

na C p T a + f (1 − na )C m T m = (na C p + f (1 − na )C m ) T ,

(4)

where na is the mass of entrained air, T a is the temperature of the entrained air, T m is the temperature of the erupting ash and exsolved volatiles, and C a , C m are the specific heats of the air and the erupting mixture. To calculate f , we note that for thermal equilibrium, the thermal diffusion time, which scales as d2 /κ , in terms of the grain size d and the thermal diffusivity κ , should be smaller than the timescale of the initial collapse. The time for an explosion to generate a small cloud of ash and particles which rises several hundred metres above the vent followed by column collapse and generation of a dilute pyroclastic density current, will be of order 10–20 s, given a vent eruption speed of order 100–120 m/s (cf. Cole et al., 2014; Clarke et al., 2002). With a thermal diffusivity of about 2 × 10−7 m2 /s, this will require particles of radius smaller than about 1 mm. Larger clasts will only supply a fraction of their thermal energy, and so f may be estimated from the grain size distribution of the material in the flow: vent explosions which lead to small column collapse events containing a significant mass of fine ash may have f close to unity while dome collapse events, in which there may be more coarser grained material, may have smaller values of f (e.g. Cole et al., 2014). In Fig. 7, we show calculations of the density of the mixture (eqn. (3); solid lines) as a function of the mass of air mixed into the flow, for different fractions of solid in thermal equilibrium with the flow. When the solid lines meet the horizontal dot-dashed line, the flow becomes buoyant. It is seen that a mass of air of order 0.3–0.6 of the mass of solid is required to generate buoyancy and so we infer that mixing of the air displaced by the current into the material circulating over the head of the flow will generate buoyancy and cause elutriation. 3.2. Sedimentation and mixing The mixing imposes a length-scale on the propagation distance of the dilute flow, being of order 9–12 times the initial scale of the flow (Fig. 5c). For example, if a pyroclastic density current produced by a small collapsing fountain has an initial scale of order 300–500 m, typical of many of short lived explosions for example at Soufriere Hills Volcano, Montserrat, then we may expect the material to be elutriated from the flow over a distance of order 3–5 km. In order to assess the balance of mixing and sedimentation in such flow, let us assume that a mass M erupts from the volcano,

and that this forms a dilute pyroclastic density current after an initial adjustment, for example through a collapsing fountain above the vent. If the flow then travels along a valley of width w, the mass of the flow, M, is related to the width w, depth h, and lateral extent L according to

M = λρ whL

(5)

where ρ is the mean density of the flow and λ is a shape factor related to the along current variation in depth, estimated to be of order 0.25–0.3 (see Sher and Woods, 2015). The typical speed of such currents follows from the classical gravity current scaling u = 0.9( g  h)1/2 , where g  is the depth averaged reduced gravity of the current and the local buoyancy g  = g (ρ − ρa )/ρa . In Fig. 7, we present calculations of the initial speed of the flow (dashed lines) corresponding to different fractions of air entrained into the flow, with 4 values of the thermal equilibrium parameter, to complement those of the density. The length scale for sedimentation of particles may then be estimated using the balance L s ∼ uL o / v s where L o is the initial length scale of the flow (cf. Sparks et al., 1993, 1997; Bursik and Woods, 1996). In Fig. 8, we show the sedimentation distance for ash particles of size 1.0 (green), 3.0 (blue) and 10.0 (black) mm for model currents of mass 108 (dotted), 3 × 108 (dashed-dotted) and 5 × 108 (dashed) kg. In each case the variation of the run-out distance is given as a function of the mass of air mixed into the flow during the initial formation of the flow. Curves are shown for the case that a fraction f = 0.5 of the material is in good thermal contact with the air. The sedimentation distance varies with the initial mass of air entrained into the flow, but has values in the range 1–10 km, with the smaller distances corresponding to currents with larger particles or a smaller mass. For this calculation, the initial scale of the flow is 500 m, and so the entrainment distance over which the material in the flow will recycle through the head of the flow is about 5000 m, (cf. Fig. 5c). Comparing this distance (red line on Fig. 8) with the sedimentation distances, we infer that particles in excess of 1–3 mm are likely to sediment from the flow whereas particles smaller than this will be elutriated from the flow. These length-scales and predictions are broadly consistent with observations, which suggest that dilute pyroclastic density currents generated from short lived eruptions dissipate, while in some cases a dense particle-rich layer, composed of material with larger grain sizes may develop at the base. The parameters chosen for the estimates shown in Fig. 8 are typical of the events which occurred at Soufriere Hills, Montserrat

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

147

Fig. 8. Estimate of the sedimentation length of different sized particles in a dilute pyroclastic density current as a function of the gas content of the initial flow. Curves are shown for particles of size 1 mm (green), 3 mm (blue) and 10 mm (black) and for the cases in which the flow has a source mass of 1 × 108 (dotted), 3 × 108 (dash-dotted) and 5 × 108 (dashed) kg of material. The solid red line denotes the distance over which all the material in the flow is expected to cycle through the head of the flow, as observed in the experiments, and hence over which all the material will mix with the air displaced by the flow, leading to generation of buoyancy in the flow. (For interpretation of the colours in this figure, the reader is referred to the web version of this article.)

(Druitt et al., 2002; Clarke et al., 2002), Augustine in 2006 (Coombs et al., 2010), Colima in 2005 (Sulpizio et al., 2014) and Tungurahua (Hall et al., 2015). In each case, the volume of material was in the range of 105 –106 m3 dense rock equivalent and the particles in the final deposits had grain sizes which varied from large clasts, tens of centimetres in scale to smaller fragments of millimetre size (e.g. Cole et al., 2014). In each of these events, the small explosions led to flows which travelled distances typically in the range of 3–6 km. Although the topography of the different volcanoes varies from case to case with the flows migrating along different size valleys, our assumption that the initial width and lateral extent of the flow is 500 m, is similar in magnitude to some of the flows and deposits reported by Ogburn et al. (2014) and Cole et al. (2014) from Soufriere Hills Volcano, Montserrat. We recognise however that for these natural flows there is a considerable possible range of values of current properties. Also, in relating the evolution of the dilute pyroclastic density current produced by a column collapse or explosive dome collapse with our experiments, it is important to recognise the simplicity of our experiments. If the coarser grains sediment from the flow to form a dense basal avalanche (Calder et al., 1997; Druitt et al., 2002) then subsequently some of the air entrained into the head of the flow may become mixed into the lower part of the flow, leading to heating and fluidisation of the particles in the flow. This process, coupled with the continual break up of particles in the flow, may lead to some re-suspension of finer particles into the dilute overlying flow, initially produced during the explosive flow above the vent (Wilson and Walker, 1982; Druitt et al., 2002). Although the fines-laden dilute pyroclastic density current and the denser particle-laden basal flow may be derived from the same source, if the topography is irregular or the pyroclastic density current is sufficiently energetic, it may become decoupled from the dense underlying avalanche flow, as for example occurred at Soufriere Hills, Montserrat when flows travelled along curved valleys and the upper parts of the flow spilled over the banks of channels (Druitt et al., 2002; Ogburn et al., 2014). The subsequent evolution of the dilute pyroclastic density current will be controlled by the balance of sedimentation and mixing of air into the head of the flow, as described in our experiments.

4. Summary A series of new analogue laboratory experiments have been carried out to explore the mixing of air into the head of a pyroclastic density current produced during a short-lived eruption from the collapse of a dense fountain of fragmented ash and pumice. The experiments have identified that there is a strong circulation in the flow so that material continuously reaches the front of the flow. Here, it rises up over the head of the flow and mixes with the air displaced by the advancing flow. Owing to the heating of the entrained air by the hot ash, the density of this mixture typically falls below that of the ambient and the material becomes elutriated from the flow. Our analogue experiments have identified that once the flow has travelled a distance of order 9–12 times the initial scale of the flow, most of the material in the current has circulated through the front and all the material in the flow has become diluted. This mixing process will therefore tend to limit the run-out distance of a dilute pyroclastic density current produced from a short-lived eruption. As the flow evolves and mixes with the air, coarser grained material can sediment from the flow, and in some cases this may lead to formation of a dense avalanche below the dilute pyroclastic density current. Acknowledgements We are very grateful for the careful and thoughtful reviews of Gert Lube and an anonymous referee, as well as the very helpful suggestions of the editor, Tamsin Mather. Appendix A. Supplementary material Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2017.03.009. References Andrews, B.J., Manga, M., 2012. Experimental study of turbulence, sedimentation, and coignimbrite mass partitioning in dilute pyroclastic density currents. J. Volcanol. Geotherm. Res. 225–226, 30–44. Bonnecaze, R.T., Huppert, H.E., Lister, J.R., 1993. Particle-driven gravity currents. J. Fluid Mech. 250, 339–369.

148

D. Sher, A.W. Woods / Earth and Planetary Science Letters 467 (2017) 138–148

Burgisser, A., Bergantz, G.W., Breidenthal, R.E., 2005. Addressing complexity in laboratory experiments: the scaling of dilute multiphase flows in magmatic systems. J. Volcanol. Geotherm. Res. 141, 245–265. Bursik, M., Woods, A.W., 1996. The dynamics and thermodynamics of large ASH flows. Bull. Volcanol. 58, 175–193. Calder, E., Sparks, R.S.J., Woods, A.W., 1997. Dynamics of co-ignimbrite plumes generated from pyroclastic flows of Mount St. Helens (7 August 1980). Bull. Volcanol. 58, 432–440. Calder, E.S., Cole, P.D., Dade, W.B., et al., 1999. Mobility of pyroclastic flows and surges at the Soufriere Hills Volcano, Montserrat. Geophys. Res. Lett. 26, 537–540. Calder, E.S., Sparks, R.S.J., Gardeweg, M., 2000. Erosion, transport and segregation of pumice and lithic clasts in pyroclastic flows inferred from ignimbrite at Lascar Volcano, Chile. J. Volcanol. Geotherm. Res. 104, 201–235. Choux, C.M., Druitt, T.H., 2002. Analogue study of particle segregation in pyroclastic density currents, with implications for the emplacement mechanisms of large ignimbrites. Sedimentology 49 (5), 907–928. Clarke, A., Voiught, B., Neri, A., Macedonia, G., 2002. Transient dynamics of vulcanian explosions and column collapse. Nature 415, 897–901. Cole, P., Calder, E., Druitt, T., Hoblitt, R., Robertson, R., Sparks, R., 1998. Pyroclastic flows generated by gravitational instability of the 1996/97 lava dome of Soufriere Hills Volcano, Montserrat. Geophys. Res. Lett. 25, 3425–3428. Cole, P.D., Smith, P.J., Stinton, A.J., Odbert, H.M., Bernstein, M.L., Komorowski, J.C., Stewarts, R., 2014. Vulcanian explosions at Soufriere Hills Volcano, Montserrat, between 2008 and 2010. In: Wadge, G., Robertson, R., Voight, B. (Eds.), Geol. Soc. Lond., Spec. Publ., The Eruption of Soufriere Hills Volcano, Montserrat from 2000 to 2010. In: Geol. Soc. Lond., Memoirs, vol. 39, pp. 93–111. Coombs, M., Bull, K., Vallance, J., Schneider, D., Thoms, E., Wessels, R., McGimsey, R., 2010. Timing, distribution and volume of proximal products of the 2006 eruptions of Augustine volcano. In: Power, J., Coombs, M., Freymuller, J. (Eds.), The 2006 Eruption of Augustin Volcano, Alaska. In: U. S. Geol. Surv. Prof. Pap., vol. 1769, pp. 145–186. Cronin, S.J., Lube, G., Dayudi, D.S., Sumarti, S., Subrandiyo, S., Surono, 2013. Insights into the October–November 2010 Gunung Merapi eruption (Central Java, Indonesia) from the stratigraphy, volume and characteristics of its pyroclastic deposits. J. Volcanol. Geotherm. Res. 261, 244–259. Dade, B., Huppert, H.E., 1996. Emplacement of the Taupo ignimbrite by a dilute turbulent flow. Nature 381, 509–512. Dellino, P., Zimanowski, B., Buttner, R., La Volpe, L., Mele, D., Sulpizio, R., 2007. Large-scale experiments on the mechanics of pyroclastic flow: design, engineering, and first results. J. Geophys. Res. 112, B04202. http://dx.doi.org/10.1029/ 2006JB004313. Dellino, P., Mele, D., Sulpizio, R., La Volpe, L., Braia, G., 2008. A method for the calculation of the impact parameters of dilute pyroclastic density currents based on deposit particle characteristics. J. Geophys. Res. 113, B07206. http://dx.doi.org/10.1029/2007JB005365. Druitt, T.H., Calder, E.S., Cole, D., Hoblitt, R.P., Loughlin, S.C., Norton, G.E., Ritchie, L.J., Sparks, R.S.J., Voight, B., 2002. Small-volume, highly mobile pyroclastic flows formed by rapid sedimentation from pyroclastic surges at Soufriere Hills Volcano, Montserrat: an important volcanic hazard. In: Druitt, T.H., Kokelaar, B.P. (Eds.), The Eruption of Soufriere Hills Volcano, Montserrat, from 1995 to 1999. In: Geol. Soc. Lond. Mem., vol. 21, pp. 263–279. Dufek, J., 2016. The fluid mechanics of pyroclastic density currents. Annu. Rev. Fluid Mech. 48, 459–485. Fisher, R.V., 1979. Models for pyroclastic surges and pyroclastic flows. J. Volcanol. Geotherm. Res. 6, 305–318. Fujii, T., Nakada, S., 1999. The 15 September 1991 pyroclastic flows at Unzen Volcano Japan, a flow model for associated ash-cloud surges. J. Volcanol. Geotherm. Res. 89, 159–172. Gertisser, R., Cassidy, N., Charbnnier, S., Nuzzo, L., Preece, K., 2012. Overbank block and ash flow deposits and the impact of valley derived flows on populated areas at Merapi volcano, Java, Indonesia. Nat. Hazards 60 (2), 623–649. Hall, M.L., Steele, A., Bernard, B., Mothes, P., Vallejo, S., Douillet, G., Ramon, R., Aguaiza, S., Ruiz, M., 2015. Sequential plug formation, disintegration by vulcanian explosions, and the generation of granular pyroclastic density currents

at Tungurahua Volcano, (2013–2014) Ecuador. J. Volcanol. Geotherm. Res. 306, 90–103. Huppert, H.E., Turner, J.S., Carey, S.N., Sparks, R.S.J., Hallworth, M.A., 1986. A laboratory simulation of pyroclastic flows down slopes. J. Volcanol. Geotherm. Res. 30, 179–199. Ishimine, Y., 2005. Numerical study of pyroclastic surges. J. Volcanol. Geotherm. Res. 139, 33–57. Komorowski, J-C., Jenkins, S., Baxter, P., Picquout, A., Lavigne, F., Charbonnier, S., Gertisser, R., Preece, K., Cholik, N., Budi-Santoso, A., Surono, 2013. Paroxysmal dome explosion during the Merapi 2010 eruption: processes and facies relationships of associated high-energy pyroclastic density currents. J. Volcanol. Geotherm. Res. 261, 260–294. Loughlin, S.C., Calder, E.S., Clarke, A., Cole, P.D., Luckett, R., Mangan, M., Pyle, D., Sparks, R., Voight, B., Watts, R., 2002. Pyroclstic flows and surges generated by the 25 June 1997 dome collapse, Soufriere Hils Volcano, Montserrat. Geol Soc. Memoirs 21, 191–209. Lube, G., Breard, E.C.P., Cronin, S.J., Jones, J., 2015. Synthesizing large-scale pyroclastic flows: experimental design, scaling, and first results from PELE. J. Geophys. Res. 120, 1487–1502. http://dx.doi.org/10.1002/2014JB011666. Ogburn, S.E., Calder, E.S., Cole, P.D., Stinton, A.J., 2014. The effect of topography on ash cloud surge generation and propagation. In: Wadge, G., Robertson, R., Voight, B. (Eds.), The eruption of Soufriere Hills Volcano, Montserrat, from 2000 to 2010. In: Geol. Soc. Lond., Memoirs, vol. 39, pp. 179–194. Samasiri, P., Woods, A.W., 2015. Mixing in axisymmetric gravity currents. J. Fluid Mech. 782, R1. Sher, D., Woods, A.W., 2015. Gravity currents: entrainment, stratification and selfsimilarity. J. Fluid Mech. 784, 130–162. Simpson, J., 1997. Gravity Currents. Camb. Univ. Press. Sparks, R.S.J., Bonnecaze, R., Huppert, H.E., Lister, J., Hallworth, M., Mader, H., 1993. Sediment laden gravity currents with reversing buoyancy. Earth Planet. Sci. Lett. 114 (2–3), 243–257. Sparks, R.S.J., Bursik, M., Carey, S., Gilbert, J., Glaze, L., Sigurdsson, H., Woods, A.W., 1997. Volcanic Plumes. Wiley. Stix, J., 2001. Flow evolution of experimental gravity currents: implications for pyroclastic flows at volcanoes. J. Geol. 109 (3), 381–398. Stix, J., Torres, R.C., Narvaez, L.M., Patricia Cortes, G.J., Raigosa, J.A., Gomez, D.M., Castonguay, R., 1997. A model of vulcanian eruptions at Galeras volcano, Colombia. J. Volcanol. Geotherm. Res. 77, 285–303. Sulpizio, R., Dellino, P., Doronzo, D.M., Sarocchi, D., 2014. Pyroclastic density currents: state of the art and perspectives. J. Volcanol. Geotherm. Res. 283, 36–65. Takahashi, T., Tsujimoto, H., 2000. A mechanical model for Merapi type pyroclastic flow. J. Volcanol. Geotherm. Res. 96, 91–115. Todesco, M., Neri, A., Ongaro, T., Papale, P., Macedonia, G., Santacroce, R., 2002. Pyroclastic flow hazard assessment at Vesuvius by using numerical modelling. I Large scale dynamics. Bull. Volcanol. 64 (3–4), 155–177. Valentine, G.A., Wohletz, K.H., 1989. Numerical models of Plinian eruption columns and pyroclastic flows. J. Geophys. Res. 94, 1867–1887. Wilson, C.J.N., Walker, G.P.L., 1982. Ignimbrite depositional facies: the anatomy of a pyroclastic flow. J. Geol. Soc. Lond. 139, 581–592. Woods, A.W., Bursik, M.I., 1994. A laboratory study of ash flows. J. Geophys. Res. B, Solid Earth Planets 99 (B3), 4375–4394. Woods, A.W., Kienle, J., 1994. The dynamics and thermodynamics of volcanic clouds: theory and observations from the April 15 and April 21, 1990 eruptions of Redoubt Volcano, Alaska. J. Volcanol. Geotherm. Res. 62, 273–299. Woods, A.W., Wohletz, K., 1991. Dimensions and dynamics of coignimbrite eruption columns. Nature 350, 225–227. Woods, A.W., Sparks, R., Ritchie, L., Batey, J., Gladstone, C., Bursik, M., 2002. The explosive decompression of a pressurized lava dome: the December 1997 collapse and explosion of Soufiriere Hills Volcano, Montserrat, from 1995 to 1999. In: Druitt, T., Kokelaar, B. (Eds.), The Eruption of Soufriere Hills Volcano. In: Geol. Soc. Lon. Memoirs, vol. 21, pp. 457–466.