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A new view of the dynamics, stability and longevity of volcanic clouds

Guillaume Carazzo ⁎, A. Mark JellinekEarth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada

a b s t r a c ta r t i c l e i n f o

Article history:Received 20 August 2011Received in revised form 18 January 2012Accepted 21 January 2012Available online xxxx

Editor: P. Shearer

Keywords:explosive volcanismash cloudsettling-driven fingeringlayeringparticle boundary layer

Powerful explosive volcanic eruptions inject ash high into the atmosphere, which spreads to form umbrellaclouds. Identifying key physical processes governing the dynamics, stability and longevity of umbrella cloudsis central to assessing volcanic hazards as well as the nature of volcanic forcings on climate. Here we present aseries of laboratory experiments producing turbulent particle-laden jets and subsequent axisymmetric intru-sive gravity currents into a stratified environment. Our experiments reproduce many of the main dynamicalregimes observed during the formation of an explosive volcanic column, and highlight new dynamics for theumbrella cloud. Theoretical predictions of column collapse from a simple model of a turbulent jet are in goodagreement with experimental observations as well as previous studies. Depending on the flow intensity, thestrength of the initial environmental density stratification and the particle concentration at the source, result-ing umbrella clouds can, however, evolve through a series of new regimes as a result of the dynamics of par-ticle sedimentation within these flows as well as from their bases. Using scaling theory we show that duringcloud spreading, internal sedimentation drives the growth and intermittent overturn of thin, gravitationallyunstable “particle boundary layers” (PBLs) as particle-rich plumes. This PBL-driven convection can have re-markable effects ranging from progressive dilution of clouds to their catastrophic overturn and collapse. Innatural eruptions, whether the dynamics of PBLs play a major role in particle sedimentation depends onthe grain size distribution inside the cloud and on eruption column height. In general, particles larger than~60 μm–1 mm are expected to settle individually, whereas finer particles will accumulate PBLs resulting inthe formation of armless mammatus clouds or dangerous gravity currents at much larger distances fromthe volcanic vent than ever considered before. Such dynamics is apparent in observations of numerousmodern eruptions and is inferred from the deposits of historic and prehistoric eruptions for where thereexist appropriate data. Consideration of the consequences of these phenomena for problems such as volcanichazards to humans and climate change may, thus, be very important in the assessment of future eruptions.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Many explosive volcanic eruptions are characterized by turbulentjets that ultimately deliver dense mixtures of gas and ash into the at-mosphere to an altitude of 20–50 km (Wilson, 1976). During a Plinianeruption the bulk density of these flows is rapidly reduced as a resultof the mechanical entrainment and thermal expansion of cold atmo-sphere (Sparks and Wilson, 1976; Woods, 1988). A major effect ofthis process is that the jet can become less dense than the atmosphereand rise as a buoyant plume to a level of neutral buoyancy (LNB). Atthis altitude, the mixture spreads as a turbulent gravity current, form-ing an umbrella cloud the structure of which is further modified bystratospheric winds and turbulent diffusion (Carey and Sparks,1986; Sparks et al., 1992).

Sedimentation of ash and pumice from these clouds presents a num-ber of potentially severe hazards. Coarse ash and lapilli can cause roof

collapses, or blockages of drinkingwater, waste disposal and power dis-tribution systems, whereas fine and very fine ash can provoke healthproblems (Hornwell, 2007) or major air travel disruptions (Casadevall,1994). The prediction of ash cloud behavior is therefore key to evaluat-ing these classes of hazards as well as well-established climatic impactslinked to these eruptions (e.g., Robock, 2000).

Analyses of pyroclastic deposits and real-time observations sug-gest that most of the volcanic fragments discharged at the vent arestill in suspension when the flow reaches the neutral buoyancy level(e.g., Bonadonna and Phillips, 2003). Sedimentation of the largestpumice and ash fragments is governed by their individual settling ve-locities, whereas particle aggregation is thought to enhance the fall-out of fine ash (Rose and Durant, 2011). The residence time of thecloud mainly thus depends on the total mass and grain-size distribu-tion of the particles injected into the atmosphere (Bursik et al., 1992).

Numerous tephra dispersal models have been developed in order tounderstand various aspects of the transport and deposition of volcanicashes (Bonadonna and Phillips, 2003; Bonadonna et al., 1998; Bursiket al., 1992; Carey and Sparks, 1986; Ernst et al., 1996; Pfeiffer et al.,2005). Despite their different levels of complexity, all these models

Earth and Planetary Science Letters 325–326 (2012) 39–51

⁎ Corresponding author.E-mail address: [email protected] (G. Carazzo).

0012-821X/$ – see front matter © 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2012.01.025

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treat sedimentation by assuming that particle loss is mainly governedby the settling velocity of each particle, which is broadly supported byfield studies and by laboratory experiments (Carey et al., 1988; Ernstet al., 1996; Sparks et al., 1991; Veitch and Woods, 2000).

Recent observations, however, suggest that processes governingsedimentation may be far more spatially complex and time-dependent than inferred from field and modeling studies. In particular,observations of the 1994 Reventador (Chakraborty et al., 2006) and1991 Mount Pinatubo eruptions (Chakraborty et al., 2009) suggestthat the dynamics of volcanic umbrella clouds can be strongly modifiedby large scale gravitational (Rayleigh–Taylor-type) instabilities drivenby processes related to internal particle sedimentation, which willlead invariably to time-dependent sedimentation. Similar buoyancy ef-fects are also observed in a large number of historical eruptions (Fig. 1).These instabilities can take several forms such as relatively large round-edmammatus clouds (Fig. 1A, B andD), particle-richfingers (Fig. 1C), orvery thin ash veils (Hobbs et al., 1991). Several mechanisms have beenproposed to explain these intriguing features (Bonadonna et al., 2002;Durant et al., 2009; Schultz et al., 2006) but their origin remains unclearin particular for mammatus clouds (e.g., Schultz et al., 2006). However,on the basis of Fig. 1 alone, one can expect that the construction of teph-ra fallout deposits should reflect the time- and space-dependent flux ofmaterial from the umbrella. However, interpreting the resulting localheterogeneities in the field in terms of dynamics for the cloud is notstraightforward especially because numerical models cannot be usedat the outcrop scale. To the best of our knowledge the only study toidentify the role of episodic sedimentation from an umbrella cloud isthe field-based work of Branney (1991) who argues that discontinuous“patches” of finely stratified pumice in theWhorneyside tuff result fromepisodic expulsion of dense particle-rich material from umbrella cloud.

The goal of this paper is to investigate whether the enigmatic buoy-ancy effects summarized in Fig. 1 play a major role in the evolution ofthe umbrella cloud as a whole. For this, we present an extensive seriesof novel laboratory experiments simulating particle-laden jets with re-versing buoyancy and capable of forming stable umbrella clouds. Dy-namic scaling laws for dilute multiphase mixtures are used to show

that our experiments are reliable analogs for natural explosive volcaniceruptions. In addition to reproduce buoyant plumes and collapsingfountains, our experiments show that resulting umbrella clouds mayfollow different unexpected dynamical regimes. The conditions leadingto the formation of either a stable plume or a collapsing fountain in ourexperiments are understood with a simple theoretical model of turbu-lent jets. A scaling theory is then used to show that when a stablecloud forms, its long termbehavior is strongly controlled by the internalsedimentation of fine particles into thin, gravitationally unstable “parti-cle boundary layers” (PBLs), which intermittently overturn. Finally, weaddress the key issue of the extent to which the dynamics of these PBLsgovern the stability and longevity of natural volcanic clouds.

Our paper is organized in the following way. Section 2 presentsthe experimental device and the scaling laws used to check that themain processes acting on the dynamics of volcanic plumes are repro-duced in laboratory. Qualitative observations of flows spanning alarge range of conditions are presented in Section 3. In Section 4 wedevelop a theoretical model and a scaling theory to understand thestability of our particle-laden jets and clouds. Implications of thiswork for natural eruptions and limitations linked to our approachare discussed in Section 5. Conclusions and future directions are pre-sented in Section 6.

2. Laboratory experiments and scaling analysis

2.1. Experimental device

The experiments are isothermal and conducted in a 0.8 m hightank with a 1 m!1 m cross-section (Fig. 2A). This tank is first filledwith an aqueous NaCl solution with either a stepwise or linear densi-ty stratification. In most experiments the tank is filled with a 0.2 m-thick basal layer of salt water and an overlying 0.4 m-thick layer offresh water that we introduce carefully to avoid mixing across thedensity interface. We conduct additional and dynamically equivalentexperiments with a continuous linear density stratification constructedusing the double bucket technique (see Section 2.3). At the start of each

Fig. 1. Photographs of large-scale instabilities in volcanic ash-clouds. Gravitational instabilities observed at the base of the umbrella cloud associated with the eruption of (A) MountSaint Helens on 18 May 1980 (photograph by T. Thomson); (B) Mount Augustine on 27 March 1986 (photograph by J. Pezzenti Jr.); (C) Monserrat volcano in September 1997(photograph by C. Bonadonna); (D) Mount Redoubt on 21 April 1990 (photograph by R. J. Clucas).

40 G. Carazzo, A.M. Jellinek / Earth and Planetary Science Letters 325–326 (2012) 39–51

experiment, we inject a well-stirred mixture of fresh water and well-sorted Custer feldspar particles (Fig. 2B) at a fixed rate using a long sy-ringe. This set-up enables us to vary themain source and environmentalconditions that govern flow dynamics: (i) the particlemass, (ii) the vol-umetric flow rate, (iii) the nozzle size, and (iv) the stratification in thetank. To cover the full range of conditions appropriate for natural condi-tionswe vary the particle concentration at the source and the inputflowrate. Table 1 lists the experiments and the conditions imposed at thesource. A typical injection lasts between 1 and 10 min and is character-ized quantitatively with an array of high-resolution video cameras. Fol-lowing the injection, a long time exposure camera records the completeevolution of the suspended particle-laden mixture.

2.2. Scaling laws of dilute multiphase mixtures

The complexity of the dynamics of explosive volcanic plumes raisesthe question of the reliability of our experiment to reproduce naturalphenomena. Here, we present a scaling analysis to ensure that our lab-oratory experiments are a suitable analog for natural eruption plumes.

A number of parameters related to the distinct dynamics of theparticles and the particle–fluid mixture in the jet and the umbrellaare required to scale our experiments. All the variables used are

specified in the Notation section. The subscripts 0 and u are used todistinguish properties at the vent (i.e., source of the jet) and at theLNB directly above the vent (i.e., source of the umbrella), where themixture spreads laterally. We note that since the height of the LNBand related properties are controlled by environmental and sourceconditions for the jet (Morton et al., 1956), scales for the cloud are ul-timately imposed by the source conditions for the jet.

The Reynolds number (Re) quantifies the importance of inertialforces and turbulent stirring in the flow of the particle–fluid mixture,

Re !VLν

; "1#

where V and L are the characteristic velocity and length scales for theflow and ν is the kinematic viscosity of the mixture. For the verticaljet, the characteristic velocity and length scales are the exit velocityU0=Q0/πR02 and the vent radius R0, respectively, with Q0 the inputflow rate. For the umbrella cloud, the characteristic length and veloc-ity scales are the overshoot height hos=zm!zb and the lateralspreading rate Wu !

!!!!!!!!!!!!!!hosg ′m

p, where zm and zb are the maximum

and neutral buoyancy heights, respectively. Here g′m=g[(ρ!ρa)/ρa]z= zm is the reduced gravity of the jet at the maximum height zm,

Fig. 2. (A) Sketch of the experimental device. The nozzle is a straight pipe with a 6.35 mm diameter. (B) Cumulative grain size distribution of the Custer feldspar particles. Particleswere sieved at 0.5ϕ interval and both the mean and the median grain sizes are found to be +1.75ϕ corresponding to a particle diameter of 300 μm. The sorting (+0.21ϕ), skewness(0.03) and kurtosis (1.02) coefficients show that the particles used are very well sorted with a grain size distribution narrowly centered on the median value. Particle density wasdetermined by measuring individual particle settling velocities (ρp=2600 kg m!3).

Table 1Experimental conditions imposed at the source. Regime: FG: fingering; LY: layering; LC: late collapse; PC: partial collapse; TC: total collapse. *: linear stratification experiment (seeFig. 3D).

Exp. !p0(!)

ρ0(kg m!3)

Q0

(m3 s!1)M0

(m4 s!2)F0(m4 s!3)

Fu(m4 s!3)

!puRegime

3 2.0!10!2 1029.7 1.7!10!5 8.8!10!6 !3.5!10!6 !5.2!10!6 1.1!10!3 FG6 2.0!10!2 1029.7 1.1!10!5 3.9!10!6 !2.3!10!6 !3.4!10!6 7.4!10!4 FG7 2.0!10!2 1029.7 4.1!10!5 5.3!10!5 !8.6!10!6 !1.3!10!5 1.8!10!3 LY8 4.1!10!2 1063.5 4.1!10!5 5.3!10!5 !2.2!10!5 !2.6!10!5 4.2!10!3 LY13 6.3!10!2 1099.6 4.1!10!5 5.3!10!5 !3.6!10!5 !4.1!10!5 6.4!10!3 LC14 9.7!10!3 1013.6 4.1!10!5 5.3!10!5 !2.2!10!6 !6.3!10!6 8.5!10!4 LY15 9.7!10!3 1013.6 1.1!10!5 3.9!10!6 !6.0!10!7 !1.7!10!6 3.1!10!4 FG16 6.3!10!2 1099.6 1.1!10!5 3.9!10!6 !9.8!10!6 – – TC17 4.1!10!2 1063.5 1.1!10!5 3.9!10!6 !6.0!10!6 – – PC18 9.7!10!3 1013.6 2.6!10!5 2.1!10!5 !1.4!10!6 !4.0!10!6 6.9!10!4 LY19 4.1!10!2 1063.5 2.6!10!5 2.1!10!5 !1.4!10!5 !1.7!10!5 4.3!10!3 LC20 5.2!10!2 1081.3 2.6!10!5 2.1!10!5 !1.8!10!5 !2.1!10!5 6.2!10!3 LC21 6.3!10!2 1099.6 2.6!10!5 2.1!10!5 !2.3!10!5 – – PC22 8.8!10!2 1138.3 2.6!10!5 2.1!10!5 !3.3!10!5 – – TC24 9.7!10!3 1013.6 2.6!10!5 2.1!10!5 !1.4!10!6 !4.0!10!6 6.9!10!4 LY25 3.2!10!2 1049.7 4.1!10!5 5.3!10!5 !1.7!10!5 !2.1!10!5 3.1!10!3 LY26⁎ 9.7!10!3 1013.6 2.6!10!5 2.1!10!5 !1.4!10!6 !4.0!10!6 6.9!10!4 LY

41G. Carazzo, A.M. Jellinek / Earth and Planetary Science Letters 325–326 (2012) 39–51

with g the acceleration of gravity, ρa the density of the ambient fluidand ρ the density of the particle–fluid mixture, which is given at anyheight by

ρ ! !pρp $ 1!!p

" #ρf ; "2#

where !p is the particle volume fraction, and ρp and ρf are the particleand fluid densities, respectively.

The evolution of a jet depends strongly on its density, which isgoverned by turbulent entrainment across the stabilizing density in-terface that defines its sides. To characterize the balance betweenthe stabilizing buoyancy and driving inertial forces governing the dy-namics of entrainment and mixing, we use a Richardson number (Ri):

Ri ! ! g ′LV2 : "3#

For the jet, L=R0, V=U0 and g′=g[(ρ!ρa)/ρa]0. Entrainmentand mixing are enhanced where !Rib1, the jet will rise as a plumewhere Ri>0 and can potentially collapse as a fountain where Rib0.

To characterize the balance between the buoyancy and additionalviscous forces governing the convection driven by the dynamics ofthin particle boundary layers at the cloud base we define a Grashofnumber (Gr):

Gr ! g ′L3

ν2 ! Ri Re2; "4#

where L=hos and g′=g′m for the umbrella cloud.In dilute mixtures, particle–particle interactions are negligible but

themechanical coupling between particles and the fluid phase is com-plex. The two-way stress coupling between the phases can be charac-terized by two dimensionless numbers. The Stokes number (St) is aratio of the time scale for the inertial response of particles τp to thetime scale for flow of the continuous phase τf and is defined as

St !τpτf

! 1fρpd

2p

18 μVL: "5#

This parameter measures the tendency of particles to stay coupledto turbulent motions. Here, f is a drag factor, dp is the particle diame-ter (or effective particle diameter for non-spherical particles (cf.,Pfeiffer et al., 2005)), and μ=νρf is the dynamic viscosity of thefluid phase. f can be related to the particle Reynolds number Rep(Burgisser et al., 2005),

f ! 1$ 0:15Rep0:687 $ 0:0175

1$ 42;500Rep!1:16 ; "6#

where

Rep !Vsdpν

; "7#

with Vs=τpg the particle terminal fall velocity. Where St>1 particlesdecouple from the fluid phase and enhance turbulence by momentumtransfer during their motion and fallout, whereas for Stb1 particles re-main coupled to eddies and reduce turbulence intensity (Elghobashi,1994).

The tendency for dense particles to remain in suspension in a tur-bulent flow is expressed with an additional sedimentation number(Σ), which is a ratio of the inertial response time of a particle τp tothe time scale for its sedimentation τg,

Σ !τpτg

! 1fρpd

2p

18 μgV! Vs

V: "8#

Thus, particle settling is enhanced for Σ>1 and inhibited for Σb1.In the framework of a turbulent jet, V=U0 and Σ indicates whetherparticles settle (Σ>1), rise (Σb1) or are neutrally buoyant (Σ=1).In the framework of an umbrella cloud, V=Wu and Σ indicates theextent to which particles settle (Σ>1) or are carried laterally (Σb1).

The Stokes and sedimentation numbers completely characterizethe behavior of particles within the jet and umbrella. For Stb1 andΣb1 particles are coupled with the fluid phase and efficiently mixedby larger eddies. This regime favors the transport and dispersion ofthe solid fraction into the environment. For St>1 and Σ>1 particlesare decoupled from the continuous phase and either settle or are ex-pelled from the flow. Intermediate configurations where St"1 andΣ"1, or Stb1 and Σ>1, or St>1 and Σb1 correspond to a thirdclass where a strong two-way coupling between fluid and particlesexists. In this regime, transient segregations of particles lead to parti-cle gathering in zones of least velocity gradient and a possible forma-tion of mesoscale structures (Agrawal et al., 2001; Burgisser et al.,2005).

2.3. Comparison between experiments and volcanic clouds

The values of the dimensionless numbers discussed above are cal-culated in our experiments and for natural volcanic clouds (Fig. 3A toC and Table 2). We note that the Reynolds numbers for explosiveeruptions vary in the range 107#Re0#109 for the vertical jet and107#Reu#1010 for the umbrella cloud. Such extreme Re are unap-proachable at the laboratory scale, although our flows are at high-Re, fully turbulent and conducted under Re conditions comparableto many published studies (e.g., Burgisser et al., 2005).

Fig. 3A shows that our experimental range of !p0is consistent with

natural flows, which implies that the degree of dilution at the sourceis well reproduced. In addition, our laboratory experiments yieldvalues of Richardson number partially within the natural range atthe base of volcanic jets. This agreement suggests that the balance be-tween the stabilizing buoyancy and driving inertial forces is also wellreproduced in our experiments.

Fig. 3B shows that our experimental range of particle volume frac-tion at LNB is significantly different to that for the natural case. Thisdifference is a consequence of the limitation imposed by the heightof the tank, which controls the maximum possible dilution by turbu-lent entrainment of salt water. Whereas explosive volcanic jets en-train atmospheric air over a few tens kilometers reducing particleconcentration by several orders of magnitude, our small scale jets en-train salt water over a few tens centimeters reducing !p0

by only oneorder of magnitude. An additional remark is the significant differencebetween the values of the Grashof number yielded in our experi-ments to that for the natural case. We note, however, that in bothcases Gr>103.

Fig. 3C shows that our experimental values of the Stokes and sed-imentation numbers fall within the wide range covered by the naturalsystems. St and Σ change by several orders of magnitude from the jetto the umbrella cloud (Fig. 3 C). Above the nozzle, particles have St"1and Σb1, which suggests that particles have no effect on the develop-ment of turbulence and that no sedimentation should occur from thejet. On the other hand, particles have Stbb1 and Σ>1 in the umbrellacloud. This suggests that particles are well mixed into the umbrellacloud, although they tend to settle rather than being dispersedlaterally.

Another key parameter controlling the flow dynamics is thestrength of the environmental stratification. The quasi-linear densitygradient observed in nature is reproduced in our experiment with asingle density interface for the sake of simplicity. This technique hasbeen applied successfully in a number of studies (Fan, 1967; Hart,1961; Kotsovinos, 2000) and does not affect the plume dynamics aslong as the scaling for the strength of the stratification is the sameas the strength of a linear density stratification (Morton et al., 1956;


Turner, 1973). This condition is verified by using the Brunt–Väisäläfrequency (N) defined as

N2 ! ! gρr

dρa

dz; "9#

where ρr is a reference density. Fig. 3D shows a direct comparison ofcolumn height between an experiment with two layers and anotherwith a linear density gradient. Our comparison confirms that(i) both types of experiment are quantitatively identical, and (ii) theneutral buoyancy height is not imposed at the interface betweenthe two layers. In the terrestrial atmosphere, the Brunt–Väisälä fre-quency is in the order of 0.01 s!1, whereas for all our experimentsN is in the order of 0.1 s!1. This difference is imposed for technicalreasons because N partially controls the maximum column height.In turn, the stratification imposed allows to reproduce geometrical as-pect ratios observed in natural eruptions (i.e. zb/zm"0.7 and zm/R0"102).

Finally, we note that contrary to natural explosive volcanic erup-tions, only isothermal plumes are produced in our experiments. Al-though variations in initial temperature may affect the plumedynamics, its effect on the flow development is relatively weak com-pared to other dynamical quantities such as the initial gas content,exit velocity and vent radius (Woods, 1988). At the LNB, the plumetemperature is imposed by surrounding environmental conditionsas a result of intense mixing with the atmosphere during the columnrise (Holasek et al., 1996). Therefore, the effect of source temperature

on conditions across the LNB is negligible and our isothermal assump-tion does not affect the quantitative conclusions presented in thisstudy.

Fig. 3. (A to C) Scaling analysis. Hot colors correspond to the range of values at the base of natural jets (orange) and in our experiments (red), whereas cold colors give the values atthe origin of natural umbrella clouds (green) and in our experiments (blue). Dashed lines correspond to critical values discussed in the text. (D) Comparison of column height (incm) as a function of time (in s) for two experiments made at N2=0.38s!2 with a linear stratification (red curve) and a single density interface (blue curve).

Table 2Common ranges of the dynamic variables in volcanic eruptions compared with those inour experiments.

Variable [Units] Experiments Volcanic eruptions

dp [m] 3!10!4 10!6–10!2

hos [m] 5!10!2–2!10!1 103–8!103

zm [m] 0.1–0.4 5!103–4!104

zm/R0 30–130 25–800zb/zm 0.5–0.75 0.7N [s!1] 0.487 0.035R0 [m] 3.175!10!3 50–200U0 [m s!1] 0.3–1.3 150–500Vs [m s!1] 7!10!2 0.5–150Wu [m s!1] 5!10!3–2.5!102 50–150Ww [m s!1] 0 0–60!po

10!3–10!1 7.5!10!4–10!1

!ppbl10!3–10!1 10!6–10!4

!pu7!10!4–7!10!3 10!6–10!5

μ [kgm!1 s!1] 10–3 3!10!5

ρa [kgm!3] 998–1008 10!3–1ρf [kgm!3] 998 0.1–1ρp [kgm!3] 2600 750–2500Gru 106–3!107 1015–7!1020

Re0 950–4100 107–109

Rep 20 10!4–106


3. Qualitative observations

Our experiments investigate the different phenomena that occuras we vary both the initial volumetric flow rate and the particle vol-ume fraction. For low particle concentrations and relatively highflow rates, the mixture of solid particles and fresh water mixes rapid-ly with the ambient salt water layer (Fig. 4). Although the particle-laden jet is denser than the surrounding fluid at the source, its densitydecreases as a result of turbulent entrainment and dilution to valueslower than the ambient density. Resultant buoyancy forces augmentthe momentum flux imparted at the source to drive the plume to aLNB, which it initially overshoots to a height that depends on its mo-mentum and the strength of the stratification, before collapsing backto the LNB as a fountain to drive a gravity current laterally, forming anumbrella. This behavior is shown in Fig. 4A (“stable plume”) and is apopular analog for the formation of a Plinian column (Wilson, 1976).

For intermediate particle concentrations and moderate flow rates,there is less entrainment and mixing of the ambient fluid. The flowseparates into a buoyant plume with a low particle concentrationand a dense fountain with a high particle concentration. In general,whereas the buoyant plume impinges and spreads along the densityinterface in the tank as an intrusion, the collapsing part generates aradially symmetric turbulent gravity current at the tank base. This be-havior is shown in Fig. 4A (“partial collapse”) and corresponds to ex-plosive volcanic eruptions in the transitional regime (Di Muro et al.,2004).

For high particle concentrations and relatively low flow rates,there is little entrainment and mixing and the mixture injected re-mains too dense to undergo a buoyancy inversion. The flow collapseson itself when its initial momentum is exhausted and forms a turbu-lent fountain feeding a radial gravity current at the bottom of thetank. This behavior is shown in Fig. 4A (“total collapse”) and is an

analog to a volcanic collapsing fountain with associated pyroclasticdensity currents (Sparks and Wilson, 1976).

These three dynamical regimes have already been observed inprevious laboratory studies of turbulent particle-laden jets (Carey etal., 1988; Sparks et al., 1991; Veitch and Woods, 2000) and jets withreversing buoyancy (Kaminski et al., 2005; Woods and Caulfield,1992). These behaviors have also been inferred from field observa-tions of past eruptions (Sparks andWalker, 1977), and are also repro-duced in numerical simulations of explosive volcanic eruptions (DiMuro et al., 2004; Suzuki et al., 2005; Valentine and Wohletz, 1989).A remarkable new finding, however, is the dynamic and highlytime-dependent nature of the evolution of umbrella clouds in the sta-ble plume regime (Fig. 4B).

For source conditions close to the partial collapse regime, the sta-ble plume forms an umbrella cloud but gravitational instabilities de-velop in the near field of the cloud where particles are moreconcentrated. Ultimately, these instabilities lead to a collapse fromthe neutral buoyancy height to the tank base with an associated grav-ity current, from which phoenix clouds may emerge (Fig. 4B andMovie 1). To our knowledge, this “late collapse” regime has notbeen observed in previous laboratory studies involving turbulentparticle-laden jets.

At lower particle concentrations, we observe two different re-gimes, depending on the injection rate. At relatively low injectionrates, the particle-laden plume overshoots the density interface inthe tank and falls back rapidly forming an umbrella cloud. The cloudpropagates slowly along the neutral buoyancy height producing littlemixing across the density interface. A fewminutes after spreading be-gins, a dense particle-rich boundary layer (PBL) forms by steady accu-mulation of particles. The growth of this particle boundary layer atcloud base is accompanied by a vertical oscillation that grows in am-plitude until the PBL becomes sufficiently thick to detach and descend

Fig. 4. Photographs of the laboratory experiments showing the different types of behavior observed as the volume flux and particle content were changed. (A) The three regimesobserved for the jet: “stable plume” (top—exp. 24), “partial collapse” (middle—exp. 17), and “total collapse” (bottom—exp. 22). Symbols at the top left corner correspond to thesymbols used in Fig. 5. (B) Evolution of the umbrella cloud in the stable plume regime; (i) the “layering” regime is characterized by the formation of layers (right—exp. 8) andthin, long, and slow fingers at the cloud base (left—exp. 25); (ii) the “settling-driven fingering” regime is characterized by a dense basal particle boundary layer (left—exp. 6),which may become sufficiently thick to detach and descend as large dense particle-rich fingers (right—exp. 3); (iii) the “late collapse” regime is characterized by the growth ofa gravitational instability in the near field of the cloud (left—exp. 20) leading to a final collapse with an associated gravity current. “Phoenix clouds” may form if the currentmixes efficiently with salt water (right—exp. 19). Note the different scales.


as large dense particle-rich fingers (Fig. 4B and Movie 2). Whereparticle-laden downwellings reach the bottom of the tank entrainedfresh water is expelled upward, driving large-scale convective flow,in turn. This “settling-driven fingering” regime has similarities withparticle-rich fingers observed in the experiments of Cardoso andZarrebini (2001).

At larger flow injection rates, the plume significantly overshootsthe density interface and falls back, resulting in extensive mixingacross the density interface. A resulting thick umbrella spreads andno oscillation is observed. Gradually, however, the umbrella breaksup into discrete (light brown) particle-laden layers separated by rel-atively thin (dark) water-rich layers a few tens of minutes after itsemplacement. A particle boundary layer forms at the base of the um-brella and the loss of particles is driven by slow settling of individualparticles within long fingers descending from the particle boundarylayer (Fig. 4B and Movie 3). In common with the fingering regime,large-scale convection starts when particle-rich fingers reach the bot-tom of the tank. However, complete particle sedimentation in thelayering regime takes one to two orders of magnitude longer thanin the fingering regime. This “layering” regime has not been observedin previous laboratory experiments simulating a volcanic ash-cloud.

4. Theory

The results presented above suggest our 300 μm-particles do notsettle individually from the cloud, but instead behave collectively andform PBLs leading to either settling-driven fingering, layering or latecollapse. To characterize the mechanisms controlling the formation ofthese PBLs and subsequent fingers, we compare our experimental re-sults with theory. Identifying the conditions in the cloud prior to PBLsformation is challenging in our experimental configuration since theconditions imposed at the nozzle are strongly modified during the jetrise. To build understanding we characterize the jet dynamics and themechanics of PBL and finger formation, in turn. Next, we address thecombined effects of these processes on the residence times of sus-pended particles and, thus, the residence time of the cloud.

4.1. Formation of a stable plume

The formation of a stable plume as opposed to a collapsing foun-tain has been extensively studied in the context of explosive volcaniceruptions as it is of crucial importance for hazard assessment(Carazzo et al., 2008a; Suzuki et al., 2005; Valentine and Wohletz,1989; Wilson et al., 1980). Here, we use our experimental data onthe onset of column collapse to constrain a simple 1D model basedon a “top-hat” formalism (see Appendix A).

Our model predicts column collapse in a way consistent with ourexperimental results (Fig. 5). We note that when partial collapse oc-curs, the top-hat formalism does not apply because the jet is not insteady state. Thus, we put partial collapse in the collapsing regime.An additional observation from Fig. 5 is that the transition from thelayering to the settling-driven fingering and late collapse regimes isobserved for a critical Richardson number at the vent of !4!10!4.Because low-Ri0 jets tend to reach greater heights in the tank thanhigh-Ri0 jets and thus promote turbulent mixing at the salt/freshwater interface when falling back from the maximum to the neutralbuoyancy heights, this result suggests that the evolution of thecloud depends strongly on the density gradient produced as a resultof mixing across the initial density interface.

The good agreement between theoretical predictions and our exper-imental results suggests that the simple top-hat formalism captures theessential dynamics of our multi-phase jets. Consequently, this modelcan be used to calculate the key dynamical quantities at the neutralbuoyancy height, which impose the conditions in the cloud.

4.2. Formation of particle boundary layers

Themajor qualitative features of the settling-driven fingering and thelayering regimes are analogous to those observed in sedimentation-driven convection (Hoyal et al., 1999b; Kerr, 1991) and in diffusiveconvection in particle-heat systems (Green, 1987; Hoyal et al., 1999a).The periodic structure of the layered clouds issuing from low-Ri0 jetshas also been observed in numerous past volcanic clouds including the2010 Eyjafjallajökull eruption (Dacre et al., 2011; Folch et al., 2012).Whereas wind shear effects have been suggested to explain the forma-tion of these thin ash layers, our experiments show that layering mayeven occur in the absence of wind, which suggests that an importantmechanism is missing in our understanding of this phenomenon. Thefull characterization of our layering regime and its implications for theinterpretation of ash concentration measurements will be addressed ingreater detail in a future study. Here, we focus on the formation ofPBLs in clouds issuing from high-Ri0 jets.

To quantify the tendency of the cloud to form a particle-rich layerat its base, we introduce the dimensionless number B such as (Marsh,1988),

B ! Vi

Vs; "10#

where Vi is the growth rate of the gravitational instability given by(Whitehead and Luther, 1975),

Vi !Δρigδ

2pbl

3 μ; "11#

where δpbl is the thickness of the PBL, and Δρi=ρpbl!ρa, with ρpbland ρa the PBL and salt water densities, respectively. The B numbercharacterizes the preferential mode of sedimentation. Where Bb1 in-dividual particle settling dominates, whereas where B>1 PBL forma-tion is enhanced. The effective density of the particle boundary layer(ρpbl) is not straightforward to estimate a priori for two reasons:(i) the time-averaged particle concentration within the PBL (!ppbl

) isnot a simple function of the source conditions, but depends also onthe dynamics of umbrella spreading; and (ii) the concentration ofparticles increases with depth across the PBL. However, the effectiveamount of particles in the PBL can be approximated using the particleconcentration in the entire cloud (!pu

) calculated using our model ofturbulent jets (Table 1). Since PBL is much thinner than the jet is

Fig. 5. Regime diagram illustrating the imposed negative Richardson number at thenozzle (!Ri0) as a function of the source particle volume fraction (!p0

) for all theexperiments reported in Table 1. Open diamonds: stable plume in the fingering re-gime; open circles: stable plume in the layering regime; open squares: stable plumein the late collapse regime; gray squares: partial collapse regime; solid squares: totalcollapse regime. Dashed line gives the theoretical plume/fountain transition calculatedwith the model presented in Appendix.


wide at the LNB, conservation of volume requires that particle con-centration in the PBL can be as much as 10 times bigger on average(i.e., !ppbl

=1!6!10!2). Replacing these values in Eq. (10) togetherwith Vs=0.07 m s!1 and δpbl$0.5!1 cm as observed in our exper-iments, we calculate B$10!400. In our experimental configuration,PBLs are therefore likely to form before particles settle individually.

4.3. Finger formation

Particle-laden fingers observed in our experiment are likely to re-sult from the growth and intermittent detachment of the PBL at thecloud base. To confirm this hypothesis, we use the simple conceptualmodel developed by Hoyal et al. (1999b) on the basis of well-established theory for turbulent thermal convection (Howard, 1964;Turner, 1973).

Assuming that mass transfer is independent of the layer depth(Howard, 1964; Turner, 1973) and thus governed by processes localto the boundary layer, the critical conditions for finger formationare defined by a local Grashof number,

Grpbl !g′pblδ

3pbl

ν2pbl

> 103; "12#

where νpbl is the effective kinematic viscosity of the particle boundarylayer, and g′pbl=g(ρpbl!ρa)/ρa is the reduced gravity of the PBL. Theeffective kinematic viscosity of the PBL can be approximated by usingthe Einstein–Roscoe formula,

νpbl ! νa 1!Γ" #!2:5; "13#

where νa is the kinematic viscosity of the salt water and Γ=!p0/!pmax

isan effective particle concentration, with !p0

the concentration at thesource and !pmax

the effective maximum concentration determinedfrom our experiments ("0.1). Applying this approximation, the vis-cosity ratio νpbl/νa is in the range of 1.3–16 for our experiments. Wenote that no turbulent motions are observed within the PBL consis-tent with earlier analyses of turbulent Rayleigh–Taylor instabilities(Linden and Redondo, 1991).

Applying the critical Grashof number definition (Eq. 12), the crit-ically unstable PBL will have a thickness that scales as

δpbl"10ν2pbl

g′pbl

" #1=3

; "14#

which has been quantitatively tested in previous laboratory experi-ments (Hoyal et al., 1999b). This relationship suggests that settling-driven fingering can always form if the particle concentration in thePBL (!ppbl

) remains large enough while the PBL grows to the criticalthickness. This condition implies that most particles do not settle in-dividually through the cloud/salt water interface (i.e., B>1), which isthe case in our experiments.

To determine whether or not the growth and destabilization ofPBLs lead to fingers formation, we analyze oscillations at the base ofthe cloud. Indeed, in settling-driven fingering systems, the verticalextent of the fingers depends on the slow diffusion of salt, which en-hances their buoyancy, and the sedimentation of particles from theirends, which reduces their buoyancy relatively more rapidly. The lossof buoyancy causes a descending finger to slow and then rise back to-wards the base of the cloud, where it overshoots the LNB and excitesan oscillation at the base of the entire umbrella. Since the thickeningof the PBL is controlled by the flux of particles entering into the layer,we expect that,

δ3pbl"TmaxQpbl; "15#

where Tmax is the longest measured period of umbrella oscillation,and Qpbl is the flux of particles. Here, Qpbl is taken to be proportionalto the flux of material cascading from the top of the jet when theflow falls back from its maximum height to the neutral buoyancyheight. Therefore, Qpbl scales as Am(g ′ zmhos)

1/2, with Am and g ′ zm thesurface area and reduced gravity of the jet at the maximum height,which can be calculated from the source conditions using our modelof jets (Appendix A). The longest period of cloud oscillation (Tmax) iscalculated using measurements of the displacement of the cloud/saltwater interface (Fig. 6A). These measurements are performedtwice for each experiment at different locations along the distancefrom the source providing a 95% confidence level. The longest peri-od of cloud oscillations is then determined from spectral analysisusing the method of Welch, 1967 and a Thompson multitaperalgorithm.

Fig. 6B shows that Eq. (15) is verified suggesting that oscillationsand fingering instabilities result from the growth and destabilizationof PBLs at the cloud bases. An additional remark is that quasi-periodic oscillatory behavior driven by convective PBL dynamics isnot ubiquitous. In particular, for higher values of TmaxQpbl initial oscil-lations grew rapidly in amplitude (Fig. 6A), leading, in turn, to a latecollapse of the entire umbrella cloud and the formation of a turbulentgravity current. This observation suggests that a further analysis ofthe stability of the PBL could lead to a prediction for this catastrophiccollapse.

Fig. 6. (A) Measurements of interface displacement as a function of time for twoexperiments in the layering regime (dotted curve) and in the late collapse regime(solid curve). (B) Comparison between the estimated critical thickness of the particleboundary layer (δpbl defined on the sketch) and the longest period of the oscillationsobserved. Each symbol corresponds to one experiment reported in Fig. 4.


4.4. Impact on the residence times

The new PBL dynamics identified in our experiments raise thequestion of the residence time of suspended material in the cloud.To quantify this effect, we introduce the dimensionless number Tsuch as

T !Tf

Ts; "16#

where Ts=H/Vs and Tf=H/Vf are the residence times when individualparticle settling and when PBL dynamics dominates, respectively.Here, Vf=g′pbl

2/5Qf1/5 is the characteristic velocity of flow into the

resulting fingers with Qf=πVsδpbl2 /4 the corresponding volume fluxinto the fingers. Replacing variables in Eq. (16) together withEq. (14), one can re-write T,

T$ 0:42 V4=5s

g′pblνpbl

h i4=15 : "17#

Replacing the parameters in this equation with consistent values,we estimate T$0.5!2 suggesting that particle-rich fingers at thebase of the cloud may either promote or impede particle sedimenta-tion in our experiments depending on the effective particle contentin the PBL. We note that in spite of the uncertainties on !ppbl

, this resultcorresponds to finger velocities Vf$3!14 cm s!1 consistent withour observations (Movies 1 & 2).

5. Implications for volcanic ash-clouds

We have shown that large-scale gravitational instabilities at thecloud bases can arise in our experiments as a result of the growthand intermittent overturn of thin PBLs formation. Our experimentalresults are well understood with a theoretical model for the jet anda scaling theory for the cloud. The scaling analysis presented inSection 2.2 suggests that our experimental multiphase flows are reli-able analog for the transport and sedimentation of fine (low St) volca-nic ash in the atmosphere. Thus, we now investigate whether or notPBLs formation influence the behavior of volcanic clouds and can ex-plain the intriguing features shown in Fig. 1.

5.1. Particle boundary layers in volcanic clouds

To quantify the tendency of volcanic clouds to form PBLs at theirbase, we use the B number introduced in Section 4.2 (Eq. 10). In vol-canic ash-clouds, however, particle settling velocities vary from largeparticles falling at high Reynolds number to small particles falling atlow Reynolds number. Using the formulae of Bonadonna et al., 1998for Vs valid for a range of particle Reynolds number leads to three for-mulations for B:

Blow$6Δρi

ρp

δ2pbld2p

for Repb0:4; "18#

Bint$7541=3

Δρiρ1=3a

ρ2=3p

δ2pblg1=2

μ2=3dpfor 0:4bRepb500; "19#

Bhigh$13Δρiρ

1=2a

ρ1=2p

δ2pblg1=2

μd1=2p

for Rep > 500: "20#

Replacing δpbl with Eq. (14) and assuming that ρf"ρa leads to a ge-neric form for B appropriate over the full range of Rep conditions:

B$kξ1=3pblρaν

2a

ρpgd3p

" #n=3

; "21#

where ξpbl=!ppbl/(1!Γ)10, k is a geometric constant and n is a con-

stant that depends on the form of the drag law. For high-Rep particles,k=33 and n=1/2, whereas k=128 and n=1 for intermediate-Repparticles, and k=600 and n=2 for low-Rep particles.

Inspection of Eq. (21) indicates that B is governed primarily byparticle size (dp) and is relatively insensitive to the particle volumefraction (!ppbl

) over the range in Rep. The latter quantity is not straight-forward to evaluate without measurements of oscillation frequency atvolcanic cloud bases. Here, we assume that particle concentrations inthe PBL lie within the maximum range of values for the entire cloud(!pu

) and up to ten times more concentrated, consistent with our ex-periments. Particle concentrations in the cloud are found to be!pu

$10!6!10!5 using the model Carazzo et al. (2008b) for varioussource and environmental conditions including gas contents at thevent ranging from 7.5!10!4 to 10!2 vol% (Table 2). This range ofvalues for !pu

is found to be fully consistent with previous theoreticalcalculations (Sparks et al., 1994; Woods, 1995) and direct measure-ments in ash clouds (Bursik et al., 1994). Thus, we retain!ppbl

=10!6!10!4 as a reasonable range for particle concentrationin the PBL.

Fig. 7 shows the expected transitional conditions (B=1) over awide range of particle sizes, densities, cloud altitudes, and for thefull range of observed Rep conditions. Estimations of B for high-Repparticles show that not surprisingly large particles (typically >1!6 mm) always settle individually (Fig. 7A). On the other hand, thesedimentation of low-Rep particles is expected to be governed byPBL dynamics (Fig. 7C). Lastly, intermediate-Rep particles are likelyto either settle individually or to form PBLs depending on the effectiveparticle concentration (Fig. 7B).

5.2. Comparison with natural data

The analysis presented above shows that the mode of particle sed-imentation in volcanic ash-clouds is mainly governed by the grainsize distribution and to a lesser extent by the altitude reached intothe atmosphere. With an aim of testing the theoretical predictionswith field observations, we reviewed data available on 16 eruptionphases including phreatomagmatic, Vulcanian and Plinian events(Fig. 8). We use total grain size distributions to determine a meanvalue and a sorting coefficient for error estimations. The cloud alti-tude is estimated by using the empirical relationship zb"0.7zm,where the maximum column height zm is inferred from satellite mea-surements (Carey et al., 1990; Holasek et al., 1996) or from the distri-bution of lithic material in the deposits around the vent (Carey andSparks, 1986).

Fig. 8 compares the collected field observations with the theoreti-cal transition B=1. Because low-Rep particles always tend to formPBLs (Fig. 7C), whereas high-Rep particles always tend to settle indi-vidually (Fig. 7A), the only relevant curves for Fig. 8 are those givenin Fig. 7B for intermediate Rep particles. We note, however, that forthe lowest !ppbl

considered, all intermediate-Rep particles should settleindividually (Fig. 7B). For this specific condition (!ppbl

=10!6), thetransition B=1 is simply given by the low-/intermediate-Rep transi-tion (Fig. 8).

The comparison between theoretical predictions and field datashows that depending on the effective amount of particles in thePBL, particles larger than 63!125 μm at sea level and 250 μm!1 mm in high atmosphere should settle individually, whereas finerparticles are more likely to settle collectively and to form PBLs. In


the majority of the Vulcanian and Plinian eruptions shown in Fig. 8sedimentation is expected to be governed by individual particle set-tling, as assumed in turbulent suspension models (Bursik et al.,1992). A number of Plinian events, however, including the wellknown 1980 Mt. St. Helens and 1982 El Chichon eruptions areexpected to be in the PBL regime.

An important remark is that whereas the population of large pum-ice and lapilli can be accurately reconstructed from deposits in thefield, the population of the finest ash is more difficult to assess be-cause small particles remain in suspension for weeks and fall out farfrom their point of emission. Therefore, the median grain-sizesreported in Fig. 8 represent maximum values and it is possible thatmore Vulcanian and Plinian eruptions could be in the PBL regime.This assumption is supported by the thorough re-analyses of the1980 Mt. St. Helens and 1982 El Chichon deposits, which show thatthe proportion of fine ash has been underestimated in previous stud-ies (Durant et al., 2009; Rose and Durant, 2008). Lastly, the collectedfield observations suggest that PBL formation may have been impor-tant in highly-explosive phreatomagmatic eruptions producing finevolcanic ash including the recent Eyjafjallajökull eruption (Fig. 8).

The origin of mammatus in atmospheric and volcanic clouds re-mains poorly understood (Schultz et al., 2006). Our results supportthe idea that mammatus clouds observed during the 1980 Mount St.Helens eruption (Fig. 1A) formed as a result of the growth of a PBLat the base of the umbrella cloud (Durant et al., 2009). Overall, ourresults suggest that internal sedimentation of the finest fraction ofparticles may lead to the formation of PBLs at the base of volcanicclouds. Whether these PBLs will result in the formation of roundedmammatus clouds, particle-rich fingers or thin ash veils depends onthe characteristics of the PBLs (Section 4.3). Consequently, morework is needed to characterize the dynamics of these PBLs in thenatural case. In particular, real-time measurements of particle sizesand concentrations at the base of volcanic clouds would be valuable.

5.3. Impact on cloud stability and longevity

In spite of the lack of field data required to interrogate the stabilityof PBLs in nature, it is interesting to quantify the effect of fingerformation on the residence time of suspended particles. For this, weuse the T number defined in Section 4.4 considering only low-Repparticles which always form PBLs,

T$0:42g ′pd

3p

ν2a

1!Γ" #5=4

ε1=2ppbl

2

4

3

58=15

; "22#

Fig. 7. Critical minimum values of particle size (in mm) below which the formation of aparticle-rich layer is predicted (B>1) as a function of the cloud altitude (in km) for(A) high-, (B) intermediate- and (C) low-particle Reynolds number. Gray areas give therange of particle sizes considered for each calculation. Dotted, solid and dashed linesgive the transition of behavior from individual particle settling (IPS) to particle boundarylayer (PBL) for !ppbl=10!6, 10!5 and 10!4, respectively. Calculations have beenmade fortypical particles densities of 700 kg m!3, 1500 kg m!3 and 2300 kg m!3 for high-,intermediate- and low- Rep particles, respectively (Bonadonna and Phillips, 2003).

Fig. 8. Maximum values of the median grain-size Md (in ϕ unit) above which theformation of a particle-rich layer is predicted (white area) as opposed to individualparticle settling (gray area), as a function of the cloud altitude (in km). Dashed, solidand dotted line give the transition for !ppbl=10!4, !ppbl=10!5, and !ppbl=10!6,respectively (see main text). White, gray and black diamonds correspond to geologicaldata available in the literature for phreato-Plinian, Vulcanian and Plinian eruptions,respectively. The sorting coefficient is used as an error bar. References used: Carey andSigurdsson, 1982, 1985, 1986; Hayakawa, 1985; Murrow et al., 1980; Nagai et al., 2002;Pyle, 1989; Rose and Durant, 2008; Rose et al., 1973; Scollo et al., 2007; Self and Sparks,1978; Sparks et al., 1981; Walker, 1980, 1981a, 1981b.


where g′p=g(ρp!ρa)/ρa. Applying typical values for volcanic ashclouds (see Section 2.3) leads to T"10!1 for 10 μm-particles andT"10!2!10!3 for 1 μm-particles. This result suggests that depend-ing on the grain-size distribution in the PBL, finger formation reducesthe residence time of fine particles in volcanic ash-clouds by at leastone and up to three orders of magnitude compared to the processof individual particle settling. These estimates should be consideredcarefully since other mechanisms affecting the dynamics of fingersmay play an important role.

Particle aggregation is a particularly important phenomenon involcanic ash clouds (Rose and Durant, 2011). Effects related to thisprocess are not observed in our experiments, either in the cloud orin the resulting deposit, most likely because conditions for aggrega-tion in water are not met for our 300 μm-particles. In natural erup-tion clouds, however, particle aggregation will cause the lowest-Repparticles to enter into higher-Rep regimes. Whether this phenomenonwill enhance individual particle setting or PBLs formation is notstraightforward to evaluate. Indeed, aggregation processes increasethe mean particle sizes, but also reduce the effective particle densitiesand to a lesser extent particle concentrations in the PBL. On the basisof Eq. (21) alone, one can infer that an increase of particle sizesshould promote individual particle settling, whereas a reduction ofparticle densities should promote PBL formation. Because both effectsalter the effective value of B in opposite manner, and also becausetheir relative importance varies according to the Rep regime, anexact treatment of this problem would require a more sophisticatedmodel that would not be supported by our experiments. Neverthe-less, we argue that a significant fraction of the original particle sizedistribution should remain in a Rep regime that favors PBL formation,as is apparent in the observations summarized in Figs. 1 and 8.

An additional important effect controlling the behavior of volcanicumbrella clouds is the presence of atmospheric winds. High velocitywinds can advect the cloud, enhance turbulent mixing and may im-pede the formation of fingers at the base of the cloud (Linden,1974). This effect can be quantified by comparing the time scale forturbulent shear Ww/H and for flow into a finger hf/Vf,

T† !WwhfVf H

; "23#

where Ww is the wind speed and hf is the finger length. Fingers willform if T†>1 and will be impeded if T†b1. The maximum fingerlength can thus be estimated by replacing T†=1. For the 1980 Mt.St. Helens eruption, we estimate Ww=30 ms!1 (Carey and Sparks,1986; Durant et al., 2009), H=10 km (Sarna-Wojcicki et al., 1981)and Vf"0.55 ms!1 consistent with a mean grain size of 4.4ϕ(Fig. 8). Replacing these values in Eq. (23) yields hf$185 m, whichseems to be consistent with observations in Fig. 1A. We note that inthe presence of very high-speed winds (Ww=60 ms!1), hf$91 mand fingers are still expected to form. An additional remark is thatin the near absence of wind (Wwb0.5 ms!1), hf$11 km and fingersare expected to reach the ground and possibly to spread as gravitycurrents. No-wind conditions during an eruption are rare, but possi-ble as inferred from Plinian fallout deposits with a radially symmetricdistribution (Papale and Rosi, 1993). We argue that in the near ab-sence of wind, the 1980 Mt. St. Helens eruption cloud could haveformed possibly dangerous gravity currents at much larger distancesfrom the volcanic vent than ever considered before.

6. Conclusions

We have presented a new set of laboratory experiments under-stood with theory in order to understand the origin of the enigmaticbuoyancy effects observed at the base of volcanic clouds. We showthat particle-laden umbrella clouds may follow unexpected dynami-cal regimes depending on the flow intensity, the strength of the initial

environmental density stratification and the particle concentration.Internal sedimentation of the fine fraction of particles during cloudspreading leads to the growth of thin PBLs at cloud bases. For naturaleruptions, whether the dynamics of PBLs play a major role in volcanicsedimentation depends on the grain size distribution, particle con-centration and to a lesser extent plume height. Although large andheavy particles settle individually, the remaining fine fraction of par-ticles is likely to form PBLs and subsequent fingers. An exhaustive re-view of available field data from historic and prehistoric eruptionsreveals that PBLs formation affected sedimentation in varied typesof sub-aqueous and subaerial explosive events. The impact of thesenew dynamics is mainly to reduce the residence time of fine particlesby one to three orders of magnitude compared to the process of indi-vidual particle settling.

Our work explains the origin of the enigmatic buoyancy effects ob-served in some recent volcanic ash-clouds (mammatus, particle-richfin-gers, ash veils, destabilization of thewhole umbrella cloud) and providesinsights into understanding the formation of finely stratified pumice de-posits (Branney, 1991). Catastrophic overturn and collapse of the um-brella could present a potentially significant and previouslyunrecognized volcanic hazard. Understandingwhether our late collapseregime could occur in nature and lead to the occurrence of late pyroclas-tic flows is therefore an exciting future direction of investigation.

Supplementary materials related to this article can be foundonline at doi:10.1016/j.epsl.2012.01.025.

Notationdp particle diameter (m)f drag factorg acceleration of gravity (m s!2)g′ reduced gravity (m s!2)hf finger length (m)hos overshoot height (m)k constantn constantxp particle mass fractionz vertical distance (m)zb neutral buoyancy height (m)zm maximum column height (m)A dimensionless buoyancy parameterAzm surface area of the jet at the maximum height (m2)D vent diameter (m)F buoyancy flux (m4 s!3)H umbrella cloud thickness (m)L characteristic length scale for the flow (m)M momentum flux (m4 s!2)N stratification parameter (s!2)Q volumetric flow rate (m3 s!1)R top-hat jet radius (m)Ts residence time for individual settling (s)Tf residence time in the fingering regime (s)Tmax longest period of umbrella oscillation (s)U top-hat jet velocity (m s!1)V characteristic velocity for the flow (m s!1)Vi growth rate of the gravitational instability (m s!1)Vs rate of settling of individual particles (m s!1)Wu lateral spreading rate (m s!1)Ww wind velocity (m s!1)B =Vi/Vs

Gr Grashof numberRe Reynolds numberRep particle Reynolds numberRi Richardson numberSt Stokes numberT time scale ratioT† time scale ratio


αe entrainment coefficientδpbl critical particle boundary layer thickness (m)!p particle volume fraction!pmax

effective maximum particle concentrationμ fluid dynamic viscosity (Pa s)ν fluid kinematic viscosity (m2 s!1)νa kinematic viscosity of the salt water (m2 s!1)ρ mixture density (kg m!3)ρa ambient density (kg m!3)ρf fluid density (kg m!3)ρp particle density (kg m!3)ρr reference density (kg m!3)τf time scale for flow (s)τg time scale for sedimentation (s)τp particle response time (s)ξpbl =εppbl

/(1!Γ)10

Δρi =ρpbl!ρa (kg m!3)Γ =εpo

/εpmax

Σ sedimentation number

Subscripts0 values at the source of the jetf values in the fingerm values at the maximum jet heightpbl values in the PBLu values at the source of the cloud

Acknowledgments

This manuscript was greatly improved by three anonymous re-viewers and by D. Ogden who gave very useful comments on a previ-ous version of this paper. The authors thank J. Unger who built up theexperimental set-up. This work was supported by NSERC, PIMS andthe Canadian Institute for Advanced Research.

Appendix A. Model for turbulent jets

For a conic-shaped jet in the Boussinesq approximation the con-servation laws of volume (πUR2) and momentum (πU2R2) fluxescan be written,

ddz

UR2" #

! 2αeUR; "24#

ddz

U2R2" #

! g ′R2; "25#

where z is the altitude, R is the jet radius, U is the vertical velocity, andαe is the entrainment coefficient, which quantifies the entrainmentrate αeU. In addition to this set of equations, we use Eq. (2) to accountfor the influence of the particle load on the bulk density. Assumingthat volume is conserved (i.e., no sedimentation from the column asobserved in our experiments), the particle mass fraction in the jet xpis given at any altitude by the conservation equation,

xpUR2

" #

z! xpUR

2" #

0; "26#

where the subscript 0 represents a quantity evaluated at the nozzle.The entrainment coefficient quantifies the rate of turbulent mix-

ing of environmental fluid within the jet (Morton et al., 1956). Here,we use a simplified version of the formula proposed by Kaminskiet al., 2005,

αe ! 0:0675$ 1! 1A

$ %Ri; "27#

where Ri=g′R/U2 is the local Richardson number, and A is a dimen-sionless parameter that depends on the flow structure (Carazzo etal., 2006). The latter parameter has been constrained using laboratorymeasurements on various jets and plumes, and can be calculatedusing Eqs. (13) to (17) of Carazzo et al., 2008b. Eqs. (24) to (27) canbe used to describe the self-similar evolution of the jet and thus topredict the conditions leading to the formation of a stable plume(Fig. 5).

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