Turbulent particle-gas feedback exacerbates the hazard impacts of pyroclastic density currents

Abstract

Causing one-third of all volcanic fatalities, pyroclastic density currents create destruction far beyond our current scientific explanation. Opportunities to interrogate the mechanisms behind this hazard have long been desired, but pyroclastic density currents persistently defy internal observation. Here we show, through direct measurements of destruction-causing dynamic pressure in large-scale experiments, that pressure maxima exceed theoretical values used in hazard assessments by more than one order of magnitude. These distinct pressure excursions occur through the clustering of high-momentum particles at the peripheries of coherent turbulence structures. Particle loading modifies these eddies and generates repeated high-pressure loading impacts at the frequency of the turbulence structures. Collisions of particle clusters against stationary objects generate even higher dynamic pressures that account for up to 75% of the local flow energy. To prevent severe underestimation of damage intensities, these multiphase feedback processes must be considered in hazard models that aim to mitigate volcanic risk globally.

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communications earth & environment Article
https://doi.org/10.1038/s43247-024-01305-x
Turbulent particle-gas feedback
exacerbates the hazard impacts of
pyroclastic density currents
Check for updates
Daniel H. Uhle 1,GertLube
1,EricC.P.Breard
2,3,EckartMeiburg 4, Josef Dufek3,JamesArdo 1,
Jim R. Jones 5,ErmannoBrosch
1, Lucas R. P. Corna1& Susanna F. Jenkins 6
Causing one-third of all volcanic fatalities, pyroclastic density currents create destruction far beyond
our current scientific explanation. Opportunities to interrogate the mechanisms behind this hazard
have long been desired, but pyroclastic density currents persistently defy internal observation. Here
we show, through direct measurements of destruction-causing dynamic pressure in large-scale
experiments, that pressure maxima exceed theoretical values used in hazard assessments by more
than one order of magnitude. These distinct pressure excursions occur through the clustering of high-
momentum particles at the peripheries of coherent turbulence structures. Particle loading modifies
these eddies and generates repeated high-pressure loading impacts at the frequency of the
turbulence structures. Collisions of particle clusters against stationary objects generate even higher
dynamic pressures that account for up to 75% of the local flow energy. To prevent severe
underestimation of damage intensities, these multiphase feedback processes must be considered in
hazard models that aim to mitigate volcanic risk globally.
Dilute pyroclastic density currents (PDCs) are lethal and recurrent hazards
from volcanoes1–5. Over 200 million people are directly endangered by these
multiphase flows of hot volcanic particles and gas6–8. Over the past decade
alone, and despite strong advances in understanding volcanic hazards,
PDCs caused more than a thousand fatalities and significant damage to
infrastructure globally9–13. So, how can we learn to forecast PDC hazards
more accurately? The key hazard agents of PDCs are the volcanic particles
carried inside them. As the main driver of PDC motion, particle con-
centration controls flow speed, destructive power and reach14–22. Carrying
most of the thermal energy, particles are also important for PDC burn
hazards, while the readily respirable particles cause inhalation injury and
asphyxia23,24. To model and mitigate against PDC hazards we must learn to
better understand the behaviour of particles, more specifically their motion
and sedimentation, inside flows1,3–5.
However, there is a fundamental roadblock hindering this endeavour:
the motion of particles within a PDC is modified through complex, long-
hypothesized but poorly understood coupling and feedback mechanisms
between particle and gas phases4,25–28. Unlike a homogenous suspension of
particlesinafluid, these interactions modify the flow and turbulence
structure in PDCs, leading to particle clustering, enhanced sedimentation,
high pore-pressure and fluidization29–35. Recent advances through large-
scale PDC experiments discovered that these interactions focus particles,
and thus mechanical and thermal energies, into large eddies, mesoscale
turbulence structures and internal gravity waves36. However, how the
feedback mechanisms between particles and gas control the runout and
hazardbehaviourofPDCsremainsunknown. The opportunity to explore
the multiphase physics of PDCs is long desired, but their ferocity, opacity
and unpredictability hampers direct observation and measurements of their
internal characteristics.
An important example of the large uncertainties for hazard planning
that result from this gap in understanding is forecasting of the destruction-
causing dynamic pressure of PDCs. To estimate local values of dynamic
pressure, researchers have systematically mapped the degree of damage to
infrastructure and vegetation in the aftermath of volcanic eruptions37–40.
Another approach uses relationships between sediment transport and
resulting deposit characteristics in turbulent fluid flow to estimate local
time-averaged values of flow velocity and density, which together define
dynamic pressure26,41–43. Recently, direct measurements in large-scale
1Volcanic Risk Solutions, Massey University, Palmerston North, New Zealand. 2School of Geosciences, The University of Edinb urgh, Edinburgh, UK. 3Department
of Earth Science, University of Oregon, Eugene, OR, USA. 4Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA,
USA. 5School of Food and Advanced Technology, Massey University, Palmerston North, New Zealand. 6Earth Observatory of Singapore, Asian School of
Environment, Nanyang Technological University, Singapore, Singapore. e-mail: d.uhle@massey.ac.nz
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experiments, natural PDCs and snowavalanchesdemonstratedthat
dynamic pressure calculated from turbulent fluctuations in velocity and
density exceed field- and theory-derived pressure estimates36.Thisfinding
demonstrates the importance of turbulent multiphase flow in volcanic
hazard assessments and raises caution regarding the applicability of current
approaches, which use (time) average flow properties.
Here we present the first high-resolution direct measurements of
destruction-causing dynamic pressure in large-scale PDC experiments to
interrogate how dynamic pressures form and evolve in PDCs. These mea-
surements reveal that dynamic pressure reaches pronounced maxima in the
peripheries of turbulence structures and generate regular pulses of high
dynamic pressure at the characteristic frequency of these structures. This
occurs through turbulent gas-particle feedbacks as particles, whose ratio of
characteristic response time to fluid motion to the characteristic timescale of
fluidmotionislessthanorequaltoone,clusteratthemarginsofeddies.We
demonstrate that this process results in two different types of dynamic
pressure effects with distinct hazard impacts to life and infrastructure.
Importantly, the resulting energy spectra of dynamic pressure are char-
acterized by peak pressure values that largely exceed pressure estimates
based on bulk flow characteristics, which are currently used for hazard
assessments.
Results
Synthesizing pyroclastic density currents and measuring
dynamic pressure in large-scale experiments
Over the last decade, the development of large-scale experimental facilities
to synthesize scaled analogues of PDCs16,44–46 has enabled a novel approach
to study their internal flow characteristics under safe conditions. The
experimental apparatuses in Italy45 and New Zealand44, which use heated
natural volcanic material, lend themselves to the interrogation of the scaled
fluid mechanic and thermodynamic processes inside fully turbulent PDC
analogues. Here we report the results of direct measurements of dynamic
pressure inside large-scale experimental PDCs conducted at the New
Zealand facility PELE (the Pyroclastic flow Eruption Large-scale Experi-
ment). At PELE, experimental PDCs are generated by the controlled
gravitational collapse of a suspension of hot volcanic particles and air from
an elevated hopper into an instrumented runout section (Supplementary
Fig. 1; Supplementary Movie). For the experiments reported here, we used a
0.7 m3hopper in which a 124 kg mixture of natural volcanic particles was
heated to 120 °C (the ambient temperature was 15 °C) over a period of 72 h
to allow for thermal equilibration and evaporation of residual moisture
inside the pre-dried mixture.
The volcanic material comprises a mixture of two well-characterised
deposits of PDCs of the 232 CE Taupo eruption in New Zealand47.Themain
components of the mixture are highly vesicular pumice, glass shards, free
crystals and rare lithic particles. The mixture has a weakly bimodal grainsize
distribution ranging from 2 µm to 16 mm, with a main mode at 250 µm and
a minor mode at 11 µm. The particle density distribution ranges from c.
300–2,600 kg m−3and is skewed towards low densities. Further details of the
material characteristics are provided in Supplementary Fig. 1 and in the
Methods section.
The hopper is lifted to a vertical drop height of 7 m. It is mounted onto
four load cells recording its mass discharge, which in this case lasts c. 4.6 s at
an average discharge rate of c. 27 kg s−1. On impact into a 0.5 m-wide and 12
m-long flumewithaslopeof6°,theaeratedparticle-airmixtureformsa
channelized dilute gravity current with an initial front velocity of c. 5.5 m s−1
and, on average, particle volume concentration of c. 0.25 vol.%. The flow is
characterized by a leading, c. 1.1–2 m thick gravity current head, which is
trailed by a gravity current wake that overlies a c. 0.9–1.6 m thick gravity
current body, and followed by a c. 1.8–3.5 m thick gravity current tail region
(Fig. 1a, b). Downstream of the inclined flume section, the experimental
PDC propagates to 17 m along a horizontal, 0.5 m wide channel-confined
section before spreading across an unconfined horizontal concrete pad.
Around 8 s after impact, the vertically density-stratified current has pro-
pagated23.5m,slowedtoc.0.5ms
−1and has emplaced approximately
99.7% of its total deposit volume. At 24 m, the depth-and time-integrated
Fig. 1 | Synthesizing pyroclastic density currents and dynamic pressure mea-
surements in large-scale experiments. a The time-variant flow structure of the
experimental PDC during channel confined propagation along a proximal measure-
ment profile,whichislocatedat1.8mdownstreamfromimpactofthehotmixtureof
volcanic material and air with the channel. The height-time kymograph is obtained by
the stacking of vertical columns of pixels recorded by a high-speed camera at the static
observer location. Pixel brightness correlates positively with, both, bulk flow particle
volume concentration and the abundance of highly reflective coarse-grained pumiceous
glass shards and plagioclase crystals. At this location, the density current structure is
fully developed comprising a leading head with a wake in its rear and a trailing density
current body. The density current tail region is not shown. bLateral view of the frontal
c. 7 m of the advancing experimental PDC across the unconfined distal runout section
approximately 1.5 m before buoyancy reversal. The red line shows the time-variant
height of the upper flow boundary. cSnapshot of the front of the experimental PDC
approaching one of the wing-shaped vertical profiles of dynamic pressure sensors. The
shapeofthewingsisdesignedtoreduceflow detachment and formation of a turbulent
wake behind the profile. The sensing elements of the piezoelectric dynamic pressure
sensors protrude, upstream from the wing, into the approaching density current.
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particle volume concentration has decreased to values smaller than
0.01 vol.% due to both deposition and entrainment of ambient air; the
current becomes positively buoyant and finally ascends as a series of ther-
mals along the flow length (Supplementary Movie).
To investigate the origin and evolution of dynamic pressure inside the
experimental PDCs, seven vertical, airfoil-shaped profiles with up to six
piezo-electric dynamic pressure sensors, which comprise circular, 15 mm
diameter frontal steel diaphragms, were placed into the flow centerline at
runout distances of 1.8, 3.35, 5.4, 9.6, 12, 16 and 20 m (Fig. 1c). Measurements
of time (t)-variant dynamic pressure P
dyn
(t, z) are recorded at a frequency of
1 kHz, and are complemented by measurements of time series, in vertical
profiles, of flow velocity u(t,z), particle volume concentration Cs(t, z), flow
density ρC(t, z),flow temperature and grain-size distribution, where zis the
height above the flow base in the direction perpendicular to slope (see
methods for details). Flow velocity components u(t,z)are measured using
high-speed video at 0.5 kHz through the flume’s tempered glass sides. The
sidewalls introduce boundary effects that are not present in unconfined real-
world flows and in the flow centerline of the experimental flows where
dynamic pressure is measured. We minimize these boundary effects through
the use of hydraulically smooth sidewalls (i.e., thickness of laminar layer/wall
roughness >1) while the flow’sReynoldsnumber,whichisinverselyrelatedto
the thickness of the viscous boundary layer, is high (Re =1.5×106). Velocity
data together with measurements of time-variant and height-variant grain-
size distribution, flow density and temperatures allow for an independent
measurement of dynamic pressure, defined as:
Pdyn Bernoulli ¼1
2ρCu
jj
2;ð1Þ
where u
jj
is the magnitude of the local time-variant velocity.
The experimental PDCs generated under these conditions scale well to
natural dilute fully turbulent PDCs (i.e., pyroclastic surges or blasts; see a
comparison of scaling parameters for natural and experimental PDCs in
Supplementary Table 1). Amongst the non-dimensional products of char-
acteristic length-, time and temperature-scales we highlight the Reynolds
number (comparing inertial and viscous forces) reaching values of 1.5 × 106,
Stokes number (comparing particle time-scale to turbulent flow time-scale)
of 10−3–100, Stability number (comparing time-scales of particle settling and
turbulent fluid motion) of 10−2–101, Richardson number (characterizing the
stability of stratification in turbulent flows) of 10−2–101,andthermal
Richardson number (assessing the ratio of forced and buoyant convection)
of 0.02–4.5. The overlap of ranges in Reynolds, Stokes and Stability numbers
in experimental and natural PDCs ensures that the complete range of
particle-gas feedback mechanisms and turbulent particle transport is
reproduced.
Two types of dynamic pressure
Figure 2a and b depict a typical example of the time series of dynamic
pressure inside the experimental PDCs (here for the vertical profile 2 at a
runout distance of 3.35 m at approximately mid-flow height of 0.45 m
from the flow base). The local time-averaged dynamic pressure takes a
value of 45 Pa, while maximum values reach several kilopascals. The wide
discrepancy between average and maximum pressures, as well as the
absolute values of recorded maximum pressure are surprising. Recent
analysis of dynamic pressure in experimental PDCs using measurements
of flow velocity and flow density and Eq. 1showed that turbulent fluc-
tuations in velocity and density generate dynamic pressures that exceed
average values by a factor of 3–536. This coincides with our measurements
of dynamic pressure through velocity and density time-series (that is
P
dyn_Bernoulli
) and Eq. 1giving maximum and average values of 79 and
Fig. 2 | Two types of dynamic pressure and their probability density spectra. All
measurements of dynamic pressure shown in this figure are obtained at the location
of 3.35 m from impact at a height 0.45 m above the flow base. aVariation of the entire
dynamic pressure P
dyn
as a function of time as recorded by piezoelectric sensor and
the corresponding probability density function shown in b. The pressure signal of
P
dyn
shows abundant near-instantaneous high-pressure peaks of several hundreds to
thousands of Pascal, which are characterized by pressure increases in less than one
millisecond. The inset highlights an example of one of the near-instantaneous high-
pressure signals, which are associated with impacts from individual particl es with the
pressure sensor. cVariation of the partial dynamic pressure signal P
impact
as a
function of time recorded by the piezoelectric sensor, which shows only those parts
of the entire pressure signal P
dyn
that are associated with near-instantaneous pres-
sure peaks. dThe probability density function of P
impact
.eVariation of the partial
dynamic pressure signal P
dusty gas
as a function of time, which is the dynamic pressure
of the continuous dusty gas phase computed as the difference between P
dyn
(t) and
P
impact
(t) via Eq. (2). The black line shows a 20-millisecond average of the timeseries
P
dusty gas
(depicted in blue) The orange line shows the corresponding timeseries of
the dynamic pressure P
Bernoulli
, computed independently from timeseries of flow
velocity and flow density via Eq. (1). fprobability density functions of P
dusty gas
(blue)
and P
Bernoulli
(orange).
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24 Pa (i.e., a ratio of c. 3.3), respectively. In stark contrast, time-averaged
(45 Pa) and maximum dynamic pressures (4830 Pa) recorded by the
dynamic pressure sensors (Fig. 2a) differ by two orders of magnitude.
They can, therefore, not be explained by turbulent fluctuations in velocity
and density of the multiphase flow. Thus, from the perspective of
understanding and mitigating hazard impacts of PDCs, an important
question arises regarding the origin and nature of these unexpectedly
large pressures.
An important clue is given by the form of those pressure signals that
exceed the theoretical values of dynamic pressure calculated through
turbulent fluctuations of flow velocity and density through Eq. 1.These
high-pressure signals are characterized by an abrupt pressure increase to
a maximum in less than one millisecond (inset of Fig. 2a; the sensor
response time (12 μs) « sampling rate (1 ms)). Furthermore, we deter-
mined that in all occurrences of these near-instantaneous high-pressure
signals, the rate of pressure change with time was always larger than
c. 220 Pa ms−1. These characteristics in the form of pressure signals are
consistent with impacts of individual particles on the pressure sensor.
Considering particle diameters and size-averaged particle densities
determined from flow samples, and local velocities measured in high-
speed video, theoretical values of dynamic pressure caused by impacts
of individual particles can be estimated (Supplementary note 1 and
Supplementary Fig. 3). At time-averaged local velocities, impacts of
particles with diameters larger than c. 100 µm generate dynamic pres-
sures larger than 500 Pa, and thus, considerably larger than theoretical
values of dynamic pressure calculated through turbulent fluctuations of
flow velocity and density and Eq. 1. Maximum measured values of
dynamic pressure (e.g., 4.8 kPa at profile 2) can be explained by impacts
of, either, low-density pumiceous particles with particle diameters larger
than c. 2 millimeters or abundant high-density plagioclase particles with
particle diameters larger than c. 600µm. Hence, the near-instantaneous
high-pressure signals are explained by individual particle impacts.
This finding allows a sub-division of the total dynamic pressure signal
P
dyn
into the dynamic pressure associated with impacts from individual
particles P
impact
(Fig. 2c and d) and the dynamic pressure of the (continuous)
dusty gas phase P
dusty gas
(Fig. 2e) where:
Pdyn ¼Pdustygas þPimpact :ð2Þ
Probability density functions of P
dusty gas
and P
dyn_Bernoulli
coincide
markedly well (Fig. 2f). This justifies the subdivision of the total dynamic
pressure into its continuous dusty gas, P
dusty gas
, and particle impact, P
impact
,
components. Furthermore, the piezoelectric signal of the dynamic pressure
sensor has a superior temporal resolution (1 kHz) in comparison to the
timeseries of dynamic pressure P
dyn_Bernoulli
computed, via Eq. 1,from
timeseries of flow density data (with a sampling rate of 20 Hz) and velocity
(sampled at 0.5 kHz). Thus, the piezoelectric signal shows a much more
detailed record of the dynamic pressure of the continuous dusty gas phase in
the high-pressure end of its spectrum.
Despite the strong differences in pressure ranges between the dynamic
pressures of the dusty gas phase (up to 390 Pa at profile 2) and particle
impacts (up to 4.8 kPa at profile 2), the probability density functions and the
time-series of both signals, and hence that of the total dynamic pressure,
share two characteristics: first, the pressure distributions are strongly skewed
towards large pressures (Fig. 2b, d and f). Second, largest pressures and
highest occurrences of large pressures occur during passages of the head
(c. 0–1sinFig.2a, c and e) and mid-body regions (c. 2.4–3sinFig.2a, c and
e) of the experimental PDC. For the dynamic pressure of particle impacts
P
impact
, time-series of the rate of particle impacts, R, provide further insights
(Fig. 3e–h). Along flow runout, the rate of particle impacts, at approxi-
mately mid-flow height (i.e., at z= 0.45 m), decays strongly from more than
275 Hz at a distance of 1.8 m, to 95 Hz at 5.4 m and no recorded impacts at
9.6 m and beyond. This suggests that dynamic pressure signals associated
with impacts from individual particles are limited to particles with a critical
Fig. 3 | Spatiotemporal variation of the frequency of particle impacts. The time-
variant flow structure of the experimental PDC at four different distances from
impact with the channel at 1.8 m (a), 3.35 m (b), 5.4 m (c) and 9.6 m (d). As in Fig. 1a,
the height-time kymograph plots are generated by the stacking of vertical columns of
pixels recorded by high-speed cameras at the static observer locations. e–hTime-
series of the frequency of particle impacts f
impact
at the four different distances. The
frequency of particle impacts is computed through convolution of time series of
binary impacts using a box function with a duration of 200 ms. Time series of binary
impacts, shown in Fig. 5, were generated by assigning times of occurrences of particle
impacts a value of 1 and times without impacts a value of zero. Due to the sampling
rate of 1 kHz, impact rates of up to 500 Hz can be resolved. The frequency strongly
declines with distance. i–lTimeseries of the depth-integrated flow density

ρCtðÞat
the four different distances. The regular low-frequency oscillations in flow density
are positively correlated in time with the oscillations of particle impacts.
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minimum momentum. We note that the pattern of decay of the number of
particle impacts with runout distance is similar to the decay of particles with
diameters of 125–500 µm in flow samples (Fig. 4). This is the grain-size
range that constitutes the coarse tail of flow grain-size distributions in
proximal to distal runout reaches.
The low numbers of particle impacts at medial to distal profile locations
(i.e., > 10 m) limit further analysis. However, at the proximal profiles, impact
numbers are sufficiently large to see that the rate of impacts obeys a regular
low-frequency oscillation (Fig. 3e and f), which is positively correlated in
time with a low-frequency oscillation in flow density (Fig. 3iandj;i.e,the
number of impacts is large when flow density is high).
Figure 5depicts timeseries of particle impacts in binary form (i.e., times
during which an impact occurs are assigned a value of 1, and times where no
impacts occur a value of zero). This shows that if a particle impact occurs, it
is typically followed by multiple further impacts. By contrast, isolated single
particle impacts are rare. The mean of the number of successive, in other
words, clustered impacts ranges from 2–14 impacts with an average number
of clustered impacts of c. 4.
Energy spectra of dynamic pressure from particle impacts and
dusty gas
Recently, low-frequency oscillations in flow density, velocity and hence
dynamic pressure have been linked to the occurrence of large-scale coherent
turbulence structures inside experimental and real-world PDCs and snow
avalanches36. The frequency fof the most energetic coherent structure in a
turbulent flow is given by the Strouhal number Str as
Str ¼fL
Uð3Þ
where Land Uare the flows’characteristic length- and velocity-scales48.For
highly turbulent flow conditions with Reynolds numbers Re >10
5,the
Strouhal number approaches a constant value of approximately 0.336,49–51.In
our high-Reynolds number experimental PDCs (Re =1.5×10
6), the
measured main frequencies of flow density oscillations of c. 1.26 Hz (i.e.,
a period of 794 ms) and particle impact rates Rof c. 1.33 Hz (a period of
752 ms) coincide closely (Supplementary Fig. 4a and b), and correspond
with the period of the visually observed occurrences of the largest flow
structures (Fig. 3a–d; Supplementary Fig. 4c). Substituting the experimen-
tally determined frequency f~ 1.3 Hz, the time-averaged height of the
gravity current body region L~ 1.15 m and the time-averaged flow velocity
U~4.76ms
−1into Eq. (3), gives a Strouhal number Str = 0.31 close to the
commonly observed value.
The energy peak associated with the most energetic coherent struc-
tures, at a frequency of f~ 1.3 Hz, is clearly visible in energy spectra of the
total dynamic pressure P
dyn
, the dynamic pressure of particle impacts
P
impacts
and the dynamic pressure of the continuum dusty gas phase P
dusty gas
at the top of their respective energy cascades (red bars in Fig. 6a–c). The
energy of P
dusty gas
decreases strongly with increasing frequency consistent
with the transfer of turbulent kinetic energy (per unit volume) to smaller
scales of coherent structures (Fig. 6c). By contrast, the energies of P
impacts
(Fig. 6b) and P
dyn
(Fig. 6a) show a markedly flatter decay of pressure energy
with increasing frequency (and decreasing length-scale of coherent turbu-
lence structure). Importantly, the maximum energy values of both, P
impacts
and P
dyn
, which also reach the energy values of the most energetic coherent
structures at f=1.3Hz,occuracrossadefined band of frequencies fof c.
7–16Hz(greybarsinFig.6a and b). The wavenumbers associated with this
frequency band correspond to length-scales of c. 0.25–0.6 m (Fig. 6d and e).
The multiphase origin of dynamic pressure fluctuations
We hypothesize that the origin of the unusually high and temporally clus-
tered dynamic pressures is rooted in the concentration of particles at the
peripheries of coherent turbulence structures. PDCs comprise a wide
spectrum of particle-gas feedback mechanisms from simple one-way cou-
pling where the motion of particles is affected by the motion of the fluid
phase but not vice versa, over two-way coupled particle-gas systems where
particle-gas interactions can modify the flow and turbulence structure, to
four-way coupling that strongly alters the flow structure4.Thedegreeof
Fig. 4 | Spatial evolution of particle impacts and flow grain-size distribution. The
number of particle impacts with the piezoelectric dynamic pressure sensors at mid-
flow height (0.45 m from the flow base) as a function of flow distance (white dia-
mond symbols). In comparison, the time-integrated cumulative grain-size dis-
tribution of the flow captured in flow samplers at heights of 0.45 m is shown as a
function of flow distance. The decrease of particle impacts with distance follows a
similar trend as the decay of particle sizes 125–500 µm in flow samples. Particles with
diameters larger than 2 mm (not shown) completely sediment from the flow by c.
1.8 m; particles with diameters >1 mm and >500 µm sediment from the flow at
distances of c. 5 m and c. 7.5 m, respectively.
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Fig. 6 | Energy spectra of dynamic pressure in Fourier space. Energy spectra of
dynamic pressure against frequency for P
dyn
(a), P
impact
(b) and P
dusty gas
(c). Energy
peaks at a frequency f~ 1.3 Hz associated with the largest coherent structures are
highlighted by a red bar. This frequency coincides with the measured frequency of
the largest coherent structures f∼1:3Hz ¼U Str
L, where Uand Lare the time-
averaged velocity and thickness of the density current body region and Str is the
Strouhal number. The highest-pressure energies occur in P
dyn
(a) and P
impact
(b)
across a narrow band of frequencies f
max
from c.7–16 Hz (where the frequency range
f
max
was visually handpicked) highlighted by a grey bar. Energy spectra of dynamic
pressure against wavenumber kfor P
dyn
(d), P
impact
(e) and P
dusty gas
(f). For P
dyn
and
P
impact
, the high-energy band associated with f
max
is highlighted by grey bars. This
band corresponds to wavenumber of c.1.

6–4 1/m or length-scales of coherent
structures 1/kof c. 0.25–0.6 m. The orange line with slope of −5/3 shows the Kol-
mogorov scaling of the inertial range.
Fig. 5 | Clustered distribution of particle impacts. Timeseries of particle impacts at
0.45 m above the flow base at four different distances from impact: 1.8 m (a), 3.35 m
(b), 5.4 m (c) and 9.6 m (d). Occurrences of particle impacts are shown in binary
form. That is times of impacts are assigned a value of 1 and times without impacts are
assigned a value of zero. The number of particle impacts is strongly decreasing with
flow distance and no particle impacts are recorded at the position at 9.6 m. When
particle impacts occur, they tend to occur in clusters of several successive impacts.
Non-clustered particle impacts are rare. The largest number of particle impacts
occur in the head region (c. 0–1 s) and in the mid-body region (c. 2.4–3 s) of the
experimental PDC.
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coupling of particles to turbulence structures can be approximated through
the particle Stokes number St defined as
St ¼τp
τε
;ð4Þ
where τpis the characteristic timescale of particles and τεis the turbulence
timescale. Particles with low Stokes numbers St ≪1 are well coupled with the
fluidphaseandtendtofollowthefluid motion; particles with St ≈1accu-
mulate at the margins of coherent turbulence structures, while high Stokes
number particles St ≫1 are decoupled from fluid turbulence and move
independent of the turbulence motion25,27,30,48,52,53. For the condition St =1of
particles concentrating at the peripheries of coherent structures it follows:
τp¼τε$τ1
p¼fε;and ð5Þ
$fε¼τ1
p¼18ρFνFF
ρPd2;ð6Þ
where fεis the frequency associated with this condition, ρFand ρPare fluid
and particle densities, respectively, νFis the kinematic viscosity of the fluid,
Fis the Stokes drag factor as defined by ref. 54.anddthe particle diameter.
Equation (6) and our experimental data of the particle size-averaged particle
density ρPðdÞcan be combined to calculate the critical frequency fεdðÞof
particle clustering at margins of coherent structures as a function of particle
diameter (Fig. 7a). For the polydisperse volcanic mixture used in our
experiments (Supplementary Fig. 1), these critical frequencies range over
four orders of magnitude from 3×10−1–4×103Hz. However, the particle
sizes associated with the measured energy maximum in P
impacts
and P
dyn
,at
fεmax ~7–16 Hz (Fig. 5a and b and grey horizontal bar in Fig. 7a),
constitute a narrow band of particle diameters of 117–229 µm (grey vertical
barinFig.7a). In flow samples, this particle size range occupies the coarse
tail of grainsize distributions (Fig. 7b). Due to sedimentation, the proportion
of particles larger than 117 µm strongly decreases from c. 70 wt.% in the
initial mixture to <5 wt.% at a flow distance of 20 m (Fig. 4). Similarly, the
dynamic pressure energy associated with particle impacts P
impacts
,which,at
a runout distance of 1.8 m, accounts forc.75%ofthetotaldynamicpressure
P
dyn
, decreases strongly downstream approximately following a power law
decay (Fig. 7c).
The largest particle size supported by turbulence in the experimental
flows, which is limited by the characteristic length- and velocity-scales of the
most energetic coherent turbulence structure (Eq. (3)) and associated with a
measured frequency f~ 1.3 Hz, corresponds to c. 2 millimetres (red vertical
barinFig.7a and b). Therefore, the experimental PDC strongly depletes in
particles larger than 2 millimetres even before a proper gravity current
structure has formed at around 1.8 m after impact. Particle sizes smaller
than 2 mm (associated with the frequency of the largest coherent structure),
but larger than 117–229 µm (associated with the frequencies at the energy
maximum of dynamic pressure fεmax of c. 7–16 Hz) do not form notable
peaks in dynamic pressure energy (Fig. 6). This is explained by the rare
abundance of particles of this size range, which occupy the coarse tail of flow
grainsize distributions (Fig. 7b).
To visualize the process of clustering of particles with critical Stokes
numbers at the margins of coherent turbulence structures we conducted a
numerical simulation of the experimental PDC using a large eddy resolving,
Eulerian-Eulerian approach with particle-fluid four-way coupling. In this
multiphase simulation, five different particle sizes are modelled (2 mm,
0.5 mm, 0.125 mm, 0.032 mm and 0.008 mm) whose relative proportions
and particle size-dependent densities are the same as in the physical
experiment (see Methods for details). Figure 8depicts contour plots of
Fig. 7 | Particle sizes of critical Stokes numbers and their sequential sedi-
mentation. a The frequency fεassociated with the condition of particle Stokes
number St = 1 as a function of grainsize. The grey horizontal bar depicts the
frequency band in fεof c.7–17 Hz of highest-pressure energies. The grey
vertical bar delimit the experimentally determined corresponding critical
grainsizes for St =1atfεof c. 127–224 µm. The red horizontal bar and the red
vertical bar mark the frequency associated with the most energetic coherent
flow structure at a frequency f~ 1.3 and the corresponding grainsize of c.
2 mm, respectively. bHistograms of time-integrated flow grainsize
distributions captured in flow samplers at flow heights of 0.45 m above the flow
base for various flowdistances.Asin‘a’, the grey vertical bar highlights the
grain-size range of c. 127–224 µm associated with fε,whiletheredverticalbar
marks the critical grainsize of c. 2 mm supported by the most energetic
coherent turbulence structures at f~ 1.3. Note the downstream depletion of the
flow in critical Stokes number particles associated with fε(c. 127–224 µm).
cThe fractional time-integrated energy of particle impacts P
impact
relative to
theentirepressureenergyP
dyn
as a function of flow distance. The black line is a
best-fit power law to the data.
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particle volume concentration of the evolving current at approximately half
of the total runout length for each particle size. High Stokes number particles
(2 mm in diameter; Fig. 8a) do not highlight any coherent turbulence
structures and have sedimented into the basal flow. Low Stokes number
particles (0.032 mm and 0.008 mm in diameter; Fig. 8d and e) remain
homogeneously suspended throughout the flow or tend to concentrate
slightly in the central regions of coherent structures. By contrast, particles
with diameters of 0.5 and 0.125 mm concentrate at the peripheries of eddies
highlighting the coherent turbulence structure of the flow (Fig. 8b and c).
Similar to our physical experiment, the highest particle concentration in
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eddy peripheries occurs for particles with diameters of 0.125 mm. The
average size of the large coherent structures (highlighted by concentrated
margins) in the numerical simulation accounts to approximately 0.5 m
(Fig. 8c). This corresponds to the length-scales of c. 0.25–0.6 m that are
associated with the narrow band of maxima in dynamic pressure as seen in
the energy spectra of dynamic pressure as a function of wavenumber (where
thelength-scaleistheinverseofthewavenumberk;Fig.6dande).
Spatiotemporal evolution of dynamic pressure fluctuations
To assess the destruction potential of PDCs, volcanologists routinely use
estimates of either bulk flow or local time-averaged flow velocity and density
values to evaluate average dynamic pressures26,41–43.Ourfinding of the
concentration of particles with critical Stokes numbers (i.e., St ¼Oð1Þ)at
the peripheries of coherent turbulence structures imply strong fluctuations
of dynamic pressure to occur at the characteristic frequency fεmax of these
structures. To prevent underestimation of the destruction potential of
PDCs, it is important to understand how turbulent fluctuations of dynamic
pressure around field-estimated average values evolve during flow
propagation.
Figure 9a compares the time-averaged dynamic pressure P
dusty
gas_ave
, the maximum dynamic pressure of the continuum phase P
dusty
gas_max
and the maximum dynamic pressure associated with particle
impacts P
impact max
as a function of flow distance. P
dusty gas_ave
(i.e, the
equivalent of the time-averaged loading pressure estimated in hazard
assessments to assess damage to infrastructure) steadily decreases with
flow distance Dfollowing a powerlaw of the form Pdusty gas ave /1=D.By
contrast, and up to 9.6 m, the maximum loading pressure P
dusty gas_max
exceeds the time-averaged pressure by an order of magnitude. In distal
reaches, D>9.6m, P
dusty gas_max
starts to decline more strongly. Max-
imum dynamic pressures from particle impacts P
impact max
exceed
P
dusty gas_ave
by two orders of magnitude, strongly decline with distance
and are restricted to the proximal flow reaches of D≤5.4 m.
Figure 9bshowsthepressureratioofP
dusty gas_max
over P
dusty gas_ave
against flow distance. This ratio assesses by how much current field-based
estimates of dynamic pressure underestimate actual, turbulence-enforced
maximum loading pressures and can be written as:
Pdusty gas max
Pdusty gas ave
¼ρmaxUmax 2
ρaveU2
ave
:ð7Þ
The pressure ratio is independent of scale, and experimental estimates
can be applied to natural flow scales. However, the spatiotemporal evolution
of the dynamic pressure ratio is limited by the abundance of large Stokes
number particles inside flows. Following the decoupling of high Stokes
number particles from the margins of coherent structures, their motion is
independent of fluid turbulence and results in their rapid sedimentation
from the flow.
Immediately following formation of a gravity current structure at c.
1.8 m and up to 5.4 m, the pressure ratio continuously increases from initial
values of c. 11.8 to maxima of c. 13 in 0.74 s (Fig. 9b). This duration coincid es
with the characteristic eddy timescale of the largest coherent structure of
τε=1/f~ 1/1.3 = 0.77 s. This suggests that the characteristic timescale of the
motion of high Stokes number particles from a homogeneous suspension
into eddy peripheries can be estimated by the overturn time of the largest
coherent structure.
After the time τε, the particle volume fraction θVof particles with
St ¼Oð1Þdeclines below 10−4. This appears to correspond to the limiting
mass loading for maximum particle clustering to occur and, downstream of
5.4 m, the pressure ratio decreases strongly. At 20m, where the volume
fraction of particles with St ¼Oð1Þhas decreased to values of
θV∼5×106, the pressure ratio approaches a value of 3.84. In the case of
exhaustion of St ~ 1 particles carried inside flows, Eq. (7) reduces to:
Pdusty gas max
Pdusty gas ave
∼Umax
Uave

4
ð8Þ
(see Supplementary note 2). Our velocity measurement of the max-
imum and average velocity at 20 m give a value of Umax=Uave

4of 3:9in
Eq. 8, which closely corresponds with the measured pressure ratio of 3.84.
Discussion
Current approaches to assess the destruction potential of pyroclastic density
currents envisage the loading force of a continuum multiphase fluid of
characteristic velocity and density across structural surfaces opposing flow
direction.e.g. 37–40 In the absence of detailed measurements inside flows,
volcanologists estimate local time-averaged values of flow velocity and
density from deposit or damage characteristics to guide assessments of
potential hazard impact15,41–43. Our simulations of pyroclastic density cur-
rents through large-scale physical experiments and numerical modelling
demonstrate a fundamental shortcoming of this approach: the modification
of the flow and turbulence structure due to coupled feedbacks between
particle and gas phases. This feedback leads to the preferential clustering of
large, high-momentum particles at the margins of coherent turbulence
structures (Fig. 10a) and generate two different types of distinct hazard
impacts (Fig. 10b–c).
The first type, the dynamic pressure of the continuous dusty gas phase
P
dusty gas
,significantly exceeds the time-integrated dynamic pressure by up
to one order of magnitude (Fig. 10d). The cause of these strong turbulent
pressure fluctuations is the modification of the flow into coherent structures
with high-density margins (Fig. 10a), spatially separating the flow into high
density (eddy peripheries) and lower density domains (central regions of
eddies). The size of the coherent structures, and hence the characteristic
frequency of high-density/high dynamic pressure flow pulsing fεmax ,is
determined by the abundance of particles whose characteristic response
time to fluid motion is equal to or smaller than the characteristic time-scale
of changes in the fluid motion (that is, particle Stokes numbers St ≥1).
Depending on the mass loading of particles with this critical Stokes number
condition, the ratio of the clustering-enforced maximum dynamic pressure
Pdusty gas and the field-estimated average pressure can range between c.4–13.
To prevent an underestimation of the intensity of hazard impact, we
strongly suggest that these factors are applied to conventional estimates of
dynamic pressure that apply bulk flow values of flow velocity and
density15,41–43. For instance, for two- to three-story, reinforced brick, stone
and concrete buildings, a mean dynamic pressure of 5 kPa results in failure
of doors and partial damage to door and window frames. By comparison,
4–13 times larger maximum clustering-enforced dynamic pressures of
20–65 kPa lead to failure of peaked roofs and front-facing exterior walls (c.
20 kPa) and complete failure of all building elements (c. 65 kPa)15.Oscil-
lation in dynamic pressure at the frequency fεmax further intensifies the
destructiveness of flows due to the progressive structural weakening of
Fig. 8 | Clustering of critical Stokes number particles at the peripheries of
coherent structures. a–eSnapshots from a numerical multiphase Eulerian-Eulerian
fluid particle four-way coupled simulation of the physical experiment at approxi-
mately mid-flow runout distance. The contour plots show the spatial variation across
the simulated PDC in the particle concentration of five modelled grainsizes of 2 mm
(a), 500 µm (b), 125 µm (c), 32 µm (d) and 8 µm (e). Technical aspects of the
numerical simulation are detailed in the Methods section. Particles with Stokes
numbers St >1(a), which are only supported by turbulence at the s cales of the largest
coherent structures, have sedimented into the basal flow and do highlight any
coherent structures at mid-flow runout. Particles with critical Stokes numbers St =1
(band c) concentrate at the peripheries of coherent structures. The effect is stronger
for particle sizes of 125 µm than for particle sizes of 500 µm because of the sig-
nificantly higher abundance of the 125 µm particles over 500 µm particles. Particles
with low Stokes numbers St <1(dand e) tend to be homogeneously suspended or
slightly concentrate in the central parts of coherent structures.
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materials amid repeated high-pressure loading. The damage inflicted
depends on the maximum dynamic pressure associated with the high-
density margins of coherent turbulence structures and the characteristic
integral length scale of these structures relative the characteristic length scale
of an infrastructure. Our experimental method does not allow us to deter-
mine the range of three-dimensional geometries of coherent turbulence
structures and future physical and numerical experiments are needed to
address this problem. However, our experimental results can give some
guidance. The characteristic length scale of the most energetic turbulence
structures with particle clusters of c. 0.25–0.6 m is of the order of the height
of the lower flow boundary to roughly half of the thickness of the body the
density current. This length scale (i.e, half the thickness of the PDC) is
considerably larger than the height of the common built environment at the
Earth’s surface. Limited by the mass loading of particles with particle Stokes
numbers of order unity in a PDC, this indicates that clustering-enforced
destructiveness will be effective in typical PDC/infrastructure interactions.
The modification of the flow and flow turbulence structure through particle-
gas feedback also implies associated modifications of the local concentration
of readily respirable fine-ash particles and local flow temperature, with
effects on the respiratory and burns hazards of PDCs.
The second type of hazard impact, the force of particle collisi ons, which
is associated with (and measured in our experiments as) the dynamic
pressure of particle impacts P
impact
, can exceed average dynamic pressures,
even stronger than P
dusty gas
, by two orders of magnitude (Fig. 10d). Unlike a
loading continuum pressure, this pressure corresponding to the force of
particle impacts results when particles with Stokes numbers St ≥1uncouple
from the flow that engulfs a structure and directly impinge onto it. The
resulting piercing particle impacts can be seen as pockmarks on trees and
infrastructure55 (Fig. 10c) and are illustrated for the case of the Merapi 2010
eruption in Supplementary Fig. 5. Piercing particle impacts from PDCs are
also likely contributing to the failure of brittle structures such as glass
windows38,55. Importantly, the magnitude of particle impact forces, because
they are distributed over relatively small impact areas of the order of the
cross-sectional area of a particle, must be considered as a potential con-
tributor to the high fatality and injury rates in PDC-forming eruptions
(Fig. 10d).
Our experiments demonstrate the role of turbulent particle-gas feed-
back in modifying the flow and turbulence structure and exacerbating the
intensities of hazard impacts. These findings are also applicable to other
types of high-Reynolds number, polydisperse particle-gas flows, such as
powder snow avalanches, dust storms, and the debris-laden basal flow
regions of tornados and explosions, and should be considered in the
assessments of their potential hazard impacts28,56–59.
Methods
Large-scale experiments
The Pyroclastic flow Eruption Large-scale Experiment (PELE), which is
fully described in ref. 44., is an international test facility to synthesize, view
and measure inside the interior of pyroclastic density currents. Experi-
mental PDCs of up to six tonnes of volcanic material and gas move at
velocities of 7–32 m s−1,are2–4.5 m thick and propagate to runout length of
>35 m. We conducted a series of three large-scale experiments to confirm
that the experimental results reported are typical. The currents are generated
by the controlled gravitational collapse of variably diluted suspensions of
pyroclastic particles and gas from an elevated hopper into an instrumented
runout section. PELE is operated inside a 16 m high, 25 m long and 18 m
wide disused boiler house. The apparatusiscomposedoffourmainstruc-
tural components: (i) Tower. A 13 m-high construct that lifts either a 4.2 m3
Fig. 9 | Spatiotemporal evolution of dynamic pressure during flow propagation.
aDynamic pressure as a function of flow distance D. The red circles show time-
averaged values of dynamic pressure Pdusty gas ave. The red line is a best-fit powerlaw
through the data that yields Pdusty gas ave ¼136D1:019 . The blue square symbols
represent the maximum dusty gas pressure Pdusty gas max. The black circles show
measurements of the maximum particle impact pressure Pimpact max .bThe pressure
ratio Pdusty gas max =Pdusty gas ave as a function of flow distance (black diamonds). The
contour plot shows the particle volume concentration of particles with diameters
>125 μm, associated with the condition St ≥O1ðÞ. The vertical red dotted lines
demark particle concentrations of, from left to right, 10−3,10
−4, and 10−5.
The secondary, non-linear horizontal time axis depicts the times of flow front arrival
corresponding to these distances. After formation of a gravity current structure at c.
1.8 m and up until 5.4 m, the pressure ratio increases slightly to maximum values of
around 13. The flow duration associated with this increase coincides with the eddy
time scale tεhighlighted on the secondary x-axi s. Downstream from 5.4 m, the
pressure ratio decreases in association with a reduction in the particle concentration
of critical Stokes number particles larger than 125 µm. The horizontal dashed line
corresponds to the condition predicted by Eq. (8) where the pressure ratio takes a
critical value of c. 3.9, when the flow is depleted in particles with St ≥1.
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hopper (for moderate to high discharge rates of 300–1,500 kg s−1)ora0.7m
3
hopper (for discharge rates of 30–200 kg s−1) to the desired discharge height.
The hoppers are equipped with internal hopper heating units to heat the
pyroclastic material to target temperatures of up to 400 °C. The heating
process is measured by thermocouples and the hopper is mounted onto four
load cells to capture the time-variant mass discharge. (ii) Column. A ≤9m
high shroud of heat-resistant cloth through which the discharge particle-air
mixtures accelerate under gravity. (iii) Chute. A 17 m long and 0.5 m wide
multi-instrumented channel section with 0.6–1.8 m high sides of
temperature-resistant glass. The first 12 m are variable adjustable to
slope angle between 5° and 25° while last 5 m of the channel is horizontal.
(iv) Outflow. A 25 m-long flat instrumented and unconfined runout section
that extends outside the building. The physical properties of the particle-gas
suspensions prior to impact with the channel (velocity, mass flux, volume
flux, particle concentration), the characteristics of the solid components
(grainsize distribution, particle density distribution, particle temperature),
and boundary conditions (substrate roughness, chute slope and channel
width)can be modified to generate a wide range of reproducible natural flow
conditions44. For the experiments reported in this study, we used the small
hopper of 0.7 m3to generate fully turbulent expe rimental PDCs with a basal
bedload region, but without a dense basal underflow, which would form at
the high discharge rates in the large hopper setup condition.
The use of pyroclastic solids material and air is an important pre-
requisite to generate natural stress coupling between the fluid and solid
Fig. 10 | The effects of gas-particle feedbacks on pyroclastic density current
hazards. a Schematic presentation of the processes of turbulent gas-particle feed-
back in PDCs at the scale of an idealized eddy at three different times. For the
polydisperse multiphase flow, the spectrum of concurrent behaviours of particles
with different degrees of coupling to turbulent fluid motion is illustrated for particles
with three different particle Stokes numbers St.Left eddy: initial stage where all
particles are homogenously dispersed. Middle eddy: intermediate stage, after the
overturn time of the largest coherent turbulence structure. St ~ 1 particles pre-
ferentially cluster on eddy margins, while St « 1 particles remain homogenously
dispersed following turbulence motion and St » 1 particles move unhindered by
turbulence. Right eddy: later stage, when clusters of dominantly St ~ 1 particles
decouple from eddy margins and sediment as mesoscale turbulence clusters.
bExample of the damage effects of clustering-enforced dynamic loading pressure
P
dusty gas
as repeated high-pressure impacts at the frequency fεmax .cExample of the
piercing damage effects of the direct impact of high St particles or particle clusters
with structures generating pockmarks on the upstream face of a concrete pole.
dSchematic probability density function of dynamic pressure P
dyn
relative to the
average dynamic pressure

Pdyn concurrently considered in hazard assessments. The
dynamic pressure of the continuum dusty gas phase P
dusty gas
exceeds the average
pressure by one order of magnitude. The dynamic pressure associated with particle
impacts P
impact
exceeds the average dynamic pressure by two orders of magnitude.
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phases. The pyroclastic material, containing particle sizes from 2 µm to
16 mm, consists of a mixture of two well-characterized ignimbrite deposits
F1 and F2 from the 232 CE Taupo eruption47.Thefirst component (F1) is a
proximal medium-ash-dominated ignimbrite deposit with a unimodal
grain-size distribution, a median diameter of 366 µm, and 4.5 wt.% of
extremely fine ash (<63 µm). The second component (F2) is a fine ash rich
facies from the base of the proximal Taupo ignimbrite deposit with a
polymodal grain-size distribution, a median diameter of 103 µm, and 36.5
wt.% of extremely fine ash. The experiments reported in this study involve a
material blend with F1 = 60 wt.% and F2 = 40 wt.% (the grain-size dis-
tribution is shown in Supplementary Fig. 2a) yielding a mixture with 20
wt.%ofparticlessmallerthan63µm.Themainsolidscomponentsofthe
pyroclastic material are highly vesicular pumice, glass shards, free crystals
and lithic particles. The relative proportion of these components vary with
grain-size. The average particle density as a function of particle diameter is
showninSupplementaryFig.2b.
The resulting experimental pyroclastic density currents are fully tur-
bulent with Reynolds numbers in the lower 106(and up to 107in proximal
regions). Dimensionless products quantifying the scaling similarity of nat-
ural and experimental currents for the bulk flow are depicted in Supple-
mentary Table 1. Further details of the experimental protocol,propertiesthe
volcanic material, and measurement techniques are reported in ref. 44,but
the measurements and analytical methods specific to the results presented
here are detailed below.
Sensors and analytical methods
Twenty fast cameras (60–120 frames per second) and three normal-speed
cameras (24–30 frames per second) positioned at different distances and
viewing angles, recorded the downstream propagation of the experimental
pyroclastic density currents. At flow distances of 1.8 m, 3.35 m, 5.4 m, and
9.6 m, four highspeed camera profiles consisting of six highspeed cameras
recorded vertical profiles of the passing flows at 500 frames per second. LED
floodlight arrays were used to achieve sufficient and even illumination,
which allowed for a detailed analysis of the gas-particle transport and
sedimentation with particle image analysis (PIV; using the algorithm
PIVlab60). Two-dimensional velocity fields were derived with PIV from the
highspeed videos at time intervals of 2 ms.
Timeseries of dynamic pressure P
dyn
(t) were measured with piezo-
electric pressure sensors (PCB Piezotronics 106B51 and signal conditioners
PCB 483 C) at the flow centerline, at flowdistancesof1.8m,3.35m,5.4m,
9.6 m, 16 m, and 20 m from impact and were recorded at a sampling rate of
1 kHz. The sensors consist of a quartz crystal encapsulated in a solid steel
casing. The deformation of the steel casing due to pressure variations is
transferred to the quartz crystal, which induces a voltage that is directly
recorded as calibrated dynamic pressure signal. In our experiments, we
exposed only the frontal face of the sensor to the flow. This frontal face is
covered by a circular, 15.7 mm diameter, frontal steel diaphragm. The
sensors were mounted into 0.1 m-long bullet-shaped sensor mounts to
reduce flow separation at the upstream-directed sensor head. The encased
pressure sensors protruded out of 1.8 m-heigh wing-shaped profiles
designed to reduce flow separation behind the profiles and to guide cabling.
In this study, we report the results of dynamic pressure measurements
obtained at approximately the mid-depth of the density current body region
at a slope-normal height z=0.45m above the flow base. Supplementary
Note 1 and Supplementary Fig. 3 show a comparison of the measured
dynamic pressure signals due to the forces of impacts of individual particles
with the sensor with theoretical estimates of impact pressures for the cases of
purely elastic and purely inelastic collisions. For the case of inelastic particle
collisions, the particle collision time is given by the ratio of the diameter of
the particle colliding with the sensor and the velocity of impact. Due to the
fast response time of the dynamic pressure sensors of 12 μsand taking a
typical flow velocity of 8 ms−1as reference, collisions of particles larger than
c. 100 μmcan be detected in our experiments.
To test the sensor response to particle impacts, we conducted addi-
tional laboratory-scale experiments using a particle gun and spherical glass
beads with three different ranges in particle diameter. The particle gun
consists of a 1 m long, 0.01 m diameter steel pipe connec ted to a compressed
air line. The air velocity was regulated through an inlet air-pressure valve
and the gas velocity was measured with a hotwire anemometer. A funnel
system in the particle gun allows the feeding of individual particles and
mixtures of particles into the airstream. The dynamic pressure sensor was
positioned 2 cm in front of the particle gun. Collision experiments were
performed with individual, spherical glass bead particles with particle dia-
meters of 170–180 µm, 300–355 µm and 400 µm and the pressure signal was
recordedatthesamesamplingrateof1kHzasinthelarge-scaleexperi-
ments. Particles were fed into the particle gun when the transient signal of
the piezoelectric dynamic pressure sensor due to the dynamic pressure of the
airflow had decayed to a zero Pascal baseline. This allowed an analysis of the
recorded dynamic pressure signal associated with the impact force of a
particle colliding with the sensor without removing the component of
dynamic pressure corresponding to the air flow alone.
As detailed in Supplementary Note 1 and Supplementary Fig. 3, the
signals of dynamic pressure recorded by the dynamic pressure sensors due
to the force of a particle colliding with the sensor diaphragm is the impact
force distributed over the surface area of the particle impact (i.e, the cross-
sectional area of the particle). This is different from a piezoelectric force
sensor where the force is distributed over the entire surface of the sensor
head. In Supplementary Note 1 and Supplementary Fig. 3 it is also shown
that the particle collisions with the dynamic pressure sensor are close to and
well approximated as purely inelastic collisions.
At flow distances of 0.5 m, 1.8 m, 3.35 m, 5.4 m, 9.6 m, 12 m, 16 m, and
20 m from impact vertical arrays of transparent sediment samplers collected
the flowing mixture. During the experiment, the sequential filling the flow
samplers was filmed with highspeed cameras. These samplers are open on
the upstream side allowing the flow to enter through the 1.69 cm2cross-
sectional area while on the downstream side, a 16 microns mesh allows only
the gas-phase of the flow to exit, leading to accumulation of the transported
particles inside the sampler. From this we measure continuous data of flow
sediment passing a position as a function of time. Downslope velocity
components u(t) of the flow at a position 5 cm upstream of each flow
sampler were obtained through PIV. The weight and density of the material
deposited inside the flow samplers was measured at selected time intervals to
calculate the time-variant porosity of the captured sediment, as well as the
sediment grain-size distribution. Particle solids-concentration C
S
are
defined as
Csz;tðÞ¼
Vdð1εÞ
uA
otð9Þ
where V
d
is the time-variant sediment accumulated volume inside the flow
sampler, uis the time-variant downslope velocity obtained through PIV at
the entrance of the flow sampler, A
0
is the cross-sectional area of the flow
sampler, tthe selected time intervals, εthe time-variant sediment porosity,
and zthe height in slope-perpendicular direction.
At each of the flow sampler locations, time-variant and height-variant
temperature T(z, t) is measured in vertical arrays of fast thermocouples (410-
345 Type K) with a sampling rate of 70 Hz. The response time of the
thermocouples is approximately 1 millisecond and hence faster than the
sampling rate. Together with the time-series of time-variant and height-
variant flow velocity u(z, t), grain-size distributions, volumetric particle
concentrations C
S
(z, t), the temperature time-series allow for the calculation
of dynamic pressure P
dyn_Bernoulli
defined by Eq. (1)wherebulkflow density
ρCz;tðÞis given by
ρC¼CSρPþPa
γgRgT1CS
 ð10Þ
where ρPistheparticledensity,P
A
is the ambient pressure, γgis the mass
fraction of the gas components (including moisture) and R
g
is their gas
constants.
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Energy spectra
For the computation of discrete Fourier spectra, the NumPy FFT function of
ref. 61. is used. From the complex output provided by the FFT functions only
the real part is used. Due to the symmetry of the Fourier transform and
physical meaning only positive frequencies are considered.
For the calculation of wave numbers, the time axis (t) of the data is
transferred into advected distances (x) by multiplication with time averaged
velocities (x¼
ut). Using the data series as function of advected distance,
Fourier transforms are calculated using the NumPy implementation. Also,
for these spectra only the real and positive part of the output is used.
Multiphase flow simulation of the PELE experiments
Numerical simulations using the Eulerian-Eulerian approach , also known as
the two-fluid method (TFM), were performed to reproduce the experi-
mental currents. We employed the open-source Multiphase Flow with
Interphase eXchanges (MFIX) solver, developed by the National Energy
Technology Laboratory (NETL) within the US Department of Energy. This
technique enables us to solve mass, momentum, and energy equations for
both fluid and solid phases, capturing solid-fluid 4-way coupling. A com-
prehensive description of all equations can be found in ref. 62.
We executed the 3D flow simulation on the ARCHER2 cluster utilizing
1200 CPU cores with 3 Tb of RAM for 15 days, employing the large-eddy-
simulations (LES) with the wall-adapting local eddy-viscosity subgrid model
WALE of ref. 63. to model subgrid turbulence. The initial and boundary
conditions for the simulations were established based on the international
benchmarking and validation exercise for PDC model64 .
The top boundary of the domain is described as a pressure boundary
that creates a stratified “atmosphere”. All other boundaries, except the inlet,
follow the no-slip boundaries for the fluid phase and partial slip for the solid
phase, following the work of ref. 65. The experimental geometry was
uploaded in MFIX as an STL file upon which we created a roughness of
approximately 0.01 m in height to emulate the basal boundary conditions.
The mesh was cut to follow the geometry using the cutcell method62.
The inlet boundary is treated as a mass inflow, where a flux of tem-
perature, fluid and solid concentration and velocity were prescribed. The
continuous grain-size distributions of the experimental mixture was dis-
cretized in five bins of particles with a diameter of 2×10−3m, 5×10−4m,
125×10−6m, 32×10−6m and 8×10−6m. This representation preserves the
mean size diameter D[3,2] (surface-mean diameter) and D[4,3] (volume-
mean diameter) consistent with the experimental counterpart. We also
discretized the solid density distribution into the same respective five bins to
ensure accurate gas-particle coupling in the simulation. In order to match
experiments closely, the inlet used time- and height-variant velocity, con-
centration, grain-size distribution and temperature profiles described
by ref. 66.
At the inlet, we assumed thermal and kinetic equilibria, resulting in
uniform temperature and no-slip velocity across all phases in each inlet
computational cell. However, the numerical simulation captured thermal
and kinetic decoupling, dictated by particle Stokes number as shown in
Fig. 8. Using the finite volume method with a second-order solver and
Superbee limiter, the MFIX solves mass, momentum and energy equations.
This approach allows us to derive the temperature, velocity, and con-
centration fields for the fluid and each solid phase in each computation cell.
The results were saved as binary VTK files, which were loaded in Paraview®
v5.11 using the Talapas HPC at the University of Oregon and subsequently
exported as images. The input and boundary conditions used in the
simulations are summarized in Supplementary table 2.
Data availability
The data generated in this study are available at https://doi.org/10.5281/
zenodo.10725051.
Code availability
The codeused to produce the data analysesof the experimental data is freely
available at https:/ww.python.org. The code used to conduct the large-eddy
resolving multiphase simulation is freely available at https://mfix.netl.doe.
gov/products/mfix/.
Received: 20 October 2023; Accepted: 4 March 2024;
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Acknowledgements
The authorswould like to thank KevinKreutz and Anja Moebisfor assistance
with running the large-scale experiments. This study was partiallysupported
by the Royal Society of New Zealand Marsden Fund(contract no. MAU1902
to GL), the Resilience to Nature’s Challenges National Science Challenge
Fund New Zealand (GNSRNC047 to GL), the New Zealand Ministry of
Business, Innovation and Employment’s Endeavour Fund (contract no.
GNS-MBIE00216 to GL), theKAVLI Institute of Theoretical Physics Program
‘Multiphase Flows in Geophysics and the Environment’(contract no. NSF
PHY-1748958 to EM, GLand JD), the NationalScience Foundation(contract
no. NSF EAR-1926025 to JD) and the National Environment Research
Council UKRI fund (contract no. NERC-IRF NE/V014242/1 to ECPB).
Author contributions
D.U., J.A.,E.B., L.C. and G.L.designed and conducted the experiments.G.L.
and D.U.co-wrote the manuscript, which wasthen revised by allthe authors.
D.U. led theanalysis and interpretationof the experimentaldata with the help
of G.L., E.C.P.B., E.M. and J.R.J., while E.C.P.B. and J.D. conducted and
post-processed the numerical simulations. E.B. and J.A. assisted with the
P.I.V., flow density and grain-size analyses. S.F.J. and G.L. analysed
pockmarks of the Merapi 2010 eruption. G.L. developed the PELE facility
together with J.R.J., E.B. and E.C.P.B.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s43247-024-01305-x.
Correspondence and requests for materials should be addressed to
Daniel H. Uhle.
Peer review information Communications Earth & Environment thanks
Pierfrancesco Dellino, Karim Kelfoun and the other, anonymous, reviewer(s)
for their contribution to the peer review of this work. Primary Handling
Editors: Domenico Doronzo and Joe Aslin. A peer review file is available
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