Coupling of turbulent and non-turbulent flow

SUPPLEMENTARY INFORMATION DOI: 10.1038/NGEO2794 Coupling of turbulent and non-turbulent flow Eric C. P. Breard, Gert Lube, Jim R. Jones, Josef Dufek, Shane J. Cronin, Greg A. Valentine and Anja Moebis Supplementary Fig. 1 Grain-size and particle density distributions of the initial experimental mixture. a, Grain-size distribution of the initial experimental mixture. b, density distribution of the natural volcanic particles composing the experimental mixture. The average particle density is 1950 kg.m -3. NATURE GEOSCIENCE www.nature.com/naturegeoscience 1

Supplementary Fig. 2 Grain-size distributions of the experimental PDC deposits in comparison to natural (ignimbrite) PDC deposits. a, Median grain-size diameter against sorting coefficient of experimental and natural deposits, grouped into fields of layers 1, 2A, 2B and 3 of the so-called standard ignimbrite unit 4. Experimental samples of layers 1, 2A, 2B and 3 were collected in vertical profiles from proximal to distal reaches. The corresponding fields of well-mapped PDC deposits depict the original data compilations of Refs.1 and 2 (Vulsini ignimbrites 1, Terceira ignimbrite 2, Campanian Ignimbrite 2, Atitlan ignimbrite 2, Vilama ignimbrite 2 ), with an addition of data from younger studies on the ignimbrite flow units T1, T2, T3 3,4 and M14 5 from Laacher See, and PDC deposits from the 1991 Unzen 6, 1991 Pinatubo 7 eruptions. b, Sketch of the experimental deposit sequence at 14 m from source highlighting layers 1, 2A, 2B, 2B PCZ (Pumice Concentration Zone) and 3. c, Grainsize distributions of layers 1, 2A, 2B, 2B PCZ and 3 shown in (b) in comparison to grain-size distributions of layers 1, 2A, 2B, and 3 of 12.9 ka ignimbrite T1 from Laacher See at 4.7±0.3 km from source 4 and the 180 166 ka Grotte di Castro ignimbrite at c.10 km from source 8. d, Median grain-size diameter (MdΦ) and sorting coefficient (σφ) of grain-size distributions shown in (b). Note the strong similarities of vertical changes in the grain-size distributions of experimental and natural deposits: the median grain-size diameter at PELE and Laacher See strongly increases from basal layer 1 to the top of layer 2 (0.06 0.25 to 2 mm), while it is relatively constant from layer to layer at Grotti di Castro, but it is characteristically finer grained in layer 3 (0.08 0.1 mm); the sorting decreases upward from layer 1 to layer 2B from poorly sorted to very poorly sorted values, but improves to poorly sorted values in layer 3.

Supplementary Fig.3 Mesoscale turbulence structures in large-scale PDC experiments. Still-images from a high-speed movie of the flow at 3.1 m from the source at 0.06 (a, b) and 0.09 (c, d) seconds after flow front arrival. Mesoscale structures occur in the middle zone of intermediate turbulence and take the form of dentritic clusters of particles. White crosses in (b) and (d), numbered 1 and 2, depict the same features in both images and illustrate the rapid sedimentation of the mesoscale structures at velocities of ~1.7 m.s -1. Vertical white bars are 0.3 m long.

Supplementary Fig. 4 Example of the frequency distribution of the thickness of mesoscale clusters. Thickness frequency distribution of mesoscale clusters measured at the observer location of 3.1 m during a 0.15 second time interval corresponding to the passage of the middle zone of the head and the frontal portion of the body of the ash-cloud. The smallest detectable cluster thickness in high-speed movies is 0.002 m.

Supplementary Fig. 5 Example of the grain-size distribution of the middle zone. Timeaveraged (0.15 second) grain-size distribution of particles transported in the middle zone at 3.1 m from source at a height of 0.3 m above the base during the passage of the head and frontal body regions. Flow sample was retrieved from transparent passive sediment sampler 9.

Parameter Nature PELE Particle diameter 10-6 10-1 10-6 10-2 (m) Particle density 300 2600 300 2600 (kg.m -3 ) Fluid density (kg.m -3 ) 0.6 1.2 1 Dynamic viscosity of the 1x10-5 4x10-3 1x10-5 5x10-3 carrier phase (kg.m -1.s -1 ) Flow velocity (m.s -1 ) 10 200 <2 20 Reynolds number 1x10 4 6.7x10 9 1.5x10 4 2x10 6 Stokes number 1.1x10-3 9.7x10 7 7.4x10-5 4.6x10 4 Stability number 2.8x10-6 9.7x10 9 7.1x10-7 4.6x10 5 Particle Froude number 0.1 20 0.3 10 Richardson number 2x10-4 (-5x10 0 *) 1.1x10 1 0 4.5x10 1 Supplementary Table 1 Bulk flow scaling of Natural PDCs 10 and PELE experimental currents. and are characteristic velocity and length scales of the flow (flow height). is the mixture density and is the ambient medium density. D is the particle diameter. and are the particle and gas densities, respectively. * Estimates of the range of negative values of the Richardson number corresponding to hot PDCs with buoyancy reversal are based on the study of volcanic plume 11 and PDCs 12.

Parameter Nature PELE Particle diameter 10-6 10-1 10-6 10-2 (m) Particle density 300 2600 300 2600 (kg.m -3 ) Fluid density (kg.m -3 ) 0.6 1.2 1 Particle volumetric 30 60 % 40 60 % concentration Dynamic viscosity of the fluid 1*10-5 4*10-5 1*10-5 3*10-5 (kg.m -1.s -1 ) Underflow velocity (m.s -1 ) 10 30 <2 15 Mass number 1*10 2 2*10 3 1*10 2 1.5*10 3 Bagnold number 1*10-2 1*10 2 1*10 0 1*10 2 With Darcy number 1*10 2 1*10 4 1*10 0 1*10 3 Froude number 0.5 10 0.5 5 Savage number 1*10-9 1*10-7 1*10-6 1*10-5 Supplementary Table 2 Underflow scaling of Natural PDCs 13 and PELE experimental currents. With and the particle and gas density, the shear rate, is the gas dynamic viscosity, D the particle diameter, h c the current height, g the acceleration of gravity. c denotes the flow concentration during propagation, c o is the maximum concentration at loose

packing, is the shear rate. k is the permeability of the granular medium. Re p is the particle Reynolds number. Initial conditions Range investigated Drop height (m) 2.5 5 (3) Impact velocity (m.s -1 ) 7 9.9 (7.5) Initial particle concentration of the mixture at 7 10 (9.8) impact (vol.%) Slope angle of the channel (degrees) 9 20 (20) Initial mass of mixture in hopper (kg) 880 1320 (1300) Median grain-size of the initial mixture (µm) 200 365 (250) Quantity of fine ash (>4Φ) in the initial 4.5 15 (10) mixture (wt.%) Supplementary Table 3 Initial and boundary conditions investigated at PELE. Range of experimental parameters investigated in large-scale experiments that led to the formation of the tripartite flow structure presented in this manuscript. Values enclosed in brackets indicate the condition of the experiment described in this manuscript.

Supplementary Note 1: Additional information on mesoscale turbulence clusters Quantitative information on mesoscale turbulence clusters in the middle zone could be derived from a high-speed video sequence recorded at 600 frames per second at 3.1 m from the impact zone. Measurements of mesoscale clusters are restricted to a 0.15 second time interval during the passing of the rear of the head and the frontal body regions. During this time, the time-averaged grain-size distribution of the middle zone has a unimodal form with a median particle diameter of 2.04 Φ and a sorting coefficient of 1.49 Φ (Supplementary Fig. 5). The time-averaged particle concentration of the middle zone is 2 ± 0.2 vol%. The particle concentration inside the mesoscale clusters is considerably higher and ranges between 4 15 vol%, and clusters occupy 10 40 % of the observation area in the middle zone. Mesoscale clusters have a characteristic range of sizes and forms. In the size limit quantifiable in our video footage (> 0.002 m), they occur as elongated and dendritic bands with lengths of 0.01 0.3 m and thicknesses of 0.0035 0.0115 m (mean of 0.0075 ± 0.0015 m (1σ); Supplementary Fig. 4). The frequency distribution of the cluster thicknesses displays a uni-modal and close to Gaussian form (Supplementary Fig. 4). The frequency of mesoscale

clusters passing a static observation point (during the 0.15 second time interval) is 280 clusters per second (280 Hz). Most clusters observed (>0.002 m thick) were already formed prior to their arrival at the observation window. Thus, a maximum time of cluster formation of 0.04 seconds is given by the duration between impact and arrival of the middle zone at the observer location. During the passage of clusters through the 1.2 m long observation window, they typically grow in size by merging during rapid settling. In many cases individual clusters can be followed through the observation window until sedimentation onto the upper surface of the underflow. These observations and measurements highlight a number of differences and similarities to mesoscale structures documented through numerical modelling and experiments on fluidized beds 14,15. In comparably low-velocity fluidized beds, clusters tend to continuously breakup and dissipate. The frequency of mesoscale clusters is significantly lower in the fluidized bed situation (0.2 Hz) 16, although the particle concentration is comparable (5 20 vol.%) 16,17. However, in both fluidized beds and our PDC experiments settling velocities of mesoscale clusters are much higher than individual particle settling velocities 15,17. References cited in Supplementary Material. 1 Sparks, R. S. J. Grain size variations in ignimbrites and implications for the transport of pyroclastic flows. Sedimentology 23, 147-188 (1976). 2 Walker, G. P. L. Grain-size characteristics of pyroclastic deposits. Journal of Geology 79, 696-714 (1971).

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