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magma flow at ionian volcanoes: Application to Pillan
Icarus 226 (2013) 1171–1176
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Near-vertical supersonic and shock-free gas/magma flow at ionian volcanoes: Application to Pillan Enzo Cataldo a,b, Ashley Gerard Davies c,⇑, Lionel Wilson b a
Dipartimento di Geologia e Geotecnologie, Università di Milano Bicocca, IT-20126 Milano, Italy Lancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UK c Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USA b
a r t i c l e
i n f o
Article history: Received 8 January 2013 Revised 28 June 2013 Accepted 29 June 2013 Available online 13 July 2013 Keywords: Io Volcanism Geological processes Jupiter, Satellites
a b s t r a c t In 1997, the Pillan volcano on Io was home to a fierce volcanic eruption that emplaced extensive lava flows and a circular plume deposit. The gas/magma flow issuing from the unresolved vent region appeared to form an almost vertical jet. We consider steady eruptions of gas and magma, and take the vent to be either a fissure or a point source. In the fissure scenario, the upper-conduit flow must reach Mach 1 in the 25– 75 m depth range to produce the vent velocities of 550–600 m/s that are required to explain the observed plume heights. Conduit wall deflections in the range 20–30° from vertical (values referring to the upper meter of the conduit) and 26–30% by mass of incorporated crustal SO2 are also needed. In the pointsource scenario, sonic flow conditions and similar velocities are achieved in the depth range 350–500 m for similar conduit wall deflections and gas mass proportions in the erupting mixture. Probably, the source of the 140-km-high plume imaged in 1997 was either a 6–11 m-wide fissure, active for 14–40 km along strike, or a circular vent 125–216 m in diameter, the former scenario being preferred. Finally, a shock-free conduit flow is more likely to sustain a tall lava fountain in a near-vacuum. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Pillan volcano (244°W, 12°S) on Io was the location of a massive eruption in 1997 that was monitored by instruments on the Galileo spacecraft (McEwen et al., 1998; Davies et al., 2001; Keszthelyi et al., 2001; Williams et al., 2001; Davies, 2007). By September 1997, 3100 km2 of lava flows approximately 10 m thick (Keszthelyi et al., 2001; Williams et al., 2001) and a 400-km diameter circular plume deposit were emplaced during an eruption episode that lasted up to about 5 months. This was followed by the emplacement of additional lava flows that covered the floor of Pillan Patera, another 2500 km2, by March 1998 (Keszthelyi et al., 2001). It is likely that all of these lava flows were fed by a fissure, initially perhaps some 40 km long (Keszthelyi et al., 2001). However, whether a circular or a fissure vent fed the 140-km-high plume (Fig. 1) is not known (Keszthelyi et al., 2001). Conduit and vent geometry play key roles in determining eruption style and conditions, especially the pressure at which the volcanic fluid reaches the surface, and previous modeling at this site (Cataldo et al., 2002) confirmed that supersonic eruption speeds are required to explain the 140-km-high plume imaged by the Solid State Imaging (SSI) experiment aboard the Galileo spacecraft (McEwen et al., 1998). During the early stages of an eruption, both ⇑ Corresponding author. E-mail address: [email protected] (A.G. Davies). 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.06.035
the upper portion of a conduit and the vent region are likely to be characterized by choked flow, a condition where the gas/magma mixture rising through the conduit up to the vent region is not allowed to exceed the velocity of sound in the mixture at those pressures and temperatures. A system of shocks in and/or above the vent will form, thus enabling the gas/magma pressure to decrease to the ambient near-vacuum values, and flow velocity to increase to supersonic (Kieffer, 1982, 1984). Our model addresses the important question of whether or not the gas/magma mixture may be accelerated to supersonic velocities that are sufficiently high to explain the Pillan plume height in the absence of shocks within the upper portion of the conduit/ fissure system and at the vent. While supersonic velocities are reached in the vent, the depth at which the flow becomes sonic (Mach number = 1) must be determined for both fissure and conduit flow. A shock-free acceleration of the erupting mixture beyond the sound velocity threshold is possible only if the following conditions are met. The upper conduit/fissure walls have to flare outwards (Wilson and Head, 1981), and the flaring has to be gradual, with the formation of smooth system walls. Also, the values of the maximum angle of flow deflection at the vent, combined with the vent velocities, will have to explain the deposits surrounding the Pillan site as imaged by Galileo in 1997 (McEwen et al., 1998). Finally, our analysis will establish whether geologically plausible scenarios may result from our assumption of shock-free and supersonic flow at the Pillan volcano.
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Fig. 1. The Pillan eruption plume as viewed by the Solid State Imaging (SSI) system aboard the Galileo spacecraft on 28 June 1997 (Galileo orbit C9). This stretched image shows the near-vertical flow structure described in this paper. Resolution is 6.2 km pixel1. Plume height is 140 km. Image width is 572 km. Part of SSI image ID C9I0015 (green filter).
of the gas/magma mixture at any given depth is not expected to differ significantly from the lithostatic pressure in the crustal rocks, so that there are minimal stresses across conduit walls. Within the vent, energy dissipation processes that are associated with an increase of entropy become less and less likely, and the flow of a gas/magma mixture becomes steadier and increasingly faster. Whether or not a gradual erosion and smoothing of conduit/ fissure walls down to the sonic depth is achieved is likely to depend on the local geology and the duration of the eruptive event. The occurrence of poorly-packed layers of pyroclasts over the upper 50 m of a fissure could make a funnel-shaped vertical profile easier to obtain. In contrast, based on the different erodibility of lavas compared with that of loosely-packed pyroclasts, the occurrence of lava layers intercalated with loosely-packed pyroclasts over the same depth range could hamper the process of obtaining a nozzle that is gradually flaring outwards to the surface, with a potential for shock generation. Hence, we have taken plausible geological scenarios where sonic depths are no deeper than 50 m for a fissure and 350–500 m for a conduit. Conduit scenarios might not be as likely as a fissure due to the higher probability of finding lavas interlayered with loose pyroclasts over a vertical profile that spans a few hundred meters.
2. Method
2.3. Supersonic and shock-free flow of gas and magma through the upper conduit/fissure
2.1. The ascent of gas and magma through the ionian crust As in previous modeling of explosive volcanic activity at this site (Cataldo et al., 2002), rising magma is assumed to incorporate 10–30 wt% liquid or gaseous SO2 from buried crustal deposits. We adopt the crustal volatiles model by Leone et al. (2011), in which SO2 may become available to rising magmas over a range of depths down to 30 km. In long-lived, energetic explosive eruptions, the volatiles being ingested by the magma are already fluid, in the form of pre-existing, horizontally-connected aquifers adjacent to magma chambers or to the dikes connecting such chambers to the surface. The range of depths at which these aquifers occur are dictated by Io’s geothermal gradient. Using Io’s average surface heat flow of 2.4 W m2 (Veeder et al., 1994), SO2 is expected to melt at a depth of 21 km, and becomes a supercritical fluid at a depth of 27 km. The large amounts of crustal volatiles referred to above have a profound effect on the magma fragmentation process. The amount of fragmentation is influenced by a number of factors – mostly the decompression rate as magma ascends, and the rate at which gases escape from the rising magma (outgassing). Volatile-rich, low-viscosity mafic magmas are likely to erupt very explosively (Lautze and Houghton, 2007) due to inertia-driven fragmentation (Namiki and Manga, 2008), and the pressure gradient difference due to the lower acceleration due to gravity than on Earth will cause the fragmentation to occur at a greater depth on Io (Wilson and Head, 1981). 2.2. The geometry of the upper conduit/fissure and its evolution over time During the early stages of an eruption, a conduit/fissure system is likely to be characterized by a parallel-sided geometry (Wilson et al., 1980; Wilson and Head, 1981), with no variation of crosssectional area as a function of depth or time. As the eruption progresses, the combination of erosion of the vent walls and accumulation of pyroclasts around the vent may progressively modify the vent geometry toward that of a De Laval nozzle, a process that is accompanied by a smooth transition to pressure-balanced flow (Wilson and Head, 1981). Under such circumstances, the pressure
We consider semi-steady eruptions of gas and magma from a vent at Pillan. At this ionian volcanic site, eruption of gas and effusion rates were almost certainly variable over a scale of a day or longer (Davies et al., 2007). This daily variability does not prevent us from treating the system as quasi-steady, based on the fact that the timescale for the passage of a given batch of magma through the conduit system, e.g. 2 h for magma rising 30 km at 5 m/ s, is much less than a day. We also model the Pillan vent to be either a fissure or a circular vent, based on the uncertainties mentioned above, and deal with supersonic and shock-free flow of gas and magma over the upper 75-500 m of a volcanic fissure/conduit. The model input parameters are the gas mass proportion in the erupting mixture, the size of the vent, the exit pressure, and the depth at which the flow becomes sonic. Estimated peak volume fluxes of 3.3 104 m3/s (based on an eruption duration of 52 days) and 1.0 104 m3/s (based on an eruption duration of 167 days) (Davies et al., 2007; Davies, 2007) are used to constrain vent areas, and we take a lava eruption temperature of 1500 K (Davies et al., 2001). As regards the fissure scenario, the only parameter that is allowed to vary in order to match the estimated volume fluxes used is fissure length (up to 40 km long), and two values (lower and upper extremes) of fissure width (4 m and 15 m) are considered. Such values fall within the range adopted for modeling explosive volcanic activity at Tvashtar Paterae on Io in November 1999 (Wilson and Head, 2001). Our goal is to determine the maximum angle of flow deflection (from vertical) as a function of depth. To do so, we use conservation of momentum to calculate the rate of change of conduit cross-sectional area A with decreasing depth z:
h i dA=dz ¼ A= qu2 ðdP=dzÞ 1 M 2 þ qg þ f qu2 =2r
ð1Þ
Here, M is the Mach number of the flow, g is the acceleration due to gravity, f is an empirically derived friction factor, r is the conduit radius or fissure half-width, and q, P and u are the density, pressure and velocity of the gas/magma mixture, respectively. We adopt a plausible range of exit pressures for the flow exiting the vent at Pillan (0.005–10 MPa) and specify a range of pressure gradients within the conduit starting from an assumed maximum depth (500 m) at which the flow regime is taken to change from subsonic to
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Table 1 Fissure scenarios involving shock-free supersonic flow of gas and magma over the uppermost portions of the ionian crust, obtained by modifying the adjustable parameters of the model, i.e. gas proportion in the erupting mixture (n), vent pressure (Pv), sonic depth (SD) and fissure width (W). Fissures lengths (L) are up to 40 km and widths 4–15 m. Results were constrained through inferred minimum and maximum peak volume fluxes (V) of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) in the vent is 1500 K. U is eruption speed, M is Mach number and h is slope of conduit wall. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. W (m)
a
L (m)
V (m3 s1)
n (mass%)
Pv (kPa)
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
h at 9–10 m (°)
h at SD (°)
SD (m)
Variable gas content and vent pressure 4.0 40,000 1.0 104 4.0 40,000 3.9 103a 5.0 40,000 1.0 104 5.0 40,000 1.0 104 5.0 40,000 6.7 103a 5.0 40,000 3.3 104
25.0 30.0 10.0 20.0 30.0 30.0
19.7 7.0 9.6 12.3 9.7 65.7
1606.1 1703.2 1569.1 1634.1 1731.0 1599.6
463.3 617.7 344.2 473.9 606.9 440.7
2.1 2.6 2.5 2.4 2.5 1.8
13.9 30.0 30.0 25.5 30.0 5.6
2.3 1.7 2.6 2.8 2.6 2.6
0.3 0.3 0.3 0.3 0.3 0.3
25.0 25.0 50.0 50.0 50.0 50.0
Variable fissure size and SD 7.0 28,485 1.0 104 7.0 31,325 1.0 104 10.0 13,794 1.0 104 10.0 15,816 1.0 104 15.0 19,475 3.3 104 15.0 20,934 3.3 104
30.0 30.0 30.0 30.0 30.0 30.0
15.0 14.4 22.6 21.4 35.8 34.9
1697.7 1651.1 1667.8 1625.2 1664.1 1638.4
586.4 555.5 561.9 518.2 553.5 528.9
2.4 2.3 2.3 2.1 2.3 2.2
30.0 30.0 30.0 30.0 30.0 30.0
1.4 0.8 6.4 5.7 4.1 9.4
0.3 0.3 0.3 0.3 0.3 0.3
50.0 25.0 50.0 25.0 75.0 50.0
Out-of-range volume flux.
Table 2 Fissure scenarios likely to explain plume observations at the Pillan site. Fissures are 6–11 m in width (W) and up to 40 km in length (L). Results were constrained through previous estimates of minimum and maximum peak volume fluxes (V) of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) is 1500 K in the vent. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. Where only minimum volume fluxes are shown, corresponding maxima (if occurring) are associated with scenarios not explaining plume observations. WSD is width at sonic depth (SD). W (m)
L (m)
V (m3 s1)
n (wt%)
Pv (kPa)
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
h at 20–21 m (°)
h at SD (°)
WSD (m)
SD (m)
6.0 6.0 6.0 6.0 9.0 9.0 9.0 9.0 9.0 11.0 11.0 11.0
37,130 39,619 25,307 40,000 15,636 16,430 17,019 14,680 17,955 34,724 35,867 37,675
1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 3.3 104 3.3 104 3.3 104
26.0 30.0 30.0 30.0 27.0 30.0 30.0 30.0 30.0 28.0 30.0 30.0
12.4 12.4 21.0 13.0 20.4 20.4 20.1 24.0 19.7 25.7 25.7 25.2
1680.0 1712.2 1673.2 1658.3 1681.6 1705.1 1676.3 1663.7 1652.7 1673.6 1688.0 1660.3
552.5 595.8 550.1 563.5 550.0 581.5 569.7 553.2 551.0 551.4 572.0 554.2
2.5 2.5 2.3 2.3 2.4 2.4 2.4 2.3 2.3 2.4 2.4 2.3
30.0 30.0 20.2 28.4 30.0 30.0 30.0 26.2 30.0 30.0 30.0 30.0
1.1 1.1 1.4 0.7 2.1 2.1 2.0 2.1 1.7 2.8 2.8 2.6
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
0.84 0.84 1.28 1.60 1.34 1.34 1.92 2.18 2.52 2.02 2.02 2.80
50.0 50.0 50.0 25.0 75.0 75.0 50.0 50.0 35.0 75.0 75.0 50.0
transonic (M = 1). The shallowest depth at which such a transition is assumed to occur is 25 m. At any given depth, the pressure of the gas/magma mixture is probably not too different from lithostatic, based on the assumption of a long-lived eruption (Wilson et al., 1980; Leone et al., 2011). To calculate the remaining flow parameters that enable us to use Eq. (1) (density and temperature of the gas/magma mixture, sound speed, and ratio of heat capacities), we treat the mixture as a pseudogas (Wallis, 1969; Lu and Kieffer, 2009), i.e., we assume that magma particles move with the gas. We assume that the viscosity of the mixture above the point of fragmentation is the same as the gas viscosity (Dobran, 1992), and calculate the Reynolds number of the flow for both a fissure and a circular vent. Reynolds numbers are used to estimate the friction factor of the flow (Wilson et al., 1980; Gilberti and Wilson, 1990; Dobran, 1992), which finally enables us to compute velocity variations with decreasing depth, du/dz in Eq. (2), by rearranging the conservation of momentum equation. Velocity values are calculated starting from the sound speed value obtained at the depth where the flow regime changes from subsonic to transonic.
du=dz ¼ ½1=ðquÞ dP=dz þ qg þ f qu2 =2r
conduit), based on the maximum angle of repose of loose basaltic materials (35–40°). As regards the fissure case, we do not attempt to model the friction/deflection process at the lateral fissure tips. 2.4. Supersonic and shock-free flow of gas and magma above the vent If no shocks form at and/or immediately above the vent, velocities continue to increase within the erupting fountain. The maximum velocity value must be equal to 709 m/s, if we want to explain the observation of the 140 km high Pillan plume. In order to calculate increasing velocities as a function of decreasing flow pressures and increasing radial distances from the vent, we decrease the pressure in a series of equal steps, starting from the vent value. We assume that the process of gas expansion is near-isothermal (Wilson et al., 1980). If the pressure has decreased to a value PR at a radial distance R from the vent, energy conservation provides the velocity uR of the expanding gas: 0:5
ð2Þ
Once all terms in Eq. (1) are known, we use conduit radius variation with depth to estimate the angle of deflection of the flow as it varies from the surface to the depth where the subsonic to transonic transition occurs. We take this angle to be no larger than 30° from vertical (value averaged over the upper meter of the fissure/
uR ¼ fu2i þ 2½ðnQT i Þ=m ln ðPi =PR Þ þ 2½ð1 nÞðPi PR Þ=qm 2ðgRÞg
ð3Þ where ui is the initial velocity, Pi is the initial pressure, n is the gas mass proportion in the erupting mixture, Q is the universal gas constant, Ti is the constant temperature, m is the molecular weight of SO2 gas and qm is the density of liquid magma.
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Table 3 Eruption scenarios involving shock-free supersonic flow of gas and magma over the uppermost portions of a circular conduit on Io, obtained by modifying the adjustable parameters of the model, i.e. gas proportion in the erupting mixture (n), vent pressure (Pv), sonic depth (SD) and conduit radius (r). All values were constrained through previously inferred minimum and maximum peak volume fluxes of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) is 1500 K in the vent. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. r (m)
V (m3 s1)
Not explaining plume 58.6 1.0 104 66.1 1.0 104 82.5 1.0 104 129.4 3.3 104
n (wt%)
Pv (MPa)
observations 10.0 0.157 20.0 0.177 30.0 0.186 30.0 0.270
Explaining plume observations 27.0 69.4 1.0 104 70.6 1.0 104 30.0 4 30.0 62.4 1.0 10 4 108.1 3.3 10 30.0 30.0 72.5 1.0 104
0.186 0.190 0.257 0.284 0.190
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
1558.4 1617.4 1581.2 1563.7
345.6 482.4 442.0 407.7
2.5 2.4 1.8 1.7
30.0 30.0 30.0 30.0
1661.1 1680.5 1659.0 1652.2 1655.2
559.8 590.3 558.7 555.6 559.0
2.4 2.4 2.3 2.3 2.3
30.0 30.0 20.3 30.0 30.0
At what distance from the vent is the maximum velocity reached? To answer this question, densities and velocities must be related to the radial distance from the vent through the continuity requirement. Mass is conserved if the mass flux leaving the vent equals the mass flux across any surface located at increasing elevations above the vent, as follows (Wilson and Keil, 1997):
M ¼ W v v bv ¼ 2hRv R bR
ð4a; bÞ
where W is the fissure width, vv is the mixture velocity at the vent, bv is the mixture density at the vent, h is the zenith distance (angle from vertical) of the edge of the flow exiting the vent and bR and vR are the mixture density and velocity at the radial distance R from the vent, respectively. Increasing radial distances from the vent are obtained by solving for R in (4b). What is the mean size of the erupted magma droplets likely to decouple from the gas flow at the newly found radial distance values? We assume that a logarithmic distribution of particle sizes characterized the erupting cloud, similar to that assumed for explosive eruptions in the lunar near-vacuum (Wilson and Head, 1981). Gas amounts up to 750 ppm wt% are thought to have driven lunar magmas and erupted particle diameters were in the range 1– 1000 lm (Wilson and Head, 1981). At the Pillan site, the larger amount of volatiles required to drive the 1997 explosive eruption is expected to have further enhanced magma fragmentation at depth, thus leading to even smaller mean particle sizes, an assumption supported by modeling based on Hubble Space Telescope (HST) observations (Jessup and Spencer, 2012). Particles decouple from the gas stream as soon as the gas density has decreased to the point that the mean free path of the gas molecules (here a function of flow pressure only) becomes much larger than the mean particle size (Knudsen and Katz, 1954). The particles cease to be accelerated by the gas and follow ballistic paths to their final landing places on the ionian surface. Finally, the erupted particles must land at a maximum distance from the vent that is consistent with the 400 km diameter fall deposit imaged by Galileo in 1997 (McEwen et al., 1998). This distance is easily calculated and is a function of velocity and the maximum angle of the flow from vertical. 3. Results Results are shown in Tables 1 and 2 for the fissure case, and Table 3 for the point-source scenarios. Tables 1 and 3 illustrate the effects of increasing gas contents and exit pressures on flow velocity, while keeping other flow parameters the same. Also, we show that flow speed is affected by changing sonic depths and fissure width/vent diameter, when the amount of gas in the erupting mixture is held constant. With application to the point-source scenar-
h at 90–91 m (°)
h at 200–201 m (°)
h at SD (°)
r at SD (m)
SD (m)
2.2 2.6
0.1 0.1 0.1 0.1
25.3 29.7 63.2 107.3
500.0 500.0 100.0 100.0
2.7 2.8 2.5 4.2 2.4
0.1 0.1 0.1 0.1 0.1
31.7 32.4 32.0 57.8 38.1
500.0 500.0 500.0 500.0 350.0
1.6 1.9
ios, an increase in vent size (corresponding to an increase in volume flux) always leads to a proportional decrease in flow velocity. Regardless of vent geometry, gas amounts lower than those reported in Tables 1–3 fail to accelerate the erupting mixture from the local sound velocity value (depth at which Mach = 1) to the required minimum vent velocity of 550 m/s. If we keep the amount of gas in the erupting mixture and the depth at which the flow regime transition occurs constant, flaring angles decrease with increasing flow pressure at the vent. Instead, they increase markedly as conduit diameters become larger, for the same vent pressure and keeping other factors constant. Increasing gas mass proportions result in larger vent areas (for a fixed deflection angle) and by decreasing the depth at which the subsonic–transonic transition occurs, vent velocities decrease (for a fixed vent pressure). Moreover, for constant gas mass proportions, vent velocities decrease as vent pressures increase. If the pressure at the vent Pv = 12.4–24.0 kPa, and the gas mass proportion in the erupting mixture n = 0.26–0.30, probably the best fit to plume observations and the most likely conduit scenarios are provided by a fissure which is 6–11 m-wide and 40 to at least 14.7 km-long, respectively. With reference to the 6–11 m wide fissures, the velocity required to explain the 140 km plume height is reached at radial distances from the vent of 17–44 m and flow pressures in the range 3.5–4.7 kPa. Under these conditions, the mean free path of the gas molecules is equal to 8.3 and 6.2 lm, respectively, consistent with the decoupling of magma droplets which are much smaller in size. Recently, a population of particles 0.035–0.12 lm in size (mean value) has been suggested for the 1997 Pillan eruption plume (Jessup and Spencer, 2012), which adds support to our results. Consistent with Galileo data, the erupted particles are found to land at radial distances of 180–240 km from the vent, the lower value referring to the smallest angle of flow deflection at the vent (Table 2). In line with expectations, the larger the volume flux and the gas mass proportion in the erupting mixture, the longer the length of fissure involved in the eruption. Only volume fluxes at the lower end of the peak estimate are consistent with the 6-m scenario, so we take this value of fissure width as the minimum possible. With reference to the 6 and 11 m wide fissures, the subsonic–transonic flow transition must occur at depths of 25–75 m, where the conduit is found to be 0.8–1.6 m and 2.0–2.8 m in width, respectively. The angles of flow deflection from the vertical obtained, referring to the last meter of the conduit, are 20° and 30° and accelerate the erupting mixture to vent velocities of 550–596 m/s and final velocities of 709 m/s, which are consistent with observed plume heights, if we take the pyroclasts above the vent to follow ballistic trajectories back to the surface (Wilson and Head, 1981).
E. Cataldo et al. / Icarus 226 (2013) 1171–1176
Wall deflection angles of 2° from vertical are reached at depths of 12–25 m. If we take the vent to be a point source and the depth of the subsonic–transonic flow transition to be between 350 and 500 m, exit velocities of 556–590 m/s are obtained for a similar range of flaring angles and gas mass proportions in the erupting mixture. Interestingly, the largest velocity value obtained for a volume flux of 3.3 104 m3 s1 reaches 555.6 m/s. The 709 m/s velocity value is reached at radial distances from the vent of 428–883 m, mostly depending on whether the lower or the upper limit peak volume flux is considered. The mean free path values range between 0.56 and 0.98 lm – smaller than in the fissure case – which implies that even smaller particles could decouple from the gas stream, keeping other flow parameters the same. The distances at which particles land on the ionian surface are similar to those found in the fissure scenarios, the lowest value occurring at the lowest angle of flow deflection at the vent (Table 3). The exit pressures, of order 0.19– 0.28 MPa, are found to be larger than their fissure counterparts and vent diameters lie in the range 125–216 m, depending on whether lower- or upper-limit peak volume fluxes are used to constrain vent areas. Corresponding wall deflection angles of 2.0° from vertical are obtained at depths of 230–250 m and 320 m for the largest volume fluxes. Other fissure/conduit geometries could explain plume observations. Yet, if we want the assumption of constant pressure gradients (with respect to depth) to hold, exit velocities must be allowed to decrease below the 550 m/s threshold. For all scenarios and with special reference to the fissure case, the maximum velocity of 709 m/s is reached at a short distance above the vent. If we allow vent velocities to be lower than 550 m/s, the mixture exiting the vent will have to travel a longer distance within the erupting fountain in order to be accelerated to the maximum velocity. Moreover, while keeping other factors constant, the distance from the vent at which the magma and the gas will start decoupling will also increase. Based on these arguments, the results presented here, though not unique, are most favoured. Based on these results, the Pillan vent could be either a fissure or a discrete, localized point source. Yet, the demonstrated strong dependence of exit velocities on volume flux combined with the wall angles requirements in the 200–350 m depth range could weaken the point-source case. Having said this, on Earth, the majority of eruptions initially issuing from a fissure show a trend toward a progressive concentration over time of individual events at one or more discrete locations along the fissure, and this might also be the case for the Pillan volcanic center. 4. Discussion There are various issues with which we have not dealt in detail. The erupting gas/magma mixture is assumed to contain 10–30 mass% of SO2 gas, resulting from the interaction of magma and crustal volatile deposits over an unspecified range of depths. Yet, the temperature at the vent is taken to be constant (1500 K), which implies the existence of a range of temperature gradients over the same depth interval down to the sonic section of the conduit, as shown in the tables. In future work, we should explore the thermodynamic and fluid dynamic conditions in the flow upstream of the sonic depth which may explain such an assumption, while specifying a range of depth values at which the interaction between magma and crustal volatiles is more likely to occur. As the gas/magma mixture ascends through the conduit up to the vent, an increasing amount of gas which was originally dissolved in the magma is exsolved from it. For the sake of completeness, a future model should also account for both exsolved and dissolved gas species in the magma expressed as a function of decreasing pressures and depths, even if we do not expect this pro-
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cess to significantly affect flow properties, due to the minimal amounts of SO2 gas likely to be originally dissolved in the ionian magma compared with those mixed in as immiscible fluids from the host rocks. Another assumption that must be supported by further arguments is the depth values at which we take the flow regime to change from subsonic to transonic. Although this depth range is regarded as being geologically plausible, a range of fluid-dynamic and thermodynamic conditions, defined over the entire length of the volcanic conduit, would need to be incorporated in any elaboration of the model described here, so as to explain the assumption. In our model, we have shown that, under a plausible range of outflow and geometry conditions, smoothing of transition and gradual erosion can result in supersonic flow through the upper portion of a conduit up to the vent region, leading to dynamics more akin to that of a very efficient jet engine. These smooth flow conditions are far more likely to sustain a hot, tall lava fountain in a near-vacuum than a case where shocks form in the conduit or vent. Notwithstanding our results, the existence of shocks in and above the vent remains a possibility. For the sake of completeness, future work should explore those scenarios within which shocks do form, possibly in response to sudden variations in key flow parameters and/or catastrophic changes in the geometry of the vent. 5. Conclusions We have described a relatively simple model of the ascent of a gas/magma mixture through the upper portions of a conduit characterized by sonic–supersonic flow conditions. This analysis has been applied to the 1997 Pillan volcanic eruption on Io. Our calculations are based on peak volume flux estimates of 1.0 104 m3/s to 3.3 104 m3/s, inferred from Galileo observations of new, extensive lava flow fields, evolving thermal emission, and a 140-km-high volcanic plume. The key parameters affecting eruption speed, as well as the value of the maximum angle of flow deflection from vertical, are the depth at which the sonic–transonic transition occurs, the vent pressure, and the gas mass proportion within the erupting mixture. Increasing the depth at which the flow regime transition occurs causes vent velocities to increase and flaring angles to decrease (for fixed exit pressures and conduit size). Flaring angles decrease with increasing flow pressure, whereas they markedly increase as conduits become larger in width (fissure eruption case) or diameter (circular vent case). Increasing the gas content in the erupting mixture causes the vent to be larger in diameter (if circular) or greater in length (in the case of a fissure, for a fixed fissure width), while keeping the angle of flow deflection the same. Importantly, we obtain vent velocities that appear to explain plume imagery of the June 1997 Pillan plume. Conduit wall deflections in the range 20–30.0° from vertical (values averaged over the last meter of the conduit) and amounts of incorporated SO2 of 26– 30% by mass are required to accelerate the erupting mixture to vent velocities of 550–600 m/s and final velocities of 709 m/s, if we model the vent to be a 6–11-m-wide fissure. These vent velocities, which are consistent with the 140-km-high Pillan plume, are obtained if we take the pressure at the vent to be in the range 12.4–25.7 kPa and the flow regime transition to occur at a depth of 25–75 m. Alternatively, similar velocities and flaring angles are obtained if we take the vent to be circular in shape, although this is true only for lower end of the peak volume flux range and requires that the sonic depth lies in the 350–500 m range. Based on these arguments, and the likelihood that the 1997 Pillan eruption emanated from a fissure that was a continuation of a fault running across a nearby mountain block (Williams et al., 2001), a fissure vent is our preferred scenario.
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Importantly, the absence of sub-surface shocks in explosive eruptions is more likely to sustain steady lava fountains on Io, and also on Mars. This impacts the modeling of jets on Io and the interpretation of images of martian lava fountain deposits. Acknowledgments We are grateful for the constructive comments of reviewers. AGD is supported by a grant from the NASA Geology and Geophysics Program. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. Ó2013 Caltech. All rights reserved. References Cataldo, E., Wilson, L., Lane, S., Gilbert, J., 2002. A model for large-scale volcanic plumes on Io: Implications for eruption rates and interactions between magmas and near-surface volatiles. J. Geophys. Res. 107 (E11). http://dx.doi.org/10.1029/ 2001JE001513.5109. Davies, A.G., 2007. Volcanism on Io: A Comparison with Earth. Cambridge University Press, Cambridge, UK, 376pp. Davies, A.G. et al., 2001. Thermal signature, eruption style, and eruption evolution at Pele and Pillan on Io. J. Geophys. Res. 106, 33079–33104. Davies, A.G., Wilson, L., Keszthelyi, L.P., Williams, D.A., 2007. Lava flow emplacement at Pillan, Io in 1997: Implications for massive basaltic flow emplacement on Earth and Mars. Eos Trans. AGU 88(52) (Fall Suppl.) #P34A-08. Dobran, F., 1992. Non-equilibrium flow in volcanic conduits and application to the eruptions of Mt. St. Helens on May 18, 1980 and Vesuvius in AD 79. J. Volcanol. Geotherm. Res. 49, 285–311. Gilberti, G., Wilson, L., 1990. The influence of geometry on the ascent of magma in open fissures. Bull. Volcanol. 52, 515–521. Jessup, K.L., Spencer, J.R., 2012. Characterizing Io’s Pele, Tvashtar and Pillan plumes: Lessons learned from Hubble. Icarus 218, 378–405. Keszthelyi, L.P. et al., 2001. Imaging of volcanic activity on Jupiter’s moon Io by Galileo during GEM and GMM. J. Geophys. Res. 106, 33025–33052.
Kieffer, S.W., 1982. Dynamics and thermodynamics of volcanic eruptions: Implications for the plumes on Io. In: Morrison, D. (Ed.), Satellites of Jupiter. Univ. of Arizona Press, Tucson, pp. 647–723. Kieffer, S.W., 1984. Factors governing the structure of volcanic jets. In: Explosive Volcanism: Inception, Evolution and Hazards. Natl. Acad. Sci. Press, Washington, DC, pp. 143–157. Knudsen, J.G., Katz, D.L., 1954. Fluid Dynamics and Heat Transfer. McGraw Hill, New York, NY, 243pp. Lautze, N.C., Houghton, B.F., 2007. Linking variable explosion style and magma textures during 2002 at Stromboli volcano, Italy. Bull. Volcanol. 69, 445– 460. Leone, G., Wilson, L., Davies, A.G., 2011. The geothermal gradient of Io: Consequences for lithosphere structure and volcanic eruptive activity. Icarus 211, 623–635. Lu, X., Kieffer, S.W., 2009. Thermodynamics and mass transport in multicomponent, multiphase H2O systems of planetary interest. Annu. Rev. Earth Planet. Sci. 37, 449–477. McEwen, A.S. et al., 1998. Active volcanism on Io as seen by Galileo SSI. Icarus 135, 181–219. Namiki, A., Manga, M., 2008. Transition between fragmentation and permeable outgassing of low viscosity magmas. J. Volcanol. Geotherm. Res. 169, 48–60. Veeder, G.J., Matson, D.L., Johnson, T.V., Blaney, D.L., Goguen, J.D., 1994. Io’s heat flow from infrared radiometry: 1983–1993. J. Geophys. Res. (Planets) 99 (E8), 17095–17162. Wallis, G.B., 1969. Introduction. In One-Dimensional Two-Phase Flow. McGraw-Hill, New York (408pp.), pp. 3–17. Williams, D.A., Davies, A.G., Keszthelyi, L.P., Greeley, R., 2001. The summer 1997 eruption at Pillan Patera on Io: Implications for ultrabasic lava flow emplacement. J. Geophys. Res. 106, 33105–33120. Wilson, L., Head, J.W., 1981. Ascent and eruption of basaltic magma on the Earth and Moon. J. Geophys. Res. 86 (B4), 2971–3001. Wilson, L., Head, J.W., 2001. Lava fountains from the 1999 Tvashtar Catena fissure eruption on Io: Implications for dike emplacement mechanisms, eruption rates, and crustal structure. J. Geophys. Res. 106, 32997–33004. Wilson, L., Sparks, R.S.J., Walker, G.P.L., 1980. Explosive volcanic eruptions – IV. The control of magma properties and conduit geometry on eruption column behaviour. Geophys. J. R. Astron. Soc. 63, 117–148. Wilson, L., Keil, K., 1997. The fate of pyroclasts produced in explosive eruptions on the asteroid 4 Vesta. Meteorit. Planet. Sci. 32, 813–823.
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Near-vertical supersonic and shock-free gas/magma flow at ionian volcanoes: Application to Pillan Enzo Cataldo a,b, Ashley Gerard Davies c,⇑, Lionel Wilson b a
Dipartimento di Geologia e Geotecnologie, Università di Milano Bicocca, IT-20126 Milano, Italy Lancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UK c Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USA b
a r t i c l e
i n f o
Article history: Received 8 January 2013 Revised 28 June 2013 Accepted 29 June 2013 Available online 13 July 2013 Keywords: Io Volcanism Geological processes Jupiter, Satellites
a b s t r a c t In 1997, the Pillan volcano on Io was home to a fierce volcanic eruption that emplaced extensive lava flows and a circular plume deposit. The gas/magma flow issuing from the unresolved vent region appeared to form an almost vertical jet. We consider steady eruptions of gas and magma, and take the vent to be either a fissure or a point source. In the fissure scenario, the upper-conduit flow must reach Mach 1 in the 25– 75 m depth range to produce the vent velocities of 550–600 m/s that are required to explain the observed plume heights. Conduit wall deflections in the range 20–30° from vertical (values referring to the upper meter of the conduit) and 26–30% by mass of incorporated crustal SO2 are also needed. In the pointsource scenario, sonic flow conditions and similar velocities are achieved in the depth range 350–500 m for similar conduit wall deflections and gas mass proportions in the erupting mixture. Probably, the source of the 140-km-high plume imaged in 1997 was either a 6–11 m-wide fissure, active for 14–40 km along strike, or a circular vent 125–216 m in diameter, the former scenario being preferred. Finally, a shock-free conduit flow is more likely to sustain a tall lava fountain in a near-vacuum. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Pillan volcano (244°W, 12°S) on Io was the location of a massive eruption in 1997 that was monitored by instruments on the Galileo spacecraft (McEwen et al., 1998; Davies et al., 2001; Keszthelyi et al., 2001; Williams et al., 2001; Davies, 2007). By September 1997, 3100 km2 of lava flows approximately 10 m thick (Keszthelyi et al., 2001; Williams et al., 2001) and a 400-km diameter circular plume deposit were emplaced during an eruption episode that lasted up to about 5 months. This was followed by the emplacement of additional lava flows that covered the floor of Pillan Patera, another 2500 km2, by March 1998 (Keszthelyi et al., 2001). It is likely that all of these lava flows were fed by a fissure, initially perhaps some 40 km long (Keszthelyi et al., 2001). However, whether a circular or a fissure vent fed the 140-km-high plume (Fig. 1) is not known (Keszthelyi et al., 2001). Conduit and vent geometry play key roles in determining eruption style and conditions, especially the pressure at which the volcanic fluid reaches the surface, and previous modeling at this site (Cataldo et al., 2002) confirmed that supersonic eruption speeds are required to explain the 140-km-high plume imaged by the Solid State Imaging (SSI) experiment aboard the Galileo spacecraft (McEwen et al., 1998). During the early stages of an eruption, both ⇑ Corresponding author. E-mail address: [email protected] (A.G. Davies). 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.06.035
the upper portion of a conduit and the vent region are likely to be characterized by choked flow, a condition where the gas/magma mixture rising through the conduit up to the vent region is not allowed to exceed the velocity of sound in the mixture at those pressures and temperatures. A system of shocks in and/or above the vent will form, thus enabling the gas/magma pressure to decrease to the ambient near-vacuum values, and flow velocity to increase to supersonic (Kieffer, 1982, 1984). Our model addresses the important question of whether or not the gas/magma mixture may be accelerated to supersonic velocities that are sufficiently high to explain the Pillan plume height in the absence of shocks within the upper portion of the conduit/ fissure system and at the vent. While supersonic velocities are reached in the vent, the depth at which the flow becomes sonic (Mach number = 1) must be determined for both fissure and conduit flow. A shock-free acceleration of the erupting mixture beyond the sound velocity threshold is possible only if the following conditions are met. The upper conduit/fissure walls have to flare outwards (Wilson and Head, 1981), and the flaring has to be gradual, with the formation of smooth system walls. Also, the values of the maximum angle of flow deflection at the vent, combined with the vent velocities, will have to explain the deposits surrounding the Pillan site as imaged by Galileo in 1997 (McEwen et al., 1998). Finally, our analysis will establish whether geologically plausible scenarios may result from our assumption of shock-free and supersonic flow at the Pillan volcano.
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Fig. 1. The Pillan eruption plume as viewed by the Solid State Imaging (SSI) system aboard the Galileo spacecraft on 28 June 1997 (Galileo orbit C9). This stretched image shows the near-vertical flow structure described in this paper. Resolution is 6.2 km pixel1. Plume height is 140 km. Image width is 572 km. Part of SSI image ID C9I0015 (green filter).
of the gas/magma mixture at any given depth is not expected to differ significantly from the lithostatic pressure in the crustal rocks, so that there are minimal stresses across conduit walls. Within the vent, energy dissipation processes that are associated with an increase of entropy become less and less likely, and the flow of a gas/magma mixture becomes steadier and increasingly faster. Whether or not a gradual erosion and smoothing of conduit/ fissure walls down to the sonic depth is achieved is likely to depend on the local geology and the duration of the eruptive event. The occurrence of poorly-packed layers of pyroclasts over the upper 50 m of a fissure could make a funnel-shaped vertical profile easier to obtain. In contrast, based on the different erodibility of lavas compared with that of loosely-packed pyroclasts, the occurrence of lava layers intercalated with loosely-packed pyroclasts over the same depth range could hamper the process of obtaining a nozzle that is gradually flaring outwards to the surface, with a potential for shock generation. Hence, we have taken plausible geological scenarios where sonic depths are no deeper than 50 m for a fissure and 350–500 m for a conduit. Conduit scenarios might not be as likely as a fissure due to the higher probability of finding lavas interlayered with loose pyroclasts over a vertical profile that spans a few hundred meters.
2. Method
2.3. Supersonic and shock-free flow of gas and magma through the upper conduit/fissure
2.1. The ascent of gas and magma through the ionian crust As in previous modeling of explosive volcanic activity at this site (Cataldo et al., 2002), rising magma is assumed to incorporate 10–30 wt% liquid or gaseous SO2 from buried crustal deposits. We adopt the crustal volatiles model by Leone et al. (2011), in which SO2 may become available to rising magmas over a range of depths down to 30 km. In long-lived, energetic explosive eruptions, the volatiles being ingested by the magma are already fluid, in the form of pre-existing, horizontally-connected aquifers adjacent to magma chambers or to the dikes connecting such chambers to the surface. The range of depths at which these aquifers occur are dictated by Io’s geothermal gradient. Using Io’s average surface heat flow of 2.4 W m2 (Veeder et al., 1994), SO2 is expected to melt at a depth of 21 km, and becomes a supercritical fluid at a depth of 27 km. The large amounts of crustal volatiles referred to above have a profound effect on the magma fragmentation process. The amount of fragmentation is influenced by a number of factors – mostly the decompression rate as magma ascends, and the rate at which gases escape from the rising magma (outgassing). Volatile-rich, low-viscosity mafic magmas are likely to erupt very explosively (Lautze and Houghton, 2007) due to inertia-driven fragmentation (Namiki and Manga, 2008), and the pressure gradient difference due to the lower acceleration due to gravity than on Earth will cause the fragmentation to occur at a greater depth on Io (Wilson and Head, 1981). 2.2. The geometry of the upper conduit/fissure and its evolution over time During the early stages of an eruption, a conduit/fissure system is likely to be characterized by a parallel-sided geometry (Wilson et al., 1980; Wilson and Head, 1981), with no variation of crosssectional area as a function of depth or time. As the eruption progresses, the combination of erosion of the vent walls and accumulation of pyroclasts around the vent may progressively modify the vent geometry toward that of a De Laval nozzle, a process that is accompanied by a smooth transition to pressure-balanced flow (Wilson and Head, 1981). Under such circumstances, the pressure
We consider semi-steady eruptions of gas and magma from a vent at Pillan. At this ionian volcanic site, eruption of gas and effusion rates were almost certainly variable over a scale of a day or longer (Davies et al., 2007). This daily variability does not prevent us from treating the system as quasi-steady, based on the fact that the timescale for the passage of a given batch of magma through the conduit system, e.g. 2 h for magma rising 30 km at 5 m/ s, is much less than a day. We also model the Pillan vent to be either a fissure or a circular vent, based on the uncertainties mentioned above, and deal with supersonic and shock-free flow of gas and magma over the upper 75-500 m of a volcanic fissure/conduit. The model input parameters are the gas mass proportion in the erupting mixture, the size of the vent, the exit pressure, and the depth at which the flow becomes sonic. Estimated peak volume fluxes of 3.3 104 m3/s (based on an eruption duration of 52 days) and 1.0 104 m3/s (based on an eruption duration of 167 days) (Davies et al., 2007; Davies, 2007) are used to constrain vent areas, and we take a lava eruption temperature of 1500 K (Davies et al., 2001). As regards the fissure scenario, the only parameter that is allowed to vary in order to match the estimated volume fluxes used is fissure length (up to 40 km long), and two values (lower and upper extremes) of fissure width (4 m and 15 m) are considered. Such values fall within the range adopted for modeling explosive volcanic activity at Tvashtar Paterae on Io in November 1999 (Wilson and Head, 2001). Our goal is to determine the maximum angle of flow deflection (from vertical) as a function of depth. To do so, we use conservation of momentum to calculate the rate of change of conduit cross-sectional area A with decreasing depth z:
h i dA=dz ¼ A= qu2 ðdP=dzÞ 1 M 2 þ qg þ f qu2 =2r
ð1Þ
Here, M is the Mach number of the flow, g is the acceleration due to gravity, f is an empirically derived friction factor, r is the conduit radius or fissure half-width, and q, P and u are the density, pressure and velocity of the gas/magma mixture, respectively. We adopt a plausible range of exit pressures for the flow exiting the vent at Pillan (0.005–10 MPa) and specify a range of pressure gradients within the conduit starting from an assumed maximum depth (500 m) at which the flow regime is taken to change from subsonic to
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Table 1 Fissure scenarios involving shock-free supersonic flow of gas and magma over the uppermost portions of the ionian crust, obtained by modifying the adjustable parameters of the model, i.e. gas proportion in the erupting mixture (n), vent pressure (Pv), sonic depth (SD) and fissure width (W). Fissures lengths (L) are up to 40 km and widths 4–15 m. Results were constrained through inferred minimum and maximum peak volume fluxes (V) of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) in the vent is 1500 K. U is eruption speed, M is Mach number and h is slope of conduit wall. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. W (m)
a
L (m)
V (m3 s1)
n (mass%)
Pv (kPa)
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
h at 9–10 m (°)
h at SD (°)
SD (m)
Variable gas content and vent pressure 4.0 40,000 1.0 104 4.0 40,000 3.9 103a 5.0 40,000 1.0 104 5.0 40,000 1.0 104 5.0 40,000 6.7 103a 5.0 40,000 3.3 104
25.0 30.0 10.0 20.0 30.0 30.0
19.7 7.0 9.6 12.3 9.7 65.7
1606.1 1703.2 1569.1 1634.1 1731.0 1599.6
463.3 617.7 344.2 473.9 606.9 440.7
2.1 2.6 2.5 2.4 2.5 1.8
13.9 30.0 30.0 25.5 30.0 5.6
2.3 1.7 2.6 2.8 2.6 2.6
0.3 0.3 0.3 0.3 0.3 0.3
25.0 25.0 50.0 50.0 50.0 50.0
Variable fissure size and SD 7.0 28,485 1.0 104 7.0 31,325 1.0 104 10.0 13,794 1.0 104 10.0 15,816 1.0 104 15.0 19,475 3.3 104 15.0 20,934 3.3 104
30.0 30.0 30.0 30.0 30.0 30.0
15.0 14.4 22.6 21.4 35.8 34.9
1697.7 1651.1 1667.8 1625.2 1664.1 1638.4
586.4 555.5 561.9 518.2 553.5 528.9
2.4 2.3 2.3 2.1 2.3 2.2
30.0 30.0 30.0 30.0 30.0 30.0
1.4 0.8 6.4 5.7 4.1 9.4
0.3 0.3 0.3 0.3 0.3 0.3
50.0 25.0 50.0 25.0 75.0 50.0
Out-of-range volume flux.
Table 2 Fissure scenarios likely to explain plume observations at the Pillan site. Fissures are 6–11 m in width (W) and up to 40 km in length (L). Results were constrained through previous estimates of minimum and maximum peak volume fluxes (V) of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) is 1500 K in the vent. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. Where only minimum volume fluxes are shown, corresponding maxima (if occurring) are associated with scenarios not explaining plume observations. WSD is width at sonic depth (SD). W (m)
L (m)
V (m3 s1)
n (wt%)
Pv (kPa)
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
h at 20–21 m (°)
h at SD (°)
WSD (m)
SD (m)
6.0 6.0 6.0 6.0 9.0 9.0 9.0 9.0 9.0 11.0 11.0 11.0
37,130 39,619 25,307 40,000 15,636 16,430 17,019 14,680 17,955 34,724 35,867 37,675
1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 1.0 104 3.3 104 3.3 104 3.3 104
26.0 30.0 30.0 30.0 27.0 30.0 30.0 30.0 30.0 28.0 30.0 30.0
12.4 12.4 21.0 13.0 20.4 20.4 20.1 24.0 19.7 25.7 25.7 25.2
1680.0 1712.2 1673.2 1658.3 1681.6 1705.1 1676.3 1663.7 1652.7 1673.6 1688.0 1660.3
552.5 595.8 550.1 563.5 550.0 581.5 569.7 553.2 551.0 551.4 572.0 554.2
2.5 2.5 2.3 2.3 2.4 2.4 2.4 2.3 2.3 2.4 2.4 2.3
30.0 30.0 20.2 28.4 30.0 30.0 30.0 26.2 30.0 30.0 30.0 30.0
1.1 1.1 1.4 0.7 2.1 2.1 2.0 2.1 1.7 2.8 2.8 2.6
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
0.84 0.84 1.28 1.60 1.34 1.34 1.92 2.18 2.52 2.02 2.02 2.80
50.0 50.0 50.0 25.0 75.0 75.0 50.0 50.0 35.0 75.0 75.0 50.0
transonic (M = 1). The shallowest depth at which such a transition is assumed to occur is 25 m. At any given depth, the pressure of the gas/magma mixture is probably not too different from lithostatic, based on the assumption of a long-lived eruption (Wilson et al., 1980; Leone et al., 2011). To calculate the remaining flow parameters that enable us to use Eq. (1) (density and temperature of the gas/magma mixture, sound speed, and ratio of heat capacities), we treat the mixture as a pseudogas (Wallis, 1969; Lu and Kieffer, 2009), i.e., we assume that magma particles move with the gas. We assume that the viscosity of the mixture above the point of fragmentation is the same as the gas viscosity (Dobran, 1992), and calculate the Reynolds number of the flow for both a fissure and a circular vent. Reynolds numbers are used to estimate the friction factor of the flow (Wilson et al., 1980; Gilberti and Wilson, 1990; Dobran, 1992), which finally enables us to compute velocity variations with decreasing depth, du/dz in Eq. (2), by rearranging the conservation of momentum equation. Velocity values are calculated starting from the sound speed value obtained at the depth where the flow regime changes from subsonic to transonic.
du=dz ¼ ½1=ðquÞ dP=dz þ qg þ f qu2 =2r
conduit), based on the maximum angle of repose of loose basaltic materials (35–40°). As regards the fissure case, we do not attempt to model the friction/deflection process at the lateral fissure tips. 2.4. Supersonic and shock-free flow of gas and magma above the vent If no shocks form at and/or immediately above the vent, velocities continue to increase within the erupting fountain. The maximum velocity value must be equal to 709 m/s, if we want to explain the observation of the 140 km high Pillan plume. In order to calculate increasing velocities as a function of decreasing flow pressures and increasing radial distances from the vent, we decrease the pressure in a series of equal steps, starting from the vent value. We assume that the process of gas expansion is near-isothermal (Wilson et al., 1980). If the pressure has decreased to a value PR at a radial distance R from the vent, energy conservation provides the velocity uR of the expanding gas: 0:5
ð2Þ
Once all terms in Eq. (1) are known, we use conduit radius variation with depth to estimate the angle of deflection of the flow as it varies from the surface to the depth where the subsonic to transonic transition occurs. We take this angle to be no larger than 30° from vertical (value averaged over the upper meter of the fissure/
uR ¼ fu2i þ 2½ðnQT i Þ=m ln ðPi =PR Þ þ 2½ð1 nÞðPi PR Þ=qm 2ðgRÞg
ð3Þ where ui is the initial velocity, Pi is the initial pressure, n is the gas mass proportion in the erupting mixture, Q is the universal gas constant, Ti is the constant temperature, m is the molecular weight of SO2 gas and qm is the density of liquid magma.
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Table 3 Eruption scenarios involving shock-free supersonic flow of gas and magma over the uppermost portions of a circular conduit on Io, obtained by modifying the adjustable parameters of the model, i.e. gas proportion in the erupting mixture (n), vent pressure (Pv), sonic depth (SD) and conduit radius (r). All values were constrained through previously inferred minimum and maximum peak volume fluxes of 1.0 104 m3 s1 and 3.3 104 m3 s1, respectively (Davies et al., 2007). Temperature (T) is 1500 K in the vent. The pressure of the magma–gas mixture at the sonic depth is the same as lithostatic. r (m)
V (m3 s1)
Not explaining plume 58.6 1.0 104 66.1 1.0 104 82.5 1.0 104 129.4 3.3 104
n (wt%)
Pv (MPa)
observations 10.0 0.157 20.0 0.177 30.0 0.186 30.0 0.270
Explaining plume observations 27.0 69.4 1.0 104 70.6 1.0 104 30.0 4 30.0 62.4 1.0 10 4 108.1 3.3 10 30.0 30.0 72.5 1.0 104
0.186 0.190 0.257 0.284 0.190
T at SD (K)
U (m/s)
M (#)
h at 0–1 m (°)
1558.4 1617.4 1581.2 1563.7
345.6 482.4 442.0 407.7
2.5 2.4 1.8 1.7
30.0 30.0 30.0 30.0
1661.1 1680.5 1659.0 1652.2 1655.2
559.8 590.3 558.7 555.6 559.0
2.4 2.4 2.3 2.3 2.3
30.0 30.0 20.3 30.0 30.0
At what distance from the vent is the maximum velocity reached? To answer this question, densities and velocities must be related to the radial distance from the vent through the continuity requirement. Mass is conserved if the mass flux leaving the vent equals the mass flux across any surface located at increasing elevations above the vent, as follows (Wilson and Keil, 1997):
M ¼ W v v bv ¼ 2hRv R bR
ð4a; bÞ
where W is the fissure width, vv is the mixture velocity at the vent, bv is the mixture density at the vent, h is the zenith distance (angle from vertical) of the edge of the flow exiting the vent and bR and vR are the mixture density and velocity at the radial distance R from the vent, respectively. Increasing radial distances from the vent are obtained by solving for R in (4b). What is the mean size of the erupted magma droplets likely to decouple from the gas flow at the newly found radial distance values? We assume that a logarithmic distribution of particle sizes characterized the erupting cloud, similar to that assumed for explosive eruptions in the lunar near-vacuum (Wilson and Head, 1981). Gas amounts up to 750 ppm wt% are thought to have driven lunar magmas and erupted particle diameters were in the range 1– 1000 lm (Wilson and Head, 1981). At the Pillan site, the larger amount of volatiles required to drive the 1997 explosive eruption is expected to have further enhanced magma fragmentation at depth, thus leading to even smaller mean particle sizes, an assumption supported by modeling based on Hubble Space Telescope (HST) observations (Jessup and Spencer, 2012). Particles decouple from the gas stream as soon as the gas density has decreased to the point that the mean free path of the gas molecules (here a function of flow pressure only) becomes much larger than the mean particle size (Knudsen and Katz, 1954). The particles cease to be accelerated by the gas and follow ballistic paths to their final landing places on the ionian surface. Finally, the erupted particles must land at a maximum distance from the vent that is consistent with the 400 km diameter fall deposit imaged by Galileo in 1997 (McEwen et al., 1998). This distance is easily calculated and is a function of velocity and the maximum angle of the flow from vertical. 3. Results Results are shown in Tables 1 and 2 for the fissure case, and Table 3 for the point-source scenarios. Tables 1 and 3 illustrate the effects of increasing gas contents and exit pressures on flow velocity, while keeping other flow parameters the same. Also, we show that flow speed is affected by changing sonic depths and fissure width/vent diameter, when the amount of gas in the erupting mixture is held constant. With application to the point-source scenar-
h at 90–91 m (°)
h at 200–201 m (°)
h at SD (°)
r at SD (m)
SD (m)
2.2 2.6
0.1 0.1 0.1 0.1
25.3 29.7 63.2 107.3
500.0 500.0 100.0 100.0
2.7 2.8 2.5 4.2 2.4
0.1 0.1 0.1 0.1 0.1
31.7 32.4 32.0 57.8 38.1
500.0 500.0 500.0 500.0 350.0
1.6 1.9
ios, an increase in vent size (corresponding to an increase in volume flux) always leads to a proportional decrease in flow velocity. Regardless of vent geometry, gas amounts lower than those reported in Tables 1–3 fail to accelerate the erupting mixture from the local sound velocity value (depth at which Mach = 1) to the required minimum vent velocity of 550 m/s. If we keep the amount of gas in the erupting mixture and the depth at which the flow regime transition occurs constant, flaring angles decrease with increasing flow pressure at the vent. Instead, they increase markedly as conduit diameters become larger, for the same vent pressure and keeping other factors constant. Increasing gas mass proportions result in larger vent areas (for a fixed deflection angle) and by decreasing the depth at which the subsonic–transonic transition occurs, vent velocities decrease (for a fixed vent pressure). Moreover, for constant gas mass proportions, vent velocities decrease as vent pressures increase. If the pressure at the vent Pv = 12.4–24.0 kPa, and the gas mass proportion in the erupting mixture n = 0.26–0.30, probably the best fit to plume observations and the most likely conduit scenarios are provided by a fissure which is 6–11 m-wide and 40 to at least 14.7 km-long, respectively. With reference to the 6–11 m wide fissures, the velocity required to explain the 140 km plume height is reached at radial distances from the vent of 17–44 m and flow pressures in the range 3.5–4.7 kPa. Under these conditions, the mean free path of the gas molecules is equal to 8.3 and 6.2 lm, respectively, consistent with the decoupling of magma droplets which are much smaller in size. Recently, a population of particles 0.035–0.12 lm in size (mean value) has been suggested for the 1997 Pillan eruption plume (Jessup and Spencer, 2012), which adds support to our results. Consistent with Galileo data, the erupted particles are found to land at radial distances of 180–240 km from the vent, the lower value referring to the smallest angle of flow deflection at the vent (Table 2). In line with expectations, the larger the volume flux and the gas mass proportion in the erupting mixture, the longer the length of fissure involved in the eruption. Only volume fluxes at the lower end of the peak estimate are consistent with the 6-m scenario, so we take this value of fissure width as the minimum possible. With reference to the 6 and 11 m wide fissures, the subsonic–transonic flow transition must occur at depths of 25–75 m, where the conduit is found to be 0.8–1.6 m and 2.0–2.8 m in width, respectively. The angles of flow deflection from the vertical obtained, referring to the last meter of the conduit, are 20° and 30° and accelerate the erupting mixture to vent velocities of 550–596 m/s and final velocities of 709 m/s, which are consistent with observed plume heights, if we take the pyroclasts above the vent to follow ballistic trajectories back to the surface (Wilson and Head, 1981).
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Wall deflection angles of 2° from vertical are reached at depths of 12–25 m. If we take the vent to be a point source and the depth of the subsonic–transonic flow transition to be between 350 and 500 m, exit velocities of 556–590 m/s are obtained for a similar range of flaring angles and gas mass proportions in the erupting mixture. Interestingly, the largest velocity value obtained for a volume flux of 3.3 104 m3 s1 reaches 555.6 m/s. The 709 m/s velocity value is reached at radial distances from the vent of 428–883 m, mostly depending on whether the lower or the upper limit peak volume flux is considered. The mean free path values range between 0.56 and 0.98 lm – smaller than in the fissure case – which implies that even smaller particles could decouple from the gas stream, keeping other flow parameters the same. The distances at which particles land on the ionian surface are similar to those found in the fissure scenarios, the lowest value occurring at the lowest angle of flow deflection at the vent (Table 3). The exit pressures, of order 0.19– 0.28 MPa, are found to be larger than their fissure counterparts and vent diameters lie in the range 125–216 m, depending on whether lower- or upper-limit peak volume fluxes are used to constrain vent areas. Corresponding wall deflection angles of 2.0° from vertical are obtained at depths of 230–250 m and 320 m for the largest volume fluxes. Other fissure/conduit geometries could explain plume observations. Yet, if we want the assumption of constant pressure gradients (with respect to depth) to hold, exit velocities must be allowed to decrease below the 550 m/s threshold. For all scenarios and with special reference to the fissure case, the maximum velocity of 709 m/s is reached at a short distance above the vent. If we allow vent velocities to be lower than 550 m/s, the mixture exiting the vent will have to travel a longer distance within the erupting fountain in order to be accelerated to the maximum velocity. Moreover, while keeping other factors constant, the distance from the vent at which the magma and the gas will start decoupling will also increase. Based on these arguments, the results presented here, though not unique, are most favoured. Based on these results, the Pillan vent could be either a fissure or a discrete, localized point source. Yet, the demonstrated strong dependence of exit velocities on volume flux combined with the wall angles requirements in the 200–350 m depth range could weaken the point-source case. Having said this, on Earth, the majority of eruptions initially issuing from a fissure show a trend toward a progressive concentration over time of individual events at one or more discrete locations along the fissure, and this might also be the case for the Pillan volcanic center. 4. Discussion There are various issues with which we have not dealt in detail. The erupting gas/magma mixture is assumed to contain 10–30 mass% of SO2 gas, resulting from the interaction of magma and crustal volatile deposits over an unspecified range of depths. Yet, the temperature at the vent is taken to be constant (1500 K), which implies the existence of a range of temperature gradients over the same depth interval down to the sonic section of the conduit, as shown in the tables. In future work, we should explore the thermodynamic and fluid dynamic conditions in the flow upstream of the sonic depth which may explain such an assumption, while specifying a range of depth values at which the interaction between magma and crustal volatiles is more likely to occur. As the gas/magma mixture ascends through the conduit up to the vent, an increasing amount of gas which was originally dissolved in the magma is exsolved from it. For the sake of completeness, a future model should also account for both exsolved and dissolved gas species in the magma expressed as a function of decreasing pressures and depths, even if we do not expect this pro-
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cess to significantly affect flow properties, due to the minimal amounts of SO2 gas likely to be originally dissolved in the ionian magma compared with those mixed in as immiscible fluids from the host rocks. Another assumption that must be supported by further arguments is the depth values at which we take the flow regime to change from subsonic to transonic. Although this depth range is regarded as being geologically plausible, a range of fluid-dynamic and thermodynamic conditions, defined over the entire length of the volcanic conduit, would need to be incorporated in any elaboration of the model described here, so as to explain the assumption. In our model, we have shown that, under a plausible range of outflow and geometry conditions, smoothing of transition and gradual erosion can result in supersonic flow through the upper portion of a conduit up to the vent region, leading to dynamics more akin to that of a very efficient jet engine. These smooth flow conditions are far more likely to sustain a hot, tall lava fountain in a near-vacuum than a case where shocks form in the conduit or vent. Notwithstanding our results, the existence of shocks in and above the vent remains a possibility. For the sake of completeness, future work should explore those scenarios within which shocks do form, possibly in response to sudden variations in key flow parameters and/or catastrophic changes in the geometry of the vent. 5. Conclusions We have described a relatively simple model of the ascent of a gas/magma mixture through the upper portions of a conduit characterized by sonic–supersonic flow conditions. This analysis has been applied to the 1997 Pillan volcanic eruption on Io. Our calculations are based on peak volume flux estimates of 1.0 104 m3/s to 3.3 104 m3/s, inferred from Galileo observations of new, extensive lava flow fields, evolving thermal emission, and a 140-km-high volcanic plume. The key parameters affecting eruption speed, as well as the value of the maximum angle of flow deflection from vertical, are the depth at which the sonic–transonic transition occurs, the vent pressure, and the gas mass proportion within the erupting mixture. Increasing the depth at which the flow regime transition occurs causes vent velocities to increase and flaring angles to decrease (for fixed exit pressures and conduit size). Flaring angles decrease with increasing flow pressure, whereas they markedly increase as conduits become larger in width (fissure eruption case) or diameter (circular vent case). Increasing the gas content in the erupting mixture causes the vent to be larger in diameter (if circular) or greater in length (in the case of a fissure, for a fixed fissure width), while keeping the angle of flow deflection the same. Importantly, we obtain vent velocities that appear to explain plume imagery of the June 1997 Pillan plume. Conduit wall deflections in the range 20–30.0° from vertical (values averaged over the last meter of the conduit) and amounts of incorporated SO2 of 26– 30% by mass are required to accelerate the erupting mixture to vent velocities of 550–600 m/s and final velocities of 709 m/s, if we model the vent to be a 6–11-m-wide fissure. These vent velocities, which are consistent with the 140-km-high Pillan plume, are obtained if we take the pressure at the vent to be in the range 12.4–25.7 kPa and the flow regime transition to occur at a depth of 25–75 m. Alternatively, similar velocities and flaring angles are obtained if we take the vent to be circular in shape, although this is true only for lower end of the peak volume flux range and requires that the sonic depth lies in the 350–500 m range. Based on these arguments, and the likelihood that the 1997 Pillan eruption emanated from a fissure that was a continuation of a fault running across a nearby mountain block (Williams et al., 2001), a fissure vent is our preferred scenario.
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Importantly, the absence of sub-surface shocks in explosive eruptions is more likely to sustain steady lava fountains on Io, and also on Mars. This impacts the modeling of jets on Io and the interpretation of images of martian lava fountain deposits. Acknowledgments We are grateful for the constructive comments of reviewers. AGD is supported by a grant from the NASA Geology and Geophysics Program. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. Ó2013 Caltech. All rights reserved. References Cataldo, E., Wilson, L., Lane, S., Gilbert, J., 2002. A model for large-scale volcanic plumes on Io: Implications for eruption rates and interactions between magmas and near-surface volatiles. J. Geophys. Res. 107 (E11). http://dx.doi.org/10.1029/ 2001JE001513.5109. Davies, A.G., 2007. Volcanism on Io: A Comparison with Earth. Cambridge University Press, Cambridge, UK, 376pp. Davies, A.G. et al., 2001. Thermal signature, eruption style, and eruption evolution at Pele and Pillan on Io. J. Geophys. Res. 106, 33079–33104. Davies, A.G., Wilson, L., Keszthelyi, L.P., Williams, D.A., 2007. Lava flow emplacement at Pillan, Io in 1997: Implications for massive basaltic flow emplacement on Earth and Mars. Eos Trans. AGU 88(52) (Fall Suppl.) #P34A-08. Dobran, F., 1992. Non-equilibrium flow in volcanic conduits and application to the eruptions of Mt. St. Helens on May 18, 1980 and Vesuvius in AD 79. J. Volcanol. Geotherm. Res. 49, 285–311. Gilberti, G., Wilson, L., 1990. The influence of geometry on the ascent of magma in open fissures. Bull. Volcanol. 52, 515–521. Jessup, K.L., Spencer, J.R., 2012. Characterizing Io’s Pele, Tvashtar and Pillan plumes: Lessons learned from Hubble. Icarus 218, 378–405. Keszthelyi, L.P. et al., 2001. Imaging of volcanic activity on Jupiter’s moon Io by Galileo during GEM and GMM. J. Geophys. Res. 106, 33025–33052.
Kieffer, S.W., 1982. Dynamics and thermodynamics of volcanic eruptions: Implications for the plumes on Io. In: Morrison, D. (Ed.), Satellites of Jupiter. Univ. of Arizona Press, Tucson, pp. 647–723. Kieffer, S.W., 1984. Factors governing the structure of volcanic jets. In: Explosive Volcanism: Inception, Evolution and Hazards. Natl. Acad. Sci. Press, Washington, DC, pp. 143–157. Knudsen, J.G., Katz, D.L., 1954. Fluid Dynamics and Heat Transfer. McGraw Hill, New York, NY, 243pp. Lautze, N.C., Houghton, B.F., 2007. Linking variable explosion style and magma textures during 2002 at Stromboli volcano, Italy. Bull. Volcanol. 69, 445– 460. Leone, G., Wilson, L., Davies, A.G., 2011. The geothermal gradient of Io: Consequences for lithosphere structure and volcanic eruptive activity. Icarus 211, 623–635. Lu, X., Kieffer, S.W., 2009. Thermodynamics and mass transport in multicomponent, multiphase H2O systems of planetary interest. Annu. Rev. Earth Planet. Sci. 37, 449–477. McEwen, A.S. et al., 1998. Active volcanism on Io as seen by Galileo SSI. Icarus 135, 181–219. Namiki, A., Manga, M., 2008. Transition between fragmentation and permeable outgassing of low viscosity magmas. J. Volcanol. Geotherm. Res. 169, 48–60. Veeder, G.J., Matson, D.L., Johnson, T.V., Blaney, D.L., Goguen, J.D., 1994. Io’s heat flow from infrared radiometry: 1983–1993. J. Geophys. Res. (Planets) 99 (E8), 17095–17162. Wallis, G.B., 1969. Introduction. In One-Dimensional Two-Phase Flow. McGraw-Hill, New York (408pp.), pp. 3–17. Williams, D.A., Davies, A.G., Keszthelyi, L.P., Greeley, R., 2001. The summer 1997 eruption at Pillan Patera on Io: Implications for ultrabasic lava flow emplacement. J. Geophys. Res. 106, 33105–33120. Wilson, L., Head, J.W., 1981. Ascent and eruption of basaltic magma on the Earth and Moon. J. Geophys. Res. 86 (B4), 2971–3001. Wilson, L., Head, J.W., 2001. Lava fountains from the 1999 Tvashtar Catena fissure eruption on Io: Implications for dike emplacement mechanisms, eruption rates, and crustal structure. J. Geophys. Res. 106, 32997–33004. Wilson, L., Sparks, R.S.J., Walker, G.P.L., 1980. Explosive volcanic eruptions – IV. The control of magma properties and conduit geometry on eruption column behaviour. Geophys. J. R. Astron. Soc. 63, 117–148. Wilson, L., Keil, K., 1997. The fate of pyroclasts produced in explosive eruptions on the asteroid 4 Vesta. Meteorit. Planet. Sci. 32, 813–823.