On Earth, Venus, and Mars Cluded by Using Methods Already Tested in Downloaded from Coarser Grid Physical Models (33)

Home , Nansen (Martian crater), North Polar Basin (Mars)

1 1 I_,S mechanism to help interpret these observa- models. Most of those efforts require contin- Paterson, J. Phys. Oceanogr. 21, 1333 (1991). tions in the future. ued growth in computer 22. J. K. Dukowicz and R. D. Smith, J. Geophys. Res. power. 99, 7991 (1994). At low latitudes, some eddies reorganize 23. A. J. Semtner, in Proceedings of the 1993 Snow- into elongated east-west currents that are REFERENCES AND NOTES mass Global Change Institute on the Global Carbon reminiscent of flows on Jupiter and Saturn. Cycle, T. Wigley, Ed. (Cambridge Univ. Press, Cam- The strong variation of the Coriolis effect 1. S. G. Philander, El Nino, La Nina, and the Southern bridge, in press). Oscillation (Academic Press, San Diego, 1990). 24. R. D. Smith, R. C. Malone, M. Maltrud, A. Semtner, in with latitude in the tropics causes the turbu- 2. S. Manabe and R. J. Stouffer, Nature 364, 215 preparation. lence there to have a preferred orientation. In (1993). 25. R. Bleck, S. Dean, M. OKeefe, A. Sawdey Parallel some southern deep basins, the Antarctic Cir- 3. F. Nansen, Oceanography of the North Polar Basin, Comput., in press. vol. 3 of Science Research (Christiania, Oslo, Nor- 26. D. Stammer and C. W. Boning, J. Phys. Oceanogr. cumpolar Current organizes into four persis- way, 1902). 22, 732 (1992). tent filaments maintained by eddy processes, 4. H. Stommel, The Gulf Stream: A Physical and Dy- 27. W. J. Schmitz and J. D. Thompson, ibid. 23, 1001 rather than being one broad stream. The cur- namical Description (Univ. of Califomia, Berkeley, (1993) rents circling Antarctica are the closest ana- 1965). 28. G. Danabasoglu, J. C. McWilliams, P. R. Gent, Sci- 5. J. C. Swallow and B. V. Harmon, Deep-Sea Res. 6, ence 264,1123 (1994). logs to atmospheric jet streams that can be 155 (1960). 29. V. Zlotnicki, J. McClean, A. J. Semtner, paper pre- found in the ocean: they are maintained by 6. K. Bryan, J. Comput. Phys. 4, 347 (1969). sented at the Annual Fall Meeting of the American similar energy sources related to the latitudi- 7. M. D. Cox, in Numerical Models ofOcean Circulation Geophysical Union, San Francisco, 5 December (National Academy of Sciences, Washington, DC, 1994. nal change of temperature, but their separa- 1975), pp. 107-120. 30. S. Ramp, J. McClean, A. J. Semtner, C. A. Collins, K. tion scale is much smaller by being tied to the 8. H. L. Dantzler, Deep-Sea Res. 23, 783 (1976). A. S. Hays, in preparation. local radius of deformation. These last two 9. W. R. Holland, J. Phys. Oceanogr. 8, 363 (1978). 31. D. Stammer, R. T. Tokmakian, A. J. Semtner, C. situations are ocean realizations of phenome- 10. J. C. McWilliams and J. H. Chow, ibid. 11, 921 Wunsch, in preparation. (1981). 32. P. B. Rhines, J. Fluid Mech. 69, 417 (1975); R. L. na anticipated from idealized turbulence stud- 11. A. J. Busalacchi and J. J. O'Brien, ibid. 10, 1929 Panetta, J. Atmos. Sci. 50, 2073 (1993). ies (32). (1980). 33. E. Maier-Reimer, Global Biogeochem. Cycles 7,645 12. M. D. Cox, ibid. 15,1312 (1985). (1993). 13. J. R. Toggweiler, K. Dixon, K. Bryan, J. Geophys. 34. R. S. Nerem, E. J. Schrama, C. J. Koblinsky, B. D. Challenges for the Future Res. 94, 8217 (1989). Beckley, J. Geophys. Res. 99, 24565 (1994). 14. A. F. Blumberg and G. L. Mellor, Three-Dimensional 35. The most recent modeling efforts discussed here are Evidently, much progress has resulted from Coastal Ocean Models, no. 4 (American Geophysi- funded by the Department of Energy's Office of Health cal Union, Washington, DC, 1987). and Environmental Research under CHAMMP (Com- improving the resolution and hydrodynami- 15. D. B. Haidvogel, J. L. Wilkin, R. E. Young, J. Comput. puter Hardware, Advanced Mathematics, Model Phys- on July 27, 2009 cal formulations of models. Some compari- Phys. 94,151 (1991). ics) and by the National Science Foundation's Physical sons are under way to determine the resolu- 16. R. Bleck and D. B. Boudra, J. Geophys. Res. 91, Oceanography Program under WOCE. The TOPEX sat- tion requirements in different applications, 7611 (1986). ellite data was provided by Caltech's Jet Propulsion 17. The FRAM Group, Eos 72, 169 (1991). Laboratory and the Goddard Space Flight Center such as climate versus forecast uses, and 18. F. 0. Bryan, C. W. Boning, W. R. Holland, J. Phys. through the support of the National Aeronautics and whether isopycnal coordinates are better Oceanogr. 25, 289 (1995). Space Administration. The computational resources for than fixed vertical levels. The two methods 19. A. J. Semtner and R. M Chervin, J. Geophys. Res. the simulations shown in the figures were provided by are probably comparable if the diffusion in 97, 5493(1992). the National Center for Atmospheric Research, Los 20. G. A. Jacobs et al., Nature 370, 360 (1994). Alamos National Laboratory, and the Pittsburgh Super- leveled models is oriented along isopycnals 21. P. D. Killworth, D. Stainforth, D. J. Webb, S. M. computing Center. or if both model grid sizes are well below the local radius of deformation. Hence, future www.sciencemag.org development will probably emphasize im- provements ofphysical components and pro- Numerical Models of cesses in models, such as the surface mixed layer and sea ice, and outflows and mixing Caldera-Scale from water-mass formation regions. Further- Volcanic Eruptions more, biogeochemical processes can be in- on Earth, Venus, and Mars cluded by using methods already tested in Downloaded from coarser grid physical models (33). An immediate goal of modelers is to Susan Werner Kieffer conduct longer term simulations, including some to full thermodynamic equilibrium. Volcanic eruptions of gassy magmas on Earth, Venus, and Mars produce plumes with Ocean models will not be fully proven to be markedly different fluid dynamics regimes. In large part the differences are caused by well formulated until they can reproduce the differing atmospheric pressures and ratios of volcanic vent pressure to atmospheric the equilibrium distributions of tempera- pressure. For each of these planets, numerical simulations of an eruption of magma ture, salinity, and other properties as well as containing 4 weight percent gas were run on a workstation. On Venus the simulated the modem spreading of dissolved anthro- eruption of a pressure-balanced plume formed a dense fountain over the vent and pogenic gases and radioactive tracers. The continuous pyroclastic flows. On Earth and Mars, simulated pressure-balanced plumes likelihood that the ocean is capable of dif- produced ash columns, ash falls, and possible small pyroclastic flows. An overpres- ferent overturning circulations if started sured plume, illustrated for Mars, exhibited a complex supersonic velocity structure and from different initial conditions needs to be internal shocks. examined. The natural variability of climate needs to be determined, including the distinct possibility that limits of climate predictability are affected by oceanic turbu- Calderas are large craters formed by the more of magma (Fig. 1A). A large caldera lence. Finally, a number of past climates and collapse of the summits of volcanoes after eruption, with mass fluxes believed to be potential future climate (including those in- eruptions of tens of cubic kilometers or >108 kg/s, has never been witnessed on fluenced by activities of mankind) should be Earth. Such "caldera-scale" The author is in the Department of Geological Sciences, eruptions can investigated with the aid of high-quality University of British Columbia, Vancouver, British Colum- produce plumes that reach the stratosphere atmospheric models coupled to global ocean bia V7W 2H9, Canada. as well as ash flows (so-called ignimbrite

SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 1385 sheets) that cover thousands of square kilo- ment methodology. Such models can guide effects that exist on other planets (10-17). meters. A well-known example is the Valles field observations, and in turn there is an Going beyond the parametric models is caldera and its deposits that cover most of ongoing need for more observations and for conceptually and computationally difficult northern New Mexico (Fig. 1A). more ways to test the simulations. Planetary because planetary volcanism occurs in a Calderas have been observed on other observations can serve several purposes wide variety of geologic and atmospheric planetary bodies such as Mars (Fig. 1B) and here: The models can guide interpretations conditions (Table 1). Atmospheric temper- Venus. Indeed, on lo, a moon ofJupiter, the of remote sensing data, and the data in turn ature and gravity vary by an order of mag- Voyager spacecraft showed that calderas oc- serve as a new nonterrestrial database for nitude from one planet to another, but at- cur as landforms and that caldera-scale constraining the models. At the present mospheric pressure varies by 14 orders of eruptions are occurring at the present time. time, the terrestrial models referenced magnitude. It is not feasible to investigate Observations of these planetary analogs can above have not been extended to other the effect of individual parameters system- provide us with a rich database for compar- planets. Instead, parametric models and atically one by one, because an inordinate ison and contrast of the processes inferred steady-flow approximations have been amount of computational time would be for Earth. Why do some of the volcanic adopted in an attempt to understand com- required. Therefore, I chose to examine landforms look so similar to our terrestrial plex volcanic plumbing systems, eruption how the fluid dynamics of a relatively gas- ones, and why do some look so different parameters, and geologic and geomorphic rich eruption on Earth would change if this (Fig. 1, A through C)? The present study sought to understand the relation between eruption dynamics and global parameters (such as gravity and atmospheric pressure and temperature) and to compare and contrast the dynamics of eruption on the different planets. Visualization of the fluid dynamics of caldera-scale eruptions is difficult because the flow fields are extremely complex: They are unsteady, three-dimensional, and mul- ticomponent. The small eruption plume of on July 27, 2009 Mount St. Helens (Fig. iD) offers some insights about volcanic plumes in general. The initial unsteady-state development of the plume can be inferred from a few tur- bulent cells far downwind. The steady-state configuration of the plume (its height and shape) is visible at the mountain summit on the upwind side. Segregation of the multi- component flow is evidenced by ash falling www.sciencemag.org out from the plume and leaving a steam- enriched column (white). A dense ground- level flow is moving down the slope to the right, and ash separating from the higher plume is drifting downward to feed the ground-hugging flow. These are complex processes can- and generally nonlinear that Downloaded from not be scaled for study under controlled Fig. 1. (A) The Valles caldera on Earth, as viewed from Landsat. The caldera diameter (center) is about laboratory conditions. 20 km. (B) NASA Viking spacecraft image of Tyrrhena Patera on Mars. This structure is believed to be The numerical modeling of eruptions is hydromagmatic in origin and to have formed early in martian history, when water was more abundant than revolutionizing theoretical volcanology be- at present (31). Note the gullies and erosional remnants on the lower flanks. (C) NASA Magellan cause it allows the study of many aspects of spacecraft perspective image of the large volcanic structure Sif Mons on Venus. The flows in the these eruptions by direct solution of the foreground are 3 to 8 km in width; see (27). (D) Eruption of Mount St. Helens in March 1980. The plume Navier-Stokes equations. These techniques is about 1 km above the summit. [Photo by S. W. Kiefferi were first introduced and applied to examine the conditions of generation of ash columns and pyroclastic flows (1-5). The phi- Table 1. Planetary parameters: g, acceleration due to gravity; T, atmospheric temperature at the surface; losophy adopted by these authors was to P, atmospheric pressure at the surface; and X, typical atmospheric and volcanic gas composition. define processes during different phases of Properties of lo and Triton are included for completeness; however, because of their unique planetary eruptions in order to provide a general histories as well as computational complexity at extremely low temperatures and low pressures, the fluid-dynamic framework for interpretation results for Triton and lo are not included in the text. of volcanic deposits in the field. Another Planet g T P X group has developed a similar set of models (cm/s2) (K) (bar) for a smaller type of eruptions-those of Earth* 980 300 1.0 H20, CO2, N2 Mount Vesuvius, Italy (6-9). This group is Venust 860 700 70 to 100t C02, H20, SO2 attempting to predict volcanic hazards, es- Mars* 380 273 6 x 10-3to 8 x 10-3§ C02, H2O pecially in the heavily populated Mount Triton 90 38 16 x 10-6 N2, CH4 Vesuvius area, by using the numerical mod- lo 180 130 10-7 to 10-12 S02, S els as a basis for formulating a risk assess- 1H2O used in model. tCO2 used in model. t70 bar used in model. §6 x 10-3 bar used in model.

1386 SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 S S eruption occurred on Venus, which has a The ratio of vent pressure to atmospher- evolve along arcuate fissures bounding the high-pressure and high-temperature atmo- ic pressure is the most important parameter caldera. Therefore, a central vent eruption sphere, and on Mars, which has a low-pres- to be specified. However, even at small is the simplest, but not necessarily only, sure and low-temperature atmosphere. The terrestrial eruptions volcanic vent pressures geometry that could be chosen. Only erup- scale chosen is typical of large stratovolcano cannot be measured directly; indeed, this is tion simulations with flat terrain are shown, to small caldera eruptions on Earth (vent a difficult measurement even in a geyser. It but the effects of topography, such as an radius of 200 m, mass fluxes of 106 to 1010 is likely that the vent pressure varies with annular rim surrounding the central vent, kg/s, and distance scales of tens of kilome- time as an eruption evolves (9). For mod- can be substantial (5). A rim can deflect ters). The mass flux and dimensions of the eling purposes, two different extremes were flows back in toward the vent or can totally plinian phase of the 18 May 1980 Mount St. examined in the literature. In one set of confine flows within the caldera. Several Helens eruption are now thought to have models, vent pressure is assumed to be equal simulations of the effect of the rim were run been within this range (conduit diameter of to atmospheric pressure; this is the so-called for Venus and Mars, and the effects were tens of meters, smaller than that considered pressure-balanced condition (11, 15, 16). generally as reported in (5). here; mass flux of -107 kg/s; water content This assumption permits many mathemati- I used the approach of Wohletz, Valen- of about 4 weight %; and exit velocities of cal simplifications that allow analytic or tine, and colleagues (1, 3, 5, 21, 22), which several hundred meters per second) (9). semianalytic solutions applicable to plane- is based on explicit numerical solutions of Although spectacular active volcanism tary problems. However, fulfillment of the the equations of conservation of mass, mo- occurs on lo and low-temperature geyser- pressure-balanced condition requires special mentum, and energy (23). A fluid is as- like plumes are observed on Triton, a moon conditions of vent friction and geometry sumed to erupt from a cylindrically symmet- of Neptune, these planetary bodies have (19). These conditions may not be obtained ric vent (Fig. 2). The erupting fluid is a such grossly different histories from those of early in eruptions before a vent is cleared, or two-component mixture of gas and dis- Earth, Venus, and Mars that they are not in short eruptions [for example, the lateral persed ash particles. The gas is described by considered further. The focus here is on the blast at Mount St. Helens (20)], or on the ideal gas equation of state and the ash three planets that have had somewhat sim- planets with low atmospheric pressure (14). particles are assumed to be incompressible. ilar origins and evolutions and therefore Therefore, a second set of models that allow The conservation equations are applied to plausibly have magmas of similar composi- for higher pressure at the vent has been the ash and gas components separately, so tions and volatile contents. developed. For example, overpressuring by that they may have different temperatures factors of 2 to 150 has been examined for and velocities. The components interact on July 27, 2009 Planetary Parameters terrestrial eruptions (3, 14, 20). These as- with each other through drag forces and sumptions are compared and contrasted in heat transfer. The governing equations of From fluid dynamics of aeronautical nozzles the calculations for Mars below. motion and constitutive relations form a (18), we know that large variations in pres- system of eight partial differential equations sure have a major influence on the fluid Approach and eight algebraic equations with 16 de- flow behavior and that atmospheric temper- pendent variables [given in (21)]. The ature, gravity, and gas composition have The calculations presented are for central equations are approximated by finite differ- only a secondary effect. Modeling the flow vent eruptions. Caldera eruptions are, in ence methods (24) and are solved on large from a high-pressure to a low-pressure con- fact, usually more complex than this: The supercomputers or standard workstations, www.sciencemag.org dition is difficult if the pressure ratio is eruptions may start at a central vent, but as depending on problem size. greater than about 10 because the flow magma is withdrawn and the volcanic sum- In the calculations, ash and gas enter the fields are nonlinear and contain traveling mit starts to collapse, the eruptions may computational domain through a vent (Fig. and standing waves. The equations are not analytically solvable and they can be numerically unstable wherever pressure gradi- Table 2. Other parameters used in the computer simulations (-y, isentropic exponent; p, density; c, heat

ents are steep. capacity; and K, kelvin). The drag coefficient cd was 1.0 in all simulations. The kinematic viscosity was Downloaded from taken to be representative of the averaged pressure and temperature conditions on the planets, and therefore varies considerably. The viscosity coefficient qO was 0.1 in all runs for which the cell size was 200 m (2), giving a mixing length of about 20 m.

Mars: Mars: Over- Parameter Earth Venus Pressure- pressured balanced y, gas phase 1.33 1.18 1.3 1.3 Vent pressure (bar) 1.0 70 0.006 1.0 Void fraction gas (%) 99.8 72.4 99.9 99.8 Mass flux at vent 1.8 x 108 2.1 x 1010 1.1 X 106 1.8 x 108 (kg s-1) Mach number 2.0 3.0 2.0 2.0 Patm' base (g cm-3) 7.88 x 10-4 5.43 x 10-2 5.20 x 10-6 5.20 x 10-6 pgs(gCm 3)at 1200K 1.99 x 10-4 3.2 x 10-2 1.18 x 10-6 1.97 x 10-4 Internal energy, gas 1.68 x 1010 1.26 x 1010 1.69 x 1010 1.69 x 1010 (ergs g-1) Ppiume' inflow (g cm-1) 4.93 x 10-3 5.74 x 10-1 2.96 x 10-5 4.91 x 10-3 cPpu(ergs 1 K- 1) 9.5 x 106 9.5 x 106 9.5 x 106 9.5 X 106 c as(ergsg 1 K 1) 1.41 X 107 1.05 x 107 1.41 X 107 1.41 X 107 Gas conductivity (ergs 5.0 x 103 5.88 x 103 5.0 x 103 5.0 X 103 Fig. 2. Schematic of the computational domain. g-1 s-' K-1) Each boundary hides one cell (the virtual cells), so Kinematic gas viscosity 1.3 9 x 10-3 211 1.3 the true grid size is equal to the number of visible (cm2 S-1) cells in each direction plus 2. SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 1387 2) beginning at time t = 0. The proportions plume (13); if the gas content is only 1.7 loading is relatively light and the mixture is of ash and gas are specified, as are the initial weight %, the volume fraction on Venus homogeneous, sound speeds are similar (145 velocity, temperature, and pressure. These would only be 50 weight %, which is an m/s) and therefore so are the Mach numbers components flow into an atmosphere that unreasonably low volume fraction for this (2.0). On Venus, the higher vent pressure has the same composition as the gas phase type of modeling. A CO2 content of 4 of 70 bar causes higher particle concentra- in the erupting fluid but may have a differ- weight % produces a void fraction of 72 tions, which reduces the sound speed to 93 ent temperature. The atmosphere is initially weight % at 70-bar pressure on Venus, and m/s; the Mach number correspondingly in- isothermal and its pressure and density de- so 4 weight % was chosen as the gas content creases to 3.0. crease exponentially with height. for all simulations. Mass flux is often taken as one of the Because the geometry is cylindrically For the simulations on Earth and Mars, controlling parameters in volcanic plume symmetric, the calculations are only per- the gas phase was assumed to be H20 so dynamics (15). However, another conse- formed for a half-space. The symmetry axis that 1-bar vent conditions on both planets quence of holding vent radius and velocity is defined as a reflecting boundary. The top could be directly compared. Although gas constant is that mass flux is not the same in and right-hand boundaries are outflow composition is included as a parameter in all of the simulations (Table 2), which di- boundaries. The bottom boundary is treated the simulations, the composition has rela- rectly reflects the effect of vent pressure on as a frictionless substrate [see (5)]. Practical tively little influence on the results com- the mixture density and mass flux at the limitations require a mesh size of 100 to 200 pared with other factors discussed here. In vent. The mass flux is the same in two of m and domain sizes of no more than 150 by particular, for plumes that are as heavily the simulations, the terrestrial and over- 150 cells; hence, these calculations are for laden with ash particles as these, the expan- pressured martian eruptions; thus, examina- large-scale, not outcrop-scale, phenomena. sion of the gas is more strongly controlled tion of these two cases enables a direct by heat transfer from the particles to the gas comparison of the other parameters on the Initial Conditions and than by the composition of the gas itself. eruption dynamics. Fluid Properties For all simulations, the temperature of the gas and ash exiting the vent was assumed to Fluid Dynamics in For even the simplest solutions, many pa- be 1200 K, the ash particle radius was 0.01 the Simulations rameters are required to describe the initial cm, and the material density of the particles and boundary conditions (atmospheric con- was 2000 kg/m3. In the simulations, vent The large-scale behavior of a volcanic ditions, gravity, and fluid composition) pressure was taken as either atmospheric eruption column is determined by the rel- on July 27, 2009 (Table 1) and fluid properties (vent condi- (Venus, 70 bar; Earth, 1 bar; Mars, 0.006 ative values of four different types of forces tions, heat capacities, and thermal and me- bar) or greater than atmospheric. For the (1, 2): inertia, pressure gradients, inter- chanical interaction parameters) (Table 2). overpressured case on Mars, the pressure at phase drag, and gravitation. In the follow- A systematic study of the variation of each the vent was taken to be 1 bar, that is, the ing, a plume comprises any of the gas and of these parameters would be prohibitively vent conditions matched the assumed ter- ash material above the vent, and a column time-consuming. Therefore, I studied one restrial vent conditions. is the main vertical part of the eruption specific type of caldera-scale eruption and A number of parameters could be held flow field above the vent. When a column included as many specific global parameters constant in the simulations, such as vent develops with sustained upward move- as possible in each simulation. radius, vent velocity, vent Mach number, ment, it is referred to by volcanologists as www.sciencemag.org The reference case is for a magma that mass flux, volume fraction volatiles, vent a plinian column (Fig. 1A), and I adopt contains 4 weight % gas. This is similar but pressure, and temperature. In the simula- that term loosely to interpret the simula- not identical to cases of plinian eruptions tions for all three planets, I chose to hold tions. A column that collapses back upon with 1.7 weight % gas that have been well the vent radius at 200 m, and the initial itself and forms a downward-moving studied numerically (3, 5, 21, 22) and in vent velocity, v, constant at 290 m/s. These sheath is referred to as a fountain, and the the field (2, 25). The increase in gas con- values produce different exit Mach numbers place where it reimpacts the ground is the

tent was required for extrapolation to the (v/a, where a is the mixture sound speed) on stagnation point or reimpact zone. Later- Downloaded from higher atmospheric pressure conditions of the three different planets because the ally moving, ground-hugging flows that Venus. A volume fraction of 70 weight % is sound speed of the erupting mixture chang- result from the fountain collapse are called usually taken as the criterion for magma es with vent pressure and particle loading. pyroclastic flows. A column that attains fragmentation and production of a dusty gas On Earth and Mars, where the particle neutral buoyancy is one that stagnates in

0 -10.5 Fig. 3 (top). A pressure- balanced venusian erup- I tion (scale, 7 x 7 km; vent and atmospheric pressure, 70 bar). The optical depth for an external observer would be approximately to I the green. Fig. 4 (bot- torn). A pressure-balanced terrestrial eruption (scale, 7 x 7 km; vent and atmospheric pressure, 1 1 bar). Same color scale as in Fig. 3.

r1-

1 388 SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 ..l 1 its ascent but does not collapse to form a ing circular wave, a hydraulic jump. Further Initially, the plume rises from the vent fountain (this is a rather special definition study of the development and properties of and develops a working surface at the top as of the term but is convenient for the these waves in multiphase fluids should a result of the entrainment of the atmo- following discussion). The working surface yield an understanding of the nonlinear sphere (Fig. 4, A and B). However, upon is the unsteady flow at the top of the dynamics inherent in these complex sys- reaching an altitude of -4 km, the working column where large-scale vorticity and en- tems. The high pressure of the venusian surface and the denser core of the plume trainment yield an increased diameter as atmosphere suppresses the immediate for- stall. Some material falls back toward the the column penetrates into the atmo- mation of a dusty plume rising vertically ground (Fig. 4, C and D) and the column sphere. In the computer-generated color over the fountain (compare Fig. 3 with Fig. begins to evolve into a classic low fountain images of different time points in the sim- 4). In fountain-forming eruptions of dense that feeds outward and inward flows (Fig. 4, ulated eruptions (Figs. 3 through 6), the material like this, the primary way that B through D; compare with Fig. 3, B parameter plotted is the logarithm of the material is lofted to high elevations above through D). However, the flow conditions volume fraction of solid particles, repre- the main fountain is by mixing of the high- are poised at the balance between those of a sented by a color scale. density plume with the lower density atmo- rising column and of a collapsing column; Venus. The initial pressure chosen for sphere. However, in this case, the formation the fountain does not become well devel- the simulated Venus eruption was 70 bar, in of the hydraulic jump and its interaction oped, and the pyroclastic flows are only balance with the venusian atmosphere. The with the main column gives rise to an elu- weakly fed (Fig. 4E). The stagnant cap of erupting material is therefore substantially triated ash cloud that eventually rises above the plume at the neutral buoyancy altitude denser than that of the terrestrial jet (note the low fountain (Fig. 3, C through E). This of about 3 km feeds the ash falls, the rising the different shades of red in the core re- evolution of the simulated eruption on Ve- plinian column, and, only intermittently, gions of Figs. 3 and 4). The jet erupts from nus resembles in most ways the well-docu- the ash flows. The eruption column consists the vent to an altitude of about 4 km and mented plinian conditions for terrestrial of a complex field of rising and falling ma- then collapses back to form a low fountain. jets with 1.7 weight % water (3). However, terial, perhaps in an oscillating manner (9). This fountain feeds pyroclastic flows that the properties of the simulated terrestrial Several of these later features in these run radially outward from the impact point eruption with 4 weight % water are very computer simulations are also visible in the of the collapsing fountain. In addition, different from those of this venusian jet or photograph of the small Mount St. Helens some of the erupted material moves back of a terrestrial eruption with 1.7 weight % eruption (Fig. ID). The dense column ris-

radially inward from the impact point to water. ing above the vent of Mount St. Helens is on July 27, 2009 recirculate back into the rising fountain. Earth. The relatively gassy initial condi- equivalent to the plinian column rising An interesting wave develops within the tion of 4 weight % water produces a terres- above the vent in the computer simulation; pyroclastic flow about 2 km radially from trial plume that is almost balanced between the fortuitous wind direction makes the the vent (Fig. 3, C through E). This wave conditions that form towering plinian gas Mount St. Helens column resemble the has many characteristics of a standing hy- and ash columns and those that produce half-space of the simulation. The formation draulic jump. Because of the assumed cylin- low fountains and dense pyroclastic flows. of the white steam-enriched cap above the drical geometry, the wave is analogous to Although the parameters cannot be quan- Mount St. Helens plume by the separation the circular hydraulic jump that can be tified for a real and complex volcanic situ- of the multiphase solid and gas (water va- produced in a kitchen-sink experiment by ation, the balance between column plinian por) components is equivalent to the sepa- www.sciencemag.org holding a flat plate under a downward spout conditions and fountain conditions is influ- ration of the ash-enriched (orange) and of water. Under most kitchen conditions, enced by the thermogravitational parame- vapor-enriched (yellow and green) compo- fluid spreads radially from the impinging jet ter, the Rouse number, the Richardson nents of the simulated plume. The coales- toward the edge of the plate in two distinct number, particle terminal velocities, the cence of the downward-falling ash into a flow regimes. Near the impingement point, pressure ratio between the vent fluid and pyroclastic flow at Mount St. Helens is the flow is shallow and fast as it spreads the atmosphere, the density ratio between equivalent to the falling ash and ground- radially, a supercritical flow regime. Toward the vent fluid and the atmosphere, and the hugging pyroclastic flow in the simulation. the edge of the plate, the flow becomes initial Mach number (3, 5, 7, 21). I de- Mars. The evolution of the pressure- Downloaded from deep and slow, a subcritical flow regime. scribe this jet as having attained a height of balanced martian simulation mimics that These two regimes are separated by a stand- neutral buoyancy. of the pressure-balanced terrestrial simula-

o -10.5 Fig. 5 (top). A pressure- balanced martian eruption (scale, 30 x 30 km; atmospheric and vent pressure, 0.006 bar). Fig. 6 (bottom). An overpressured martian eruption (scale, 30 x 30 km; atmospheric pressure, at 0.006 bar; vent pressure, 1 bar). Same color scale as in Fig. 5.

SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 1389 tion (Fig. 5, A through E), even though shows the position of this shock. Lateral on Venus are much hotter than those on there is a 166-fold difference in absolute oblique shocks (not readily visible in the Earth for much longer distances and, pre- pressures. The general yellow and green plots shown) determine the shape of the jet. sumably, for much longer times because they hues in the martian simulation reflect the [A relatively common terrestrial analog can are entraining a much hotter atmosphere much lower density of the plume. The be seen in the shape of supersonic plumes (700 K) than such flows on Earth or Mars. distance scale of the affected area on Mars above many geothermal wells (26)]. The temperatures are high enough that sub- is much larger than on Earth (tens of This near-vent flow pattern is identical stantial welding of the ash particles may kilometers in each direction rather than a to that proposed for supersonic flow out of occur as the flows slow down and the ash few kilometers). The times to reach equiv- the vent during the lateral blast at Mount particles come in contact with each other. alent column configurations are corre- St. Helens, 18 May 1980 (20). The large Thus the material, which was initially a dis- spondingly longer, on the order of 1000 pressure gradients between the vent and persed mixture ofgas and ash when it left the seconds instead of a few hundred seconds. the atmosphere produce accelerations that vent, evolves to a liquid-like state. In this The plume reaches a height of neutral are large compared to gravitational accel- state, it can even continue flowing as if it buoyancy and ash rises or falls only inter- erations. As a result, material is thrown were a liquid lava, and it may ultimately mittently and slowly (Fig. 5, C through E). much farther from the vent than under come to rest with geomorphic features re- In contrast, the simulation of the over- pressure-balanced conditions. After mate- flecting its secondary liquid-like state rather pressured martian eruption exhibits a fasci- rial passes through the shock waves, it than its initial ash and gas state (a process nating array of supersonic flow features near decelerates and gravitational forces be- called rheomorphism). Because of this com- the vent and out to a distance of approxi- come important. Some of the fluid falls plexity, pyroclastic deposits around calderas mately 10 km (Fig. 6, A through E). The back to the ground, reimpacting at a dis- may be difficult to recognize on Venus. first fluid out of the vent mixes with the tance of - 10 km. From this reimpact zone, For a second example of how knowledge atmosphere and forms a large working sur- material forms a ground-hugging pyroclas- of the fluid-dynamic structure of a plume face that reaches an altitude of 20 km with- tic flow. A supersonic jet of this type might influence interpretation of features on in 100 s (Fig. 6A). This working surface develops a broad umbrella that covers a a volcano, consider the striking sinuous appears to break off and rise above 30 km much larger area and generates substantial channels visible on the lower flanks of such (Fig. 6, B and C). Detailed analysis of this high-velocity activity at distances many calderas as Hecates Tholus or Tyrrhena Pa- breakup is not warranted because the vis- vent diameters from the main eruption. tera (Fig. 1B). These channels typically start cosity and entrainment assumptions in the tens of kilometers downslope from the sum- on July 27, 2009 simulation are so simplified that they may Planetary Interpretations mit calderas. They have been variously in- cause artifices in the behavior of the work- terpreted as originating from volcanic densi- ing surface at long simulation times. Numerical simulations provide a rich re- ty currents (28) or as fluvial channels (29). Near the vent, the column emerges in source for learning about nonlinear fluid Our conventional terrestrial-based under- the typical configuration of a supersonic jet dynamic processes because powerful com- standing of plumes as tall but relatively nar- (20). The rapid change of color from the puters can now solve relatively complex row plinian columns would predict that deep red of vent conditions of 1 bar to the systems of equations, and because visualiza- channels resulting from volcanic density cur- lighter colors illustrates how rapidly the gas tion tools are excellent. The influence of rents should start relatively high on the decompresses. Fluid accelerates outward in the variation of global planetary parameters slopes because the reimpact zones are rela- www.sciencemag.org all directions from the vent, covering a on volcanic eruption dynamics, including tively close to the summits in terrestrial plin- much larger near-vent area than does the the shape, extent, and internal structure of ian eruptions. However, the simulation of pressure-balanced jet (compare the red complex plumes, has been illustrated in the the overpressured jet on Mars (Fig. 6) sug- zones in Figs. 5B and 6B to see vent size and simulations presented here. gests a fluid-dynamic reason that the gullies supersonic spreading). The fluid emerges As an example of how the consideration may start so far down the slopes: An over- from the vent and accelerates to about 7 km of the fluid-dynamic structure of plumes may pressured eruption blasts material out to 10

where it forms a shock wave, the so-called influence our interpretation of photographs km or more, where it falls back to a reimpact Downloaded from Mach disk shock in aeronautics. The slight of features on the planets, consider the flows zone. The reimpact zone is at much greater color inflection at an altitude of - 7 km on Venus (Fig. 1C) and the gullied flanks of distances from the vent than on Earth or the volcano on Mars (Fig. 1B). There has Venus. The pyroclastic flows emanating been considerable controversy about wheth- from this zone have high velocities and could * B er pyroclastic volcanism can occur on Venus cause the distal gullying observed. In this | because the high atmospheric surface pres- case, the initial fluid-dynamic conditions sure inhibits bubble formation and magma within a volcanic plume are the cause of fragmentation. Gas contents in excess of 4 erosional features in the landscape. Subse- weight % are required for fragmentation, as quent meteorologic erosional processes such discussed above. Evidence for volcanism on as rainfall might enhance an initial channel- Venus is abundant, but obvious pyroclastic ized volcanic topography. Combined volca- (ash) deposits are noticeably rare (27). Flows nic-climatic processes of this type occurred such as those in Fig. 1C have generally been at Mount St. Helens: The lateral blast erod- 1200 K 250 K assumed to be lava flows (that is, flows of a ed nearly horizontal furrows into some Fig. 7. Comparison of liquid, not gassy, mixture). However, it may slopes, and these were subsequently en- temperature fields. (A) be difficult to distinguish between a solidi- hanced and then modified by later rains The terrestrial eruption fied lava flow and a cooled pyroclastic flow (30). However, there has not always been a (Fig. 4, 7 x 7 km, at 300 s). (B) The venu- on Venus. Comparison of the temperatures wet atmosphere on Mars, and it is important sian eruption (Fig. 3, 7 within the flow fields of the simulated erup- to keep in mind that the dynamics of the x 7 km, at 300 s). (C) ---- tions shows that the thermal evolution of eruptions themselves may be complex The overpressured martian eruption (Fig. 6, 30 x pyroclastic ejecta on Earth, Mars, and Venus enough to produce complicated erosional 30 km, at 500 s). is quite different (Fig. 7). Pyroclastic flows features far down the slopes of the volcanoes.

1390 SCIENCE * VOL. 269 * 8 SEPTEMBER 1995 m ML..Ll1ILMm

Conclusions Res. 94, 1867 (1989). 19. L. Wilson, Geophys. J. R. Astron. Soc. 63, 117 4. , Geology 7, 641 (1989). (1980). 5. S. W. Kieffer, Geol. Soc. Am. Bull. 104,154 20. S. W. Kieffer, U.S. Geol. Surv. Prof. Pap. 1250, Many processes need to be considered in (1992). (1981), p. 379. interpretations of terrestrial and planetary 6. F. Dobran, Ed., Prospects for the Simulation of Vol- 21. K. H. Wohletz and G. A. Valentine, in Magma Stor- landforms. Until the advent of modern canic Eruptions (Giardini, Pisa, Italy, 1991); J. Volca- age and Transport, M. Ryan, Ed. (Wiley, New York, nol. Geotherm. Res. 49, 285 (1992). 1990). computers, complex internal fluid-dynam- 7. _ , A. Neri, G. Macedonio, J. Geophys. Res. 98, 22. G. A. Valentine, K. H. Wohletz, S. W. Kieffer, J. Geo- ic processes such as those illustrated here 4231 (1993). phys. Res. 96, 21887 (1991). 8. F. Dobran, A. Neri, M. Todesco, Nature 367, 551 23. F. H. Harlow and A. A. Amsden, J. Comput. Phys. could not be easily considered because the 17,19 (1975). processes are not suscep- (1994); G. Macedonio, F. Dobran, A. Neri, Earth highly nonlinear Planet. Sci. Lett. 121, 137 (1993). 24. DASH is a computer code developed at Los Alamos tible to analytic or semianalytic analyses. 9. P. Papale and F. Dobran, J. Geophys. Res. 99, 4355 National Laboratory to study dusty air shocks. The The use of numerical simulations to solve (1994). simulations reported here took several to a dozen hours on an SGI Indigo II workstation. and visualize fluid-dynamic processes and 10. L. Wilson, Geophys. J. R. Astron. Soc. 30, 381 (1972); ibid. 45, 543 (1976). 25. G. Valentine, Bull. Volcanol. 49, 616 (1987). can W. constraints be combined with labora- 11. __, R. Sparks, T. C. Huang, N. Watkins, J. Geo- 26. S. Kieffer, Rev. Geophys. 27, 3 (1989). tory and field observations to enhance our 27. J. W. Head et al., Science 252, 276 (1991). phys. Res. 83, 1829 (1978); L. Wilson, J. Volcanol. 28. C. E. Reimers and P. D. Komar, Icarus 39,88 (1979). understanding of complex geologic phe- Geotherm. Res. 8, 297 (1980). 29. P. J. Mouginis-Mark, L. Wilson, J. W. Head Ill, J. nomena on Earth and on the other plan- 12. L. Wilson and J. W. Head Ill, J. Geophys. Res. 86, Geophys. Res. 87, 9890 (1982). 2971 (1981). ets. 30. S. W. Kieffer and B. Sturtevant, ibid. 93, 14793 13. J. W. Head Ill and L. Wilson, ibid. -91, 9407 (1986). (1988). 14. S. W. Kieffer, in Explosive Volcanism: Inception, Evo- 31. R. Greeley and D. A. Crown, ibid. 95, 7133 (1990). REFERENCES AND NOTES lution, and Hazards (National Academy Press, 32. Supported by NASA grants NAGW-1740 (at Arizona Washington, DC, 1984), p. 143. State University) and 5-56791 (at the University of 1. K. H. Wohletz, T. R. McGetchin, M. T. Sanford II, E. 15. L. Wilson, H. Pinkerton, R. MacDonald, Annu. Rev. British Columbia). Related preliminary work on M. Jones, J. Geophys. Res. 89, 8269 (1984). Earth Planet. Sci. 15, 73 (1987). DASH was supported by Los Alamos National Lab- 2. G. A. Valentine, thesis, University of California, Santa 16. L. Wilson and G. P. L. Walker, Geophys. J. R. Astron. oratory Institute of Geophysics and Planetary Phys- Barbara (1988); also as Field and Theoretical As- Soc. 89, 657 (1987). ics. was greatly assisted in various stages of this pects of Explosive Volcanic Transport Processes 17. J. W. Head and L. Wilson, J. Geophys. Res. 97, project by A. Levine, T. Morino, M. Morrissey, M.-L. (Los Alamos Nati. Lab. Rep. LA-11441 -T, UC-702, 3877 (1992). Woo, and G. Yuan. Special thanks are due to G. 1988). 18. P. A. Thompson, Compressible-Fluid Dynamics Valentine and K. Wohletz for continued wisdom on 3. G. A. Valentine and K. H. Wohletz, J. Geophys. (McGraw-Hill, New York, 1972). DASH. on July 27, 2009

AAAS-Newcomb Cleveland Prize www.sciencemag.org To Be Awarded for a Report, Research Article, or an Article Published in Science Downloaded from The AAAS-Newcomb Cleveland Prize is awarded invited to nominate papers appearing in the Reports, to the author of an outstanding paper published in Research Articles, or Articles sections. Nominations Science. The value of the prize is $5000; the winner must be typed, and the following information pro- also receives a bronze medal. The current competition vided: the title of the paper, issue in which it was period began with the 2 June 1995 issue and ends with published, author's name, and a brief statement of the issue of 31 May 1996. justification for nomination. Nominations should be submitted to the AAAS-Newcomb Cleveland Prize, Reports, Research Articles, and Articles that in- AAAS, Room 924, 1333 H Street, NW, Washington, clude original research data, theories, or syntheses and DC 20005, and must be received on or before 30 are fundamental contributions to basic knowledge or June 1996. Final selection will rest with a panel of technical achievements of far-reaching consequence distinguished scientists appointed by the editor-in- are eligible for consideration for the prize. The paper chief of Science. must be a first-time publication of the author's own The award will be presented at the 1997 AAAS work. Reference to pertinent earlier work by the author annual meeting. In cases of multiple authorship, the may be included to give perspective. prize will be divided equally between or among the Throughout the competition period, readers are authors.

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