3D numerical simulation of volcanic eruption clouds during the 2011 Shinmoe-dake eruptions
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2013
Received: 31 October 2012
Accepted: 16 March 2013
Published: 8 July 2013
We present simulations of the development of volcanic plumes during the 2011 eruptions of the Kirishima-Shinmoe-dake volcano, Japan, using a new three-dimensional (3D) numerical model that calculates eruption cloud dynamics and the wind-borne transport of volcanic ash. This model quantitatively reproduces the relationship between the eruption conditions (e.g., magma discharge rate) and field observations, such as plume height and ash fall area. The simulation results indicate that the efficiency of turbulent mixing between ejected material and ambient air was substantially enhanced by strong winds during the 2011 Shinmoe-dake eruptions, which caused a significant decrease in the maximum height of the plumes compared with those that develop in still environment. Our 3D simulations also suggest that the existing 1D plume model tends to overestimate the effect of wind on turbulent mixing efficiency, and hence, to underestimate plume height in a strong wind field for a given magma discharge rate.
Explosive eruptions are characterized by the formation of buoyant plumes and widespread dispersal of volcanic ash. During such eruptions, a mixture of solid pyroclasts (volcanic ash) and volcanic gas is ejected from vents into the atmosphere. The ejected material (i.e., the mixture of solid pyroclasts and volcanic gas) generally has an initial density several times higher than that of the atmosphere, since it is composed of more than 90 wt% solid pyroclasts. As the ejected material entrains ambient air, expansion of this air during mixing with the hot pyroclasts drastically decreases the density of the mixture, so that it becomes less dense than the surrounding atmosphere. This results in the development of a buoyant volcanic plume with a height that can exceed several kilometers.
Volcanic plume height is one of the key observable quantities to estimate eruption conditions, including eruption intensity (i.e., magma discharge rate). Eruption column dynamics are controlled mainly by the balance between thermal energy ejected from the vent and the work done during transportation of ejected material and entrained air through atmospheric stratification. This means that when magma properties (i.e., temperature, volatile content, and heat capacity) are fixed, plume height is dependent on the efficiency of turbulent mixing, the magma discharge rate and atmospheric conditions (Morton et al., 1956; Sparks, 1986; Carazzo et al., 2008); at given atmospheric conditions (e.g., temperature and moisture stratifications) the plume height increases as magma discharge rates increase and turbulent mixing efficiencies decrease.
The flow patterns of a volcanic plume are also strongly dependent on whether plume vertical velocities are faster or slower than wind speeds (Bonadonna et al., 2005). Plume trajectories are not wind-affected at high eruption intensities and/or under weaker wind speeds. The vertically rising plume spreads horizontally at the level where cloud density is equal to that of the atmosphere, termed the neutral buoyancy level (NBL; Sparks, 1986). In comparison, if eruption intensity is weak and/or wind speeds are high, volcanic plumes are highly wind-distorted, leading to a bent-over trajectory, and the deposition of volcanic ash at significant distances from the vent. Recently, Bursik (2001) proposed a theoretical model of bent-over plume, and suggested that wind enhances the efficiency of turbulent mixing, leading to a decrease in plume height. However, the effects of wind on turbulent mixing efficiency and plume height are not fully understood.
In the first stage of the 2011 Kirishima-Shinmoe-dake volcano eruptions in Japan, three volcanic plumes were strongly affected and distorted by a westerly wind with volcanic ash transported toward the southeast. Weather radar echo measurements indicated that these plumes reached heights of up to 6.5–8.5 km above sea level (asl; Shimbori and Fukui, 2012). Kozono et al. (2013) demonstrated that these plume heights were significantly lower than those predicted by a simple plume height model. This implies that environmental winds enhance turbulent mixing and cause a decrease in plume height, as was suggested by Bursik (2001). Here, we present a new 3D numerical model of bent-over plumes and attempt to reproduce the plume height and ash fall area for the 2011 Shinmoe-dake eruptions. We discuss the effects of wind on the efficiency of turbulent mixing and the plume height.
2. Numerical Model
Our numerical model is designed to simulate the injection of a mixture of solid pyroclasts and volcanic gas from a circular vent above a flat earth surface in a stratified atmosphere, using a combination of a pseudo-gas model for fluid motion and a Lagrangian model for particle motion. We ignore the separation of solid pyroclasts from the eruption cloud during fluid dynamics calculations, treating an eruption cloud as a single gas with a density calculated using a mixing ratio between ejected material and entrained air. The fluid dynamics model solves a set of partial differential equations that describe the conservation of mass, momentum, and energy, and constitutive equations describing the thermodynamic state of the mixture of pyroclasts, volcanic gas, and air. These equations are solved numerically by a general scheme for compressible flow (van Leer, 1977; Roe, 1981). Details of the numerical procedures used in this study are described in Suzuki et al. (2005).
Calculations were performed in a 3D domain with a nonuniform grid; a computational domain extends 13 km vertically (Z-direction) and 24 × 12 km horizontally (X- and Y-directions, respectively). The boundaries are located 2 km north, 10 km south, 1 km west, and 23 km east from the volcanic vent center, which is at 1400 m asl. A free-slip condition is applied at the ground boundary for ejected material and air velocities, with mass, momentum, and energy fluxes at the upper and other boundaries of the computational domain assumed to be continuous; these boundary conditions correspond to free outflow and inflow for these quantities.
Entrainment of ambient air by turbulent mixing plays a central role in the dynamics of eruption clouds, primarily because the cloud density is controlled by the mixing ratio between ejected material and ambient air. Generally speaking, the efficiency of entrainment is a function of the Reynolds number. However, it is independent of the Reynolds number when the turbulence is fully developed (Dimotakis, 2000). Because the flow of volcanic plume is considered to be fully turbulent, to correctly reproduce the entrainment efficiency in the plume, our simulations must use a sufficiently high spatial resolution (Suzuki et al., 2005). This means that during simulation, grid sizes were set to be smaller than D0/16 near the vent, where D0 is the vent diameter, and to increase at a constant rate (by a factor of 1.02) with distance from the vent up to D0/2, such that the grid size is small enough to resolve turbulent flow at locations far from the vent (cf. Suzuki and Koyaguchi, 2010).
3. Simulation Input Parameters
Material properties, physical parameters, and input parameters for simulation.
Gravitational body force per unit mass, g
9.81 m s−2
Density of solid pyroclasts, σ
1000 kg m−3
Specific heat of solid pyroclasts, Cvs
1100 J kg−1 K−1
Specific heat of volcanic gas, Cvg
1348 J kg−1 K−1
Specific heat of air, Cva
713 J kg−1 K−1
Gas constant of volcanic gas, Rg
462 J kg−1 K−1
Gas constant of air, Ra
287 J kg−1 K−1
Altitude of vent
Volatile content, ng0
Magma temperature, T0
Initial mixture density, ρ0
5.74 kg m−3
Mass discharge rate,m0
1.5 × 106 kg s −1
Exit velocity, w0
134 m s−1
Vent diameter, D0
Magmatic properties (i.e., volatile content and magma temperature) were estimated from petrological data, with Suzuki et al. (2013) documenting that volatile contents (H2O) ranges from 3 to 5 wt% with magma temperatures around 1273 K. On the basis of these data, the volatile content ng0 and magma temperature T0 in the simulations presented here are set to be 3 wt% and 1273 K, respectively.
Magma discharge rates were precisely estimated using a combined geodetic and satellite observation-based method (Kozono et al., 2013). A combination of geodetic volume change and lava effusion volume enabled an estimation of the magma discharge rate during the sub-Plinian events, at 450–741 m3 s−1, corresponding to 1.13−1.85×106 kg s−1. These results are consistent with an estimate based on the total amount of tephra fall deposits divided by the eruption duration (Maeno et al., 2012). Here, we assume that the magma discharge rate was 1.5 × 106 kg s−1.
4. Simulation Results
The simulated plume height and shape are quantitatively consistent with the weather radar echo observation at heights of 6.5–8.5 km (Shimbori and Fukui, 2012). The result illustrated in Fig. 5(a) also agrees with visible and infrared satellite images sequentially captured by JMA that show clouds drifting toward the east-southeast. In addition, Fig. 5(b) indicates that the dispersal axis of the main fall deposit within our simulations is consistent with field observations (Maeno et al., 2012). As mentioned above, our model predicts some interesting features of the fall deposits, with the size of particles deposited on the ground decreasing with increasing horizontal distance from the vent, and the orientation of the main axis potentially being grain size dependent (see colors in Fig. 5(b)). More detailed and quantitative comparisons between simulation results (using a much larger number of marker particles) and field observations are needed to provide more realistic depositional patterns.
Our simulations successfully reproduce the basic features of syn- and post-eruptive field observations such as the height and shape of the plume, the direction of the horizontally moving cloud and the dispersal axis of the main fall deposit. In particular, the plume height in our 3D model quantitatively agrees with observed plume heights (6.5–8.5 km); this is important, as plume height is one of the key observable quantities used in estimating magma discharge rates (e.g., Suzuki and Koyaguchi, 2009). Magma discharge rates during explosive eruptions in a still environment have been estimated using steady one-dimensional (1D) volcanic plume models (e.g., Woods, 1988; Carrazo et al., 2008). Here, we present a detailed comparison between our 3D results and predictions using a steady 1D model, and discuss how the relationship between magma discharge rate and plume height changes when wind effects are taken into account.
The features observed in Fig. 7(a) cannot be obtained using Eq. (5), which is based on a simple sum of geometrical effects and wind entrainment. Quantitative estimation of effect of the vortical structure shown in Fig. 7(a) on the efficiency of turbulent mixing and plume height needs more systematic 3D model-based analyses, and they are currently in progress. This research will provide a better understanding of mixing processes in volcanic plumes and lead to improved analytical models that allow the rapid assessment of magma discharge rates from plume height (e.g., Degruyter and Bonadonna, 2012).
6. Concluding Remarks
We used a 3D numerical model of an eruption cloud to simulate the development of a volcanic plume that was strongly bent over by winds during the 2011 Shinmoe-dake eruptions. These simulation results, such as the height and shape of the plume, agree well with observations based on satellite images and weather radar echo measurements. These plume height simulations indicate that wind substantially enhances the efficiency of turbulent mixing between the eruption cloud and ambient air, leading to a decrease in plume height compared with plumes that form in still environments.
Our results also suggest that the previous 1D wind model overestimates the effects of wind on turbulent mixing efficiency (i.e., the value of β), and hence, underestimates plume height in a strong wind field for a given magma discharge rate. In order to improve the plume height estimations by the 1D wind model, systematic 3D numerical studies that determine the preferable value of β are required.
Our simulation results also clearly indicate that fine ash particles suspended in horizontally moving clouds were transported toward the east-southeast by high-altitude winds, whereas the distribution of fallout from the eruption cloud was strongly controlled by low-altitude winds. This led to the dispersal axis of the main fall deposit extending to the southeast, agreeing well with field observations. However, some of the quantitative features of depositional patterns determined during our simulations are not necessarily consistent with observations during the 2011 Shinmoe-dake eruptions. For example, minor large clasts with 70–80 mm in diameter were observed ~7 km away from the vent, whereas our simulations predict that such large clasts are limited near the vent (within 1–2 km). This inconsistency is considered to result from the assumption in our model that the gas-pyroclasts mixture is ejected at the atmospheric pressure with the sound velocity (134 m s−1). On this assumption, the large clasts whose terminal velocities is higher than the above exit velocity necessarily leave from the plume at low level and fall to the ground near the vent. On the other hand, in reality, the eruption intensity fluctuates with time and the exit pressure can be higher than the atmospheric pressure. Under these conditions, the flow just above the vent becomes supersonic and transports large clasts up to higher levels (e.g., Koyaguchi et al., 2010). Further studies are needed to evaluate the effects of these processes on turbulent mixing and ash dispersal.
We acknowledge Akihiro Hashimoto for providing data on atmospheric conditions, and we thank the Earth Simulator Center of the Japan Agency for Marine-Earth Science and Technology, and the Research Institute for Information Technology at Kyushu University for supporting this study. The manuscript was improved by comments from Mie Ichihara, Larry Mastin and an anonymous reviewer. Part of this study was supported by the ERI Cooperative Research Program and the Special Coordination Funds for Promoting Science and Technology from MEXT, “Urgent Study on the 2011 Eruption of Kirishima-Shinmoe-dake Volcano”. The satellite image was provided by Center for Environmental Remote Sensing, Chiba University.
- Bonadonna, C., J. C. Phillips, and B. F. Houghton, Modeling tephra sedimentation from a Ruapehu weak plume eruption, J. Geophys. Res., 110, B08209, 2005.Google Scholar
- Bursik, M., Effect of wind on the rise height of volcanic plumes, Geophys. Res. Lett., 28(18), 3621–3624, 2001.View ArticleGoogle Scholar
- Carazzo, G., E. Kaminski, and S. Tait, On the dynamics of volcanic columns: A comparison of field data with a new model of negatively buoyant jets, J. Volcanol. Geotherm. Res., 178, 94–103, 2008.View ArticleGoogle Scholar
- Chong, M. S., A. E. Perry, and B. J. Cantwell, A general classification of three-dimensional flow fields, Phys. Fluids A, 2, 765–777, 1990.View ArticleGoogle Scholar
- Degruyter, W. and C. Bonadonna, Improving on mass flow rate estimates of volcanic eruptions, Geophys. Res. Lett., 39, L16308, 2012.View ArticleGoogle Scholar
- Dimotakis, P. E., The mixing transition in turbulent flows, J. Fluid Mech., 409, 69–98, 2000.View ArticleGoogle Scholar
- Fric, T. F. and A. Roshko, Vortical structure in the wake of a transverse jet, J. Fluid Mech., 279, 1–47, 1994.View ArticleGoogle Scholar
- Hashimoto, A., T. Shimbori, and K. Fukui, Tephra fall simulation for the eruptions at Mt. Shinmoe-dake during 26–27 January 2011 with JMANHM, SOLA, 8, 37–40, 2012.View ArticleGoogle Scholar
- Hewett, T. A., J A. Fay, and D. P. Hoult, Laboratory experiments of smokestack plumes in a stable atmosphere, Atmos. Environ., 5, 769–789, 1971.View ArticleGoogle Scholar
- Koyaguchi, T., Y. J. Suzuki, and T. Kozono, Effects of the crater on eruption column dynamics, J. Geophys. Res., 115, B07205, 2010.Google Scholar
- Kozono, T., H. Ueda, T. Ozawa, T. Koyaguchi, E. Fujita, A. Tomiya, and Y. J. Suzuki, Magma discharge variations during the 2011 eruptions of Shinmoe-dake volcano, Japan, revealed by geodetic and satellite observations, Bull. Volcanol., 75:695, 2013.View ArticleGoogle Scholar
- Kunii, D. and O. Levenspiel, Fluidization Engineering, John Wiley, New York, 1969.Google Scholar
- Maeno, F., M. Nagai, S. Nakada, R. Burden, S. Engwell, Y. Suzuki, and T. Kaneko, Constraining tephra dispersion and deposition from cyclic subplinian explosions at Shinmoedake volcano, Kyushu, Japan, 2011, Japan Geoscience Union Meet., SVC50-07, 2012.Google Scholar
- Morton, B. R., G. I. Taylor, and J. S. Turner, Turbulent gravitational convection from maintained and instantaneous sources, Proc. R. Soc. London, Ser. A, 234(1196), 1–23, 1956.View ArticleGoogle Scholar
- Ogden, D. E., K. H. Wohletz, G. A. Glatzmaier, and E. E. Brodsky, Numerical simulations of volcanic jets: importance of vent overpressure, J. Geophys. Res., 113, B02204, 2008.Google Scholar
- Roe, P. L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43, 357–372, 1981.View ArticleGoogle Scholar
- Sarna-Wojcicki, A. M., S. Shipley, R. B. Waitt Jr., D. Dzurisin, and S. H. Wood, Areal distribution, thickness, mass, volume, and grain size of air-fall ash from the six major eruptions of 1980, in The 1980 Eruptions of Mount St. Helens, edited by P. W. Lipman and R. L. Christiansen, 577–601, U. S. Geological Survey, 1981.Google Scholar
- Shimbori, T. and K. Fukui, Time variation of the eruption cloud echo height from Shinmoe-dake volcano in 2011 observed by Tanegashima and Fukuoka weather radars: Part II, Rep. Coord. Comm. Predict. Volcan. Erup. 109, 2012 (in Japanese) (in Printing).Google Scholar
- Sparks, R. S. J., The dimensions and dynamics of volcanic eruption columns, Bull. Volcanol., 48, 3–15, 1986.View ArticleGoogle Scholar
- Suzuki, Y., A. Yasuda, N. Hokanishi, T. Kaneko, S. Nakada, and T. Fu-jii, Syneruptive deep magma transfer and shallow magma remobiliza-tion during the 2011 eruption of Shinmoe-dake, Japan—Constraints from melt inclusions and phase equilibria experiments—, J. Volcanol. Geotherm. Res., 257, 184–204, 2013.View ArticleGoogle Scholar
- Suzuki, Y. J. and T. Koyaguchi, A three-dimensional numerical simulation of spreading umbrella clouds, J. Geophys. Res., 114, B03209, 2009.Google Scholar
- Suzuki, Y. J. and T. Koyaguchi, Numerical determination of the efficiency of entrainment in volcanic eruption columns, Geophys. Res. Lett., 37, L05302, 2010.View ArticleGoogle Scholar
- Suzuki, Y. J., T. Koyaguchi, M. Ogawa, and I. Hachisu, A numerical study of turbulent mixing in eruption clouds using a three-dimensional fluid dynamics model, J. Geophys. Res., 110, B08201, 2005.Google Scholar
- van Leer, B., Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow, J. Comput. Phys., 23, 263–275, 1977.View ArticleGoogle Scholar
- Wang, H. and A. W.-K. Law, Second-order integral model for a round turbulent buoyant jet, J. Fluid Mech., 459, 397–428, 2002.Google Scholar
- Woods, A. W., The fluid dynamics and thermodynamics of eruption columns, Bull. Volcanol., 50, 169–193, 1988.View ArticleGoogle Scholar
- Woods, A. W. and S. M. Bower, The decompression of volcanic jets in a crater during explosive volcanic eruptions, Earth Planet. Sci. Lett., 131, 189–205, 1995.View ArticleGoogle Scholar