Abstract
Based on the full mathematical model of a viscous magma melt flow ascending in the gravity field behind a decompression wave front, an unsteady two-dimensional axisymmetric problem of the melt state dynamics at the initial stage of an explosive volcanic eruption and specific features of the flow in the vicinity of the channel wall for the cases of stationary and dynamically increasing viscosity are studied. The evolution of the boundary layer is numerically analyzed for a constant melt viscosity equal to µ = 10 3, 10 5, and 10 7 Pa · sec. It is demonstrated that a boundary layer is formed on the wall of the channel with a radius of 100 m as the melt viscosity is changed in the range of 10 3–10 5 Pa · sec, and the boundary layer thickness increases from 2 to 15 m. As the magma viscosity increases to 10 7 Pa · sec, the boundary layer chokes the major part of the channel, thus, locking the flow in the vicinity of the axis of symmetry of the channel almost over the entire channel length. Substantial changes in the flow structure caused by dynamically increasing viscosity are demonstrated by an example of the melt in the channel with a radius of 10 m. By the time t = 1.1 sec, the boundary layer thickness in the channel cross section at a height of approximately 1000 m reaches almost 8 m, the boundary layer acquires the shape similar to a “diaphragm,” penetrates inward the channel by 200 m (with the mass velocity ranging from 0 to 15 m/sec), and locks the flow in a zone with a radius of approximately 2 m around the axis of symmetry of the channel.
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References
H. M. Gonnermann and M. Manga, “The fluid mechanics inside a volcano,” Annu. Rev. Fluid Mech., 39, 321–356 (2007).
C. Jaupart and S. Vergniolle, “Laboratory models of hawaiian and strombolian eruptions,” Nature, 331, 58–60 (1988).
E. A. Parfitt, “A discussion of the mechanisms of explosive basaltic eruptions,” J. Volcanol. Geotherm. Res., 134, 77–107 (2004).
E. A. Blackburn, L. Wilson, and S. Sparks, “Mechanism and dynamics of strombolian activity,” J. Geol. Soc. London, 132, 429–440 (1976).
L. Wilson, “Relationships between pressure, volatile content and eject a velocity in three types of volcanic explosion,” J. Volcanol. Geotherm. Res., 8, 297–313 (1980).
V. K. Kedrinskii, A. I. Makarov, S. V. Stebnovskii, and K. Takayama, “Explosive eruption of volcanoes: some approaches to simulation,” Combust., Expl., Shock Waves, 41, No. 6, 777–786 (2005).
V. K. Kedrinskii and A. I. Makarov, “Dynamics of cavitating magma state at explosive eruption,” in: Proc. of the 6th Int. Symp. on Cavitation (CAV2006) (Wageningen, Netherlands, September 11–15, 2006), Maritime Res. Inst. Netherlands, Wageningen (2006), Paper No. 167, pp. 1–8.
S. Vergniolle and C. Jaupart, “Dynamics of degassing at Kilauea volcano, Hawaii,” J. Geophys. Res., 95, 2793–2809 (1990).
D. A. Swanson and R. T. Holcomb, “Regularities in growth of the Mount St. Helens dacite dome 1980–1986,” in: J. H. Fink (ed.), Lave Flows and Domes: Emplacement Mechanisms and Hazard Implications, Springer Verlag, Berlin (1990), pp. 3–24.
B. Voight, S. Sparks, A. D. Miller, et al., “Magma flow instability and cyclic activity at Soufriere Hills Volcano, Montserrat, British West Indies,” Science, 283, 1138–1142 (1999).
V. K. Kedrinskii, “Explosive eruptions of volcanoes: simulation, shock tube methods and multi-phase mathematical models (plenary lecture),” in: Proc. of the 26th Int. Symp. on Shock Waves (Goettingen, Germany, July 17–21, 2007), Vol. 1, Springer Verlag, Berlin-Heidelberg (2009), pp. 19–26.
R. P. Denlinger and R. P. Hobitt, “Cyclic eruptive behavior of silicic volcanoes,” Geology, 27, 459–462 (1999).
A. Barmin, O. Melnic, and S. Sparks, “Periodic behavior in lava dome eruptions,” Earth. Planet. Sci. Lett., 199, 173–184 (2002).
K. L. Mitchel, “Coupled conduit flow and shape in explosive volcanic eruptions,” J. Volcanol. Geotherm. Res., 143, 187–203 (2005).
A. M. Rubin, “Propagation of magma-filled cracks,” Annu. Rev. Earth Planet. Sci., 23, 287–336 (1995).
A. Gerst, M. Hort, P. R. Kyle, and M. Voege, “The first second of a strombolian eruption: velocity observations at Erebus volcano, Antarctica,” EOS, Trans. Am. Geophys. Union, 87, No. 52 (2005), Fall Meet. Suppl. Abstr. V31G-04.
V. K. Kedrinskii, M. N. Davydov, A. A. Chernov, and K. Takayama, “Initial stage of the explosive eruption of volcanoes: magma state dynamics in unloading waves,” Dokl. Ross. Akad. Nauk, 407, No. 2, 190–193 (2006).
V. K. Kedrinskii, M. N. Davydov, A. A. Chernov, and K. Takayama, “Generation and evolution of cavitation in magma under dynamic unloading,” J. Appl. Mech. Tech. Phys., 46, No. 2, 208–215 (2005).
E. S. Persikov, “The viscosity of magmatic liquids: experiment, generalized patterns. A model for calculation and prediction. Applications,” in: Physical Chemistry of Magmas, Vol. 9: Advances in Physical Geochemistry, Springer Verlag, New York (1991), pp. 1–40.
V. K. Kedrinskii and S. Plaksin, “Rarefaction wave structure in a cavitating liquid,” in: Proc. of the 11th Symp. on Nonlinear Acoustics (Novosibirsk, August 24–28, 1987), Vol. 1, Sib. Branch USSR Acad. Sci. (1987), pp. 51–55.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 4, pp. 95–105, July–August, 2010.
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Kedrinskii, V.K., Davydov, M.N. Dynamics of boundary layer formation in a volcano channel in a cavitating high-viscosity magma flow. J Appl Mech Tech Phy 51, 529–537 (2010). https://doi.org/10.1007/s10808-010-0069-z
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DOI: https://doi.org/10.1007/s10808-010-0069-z