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A model for the spreading and compaction of two-phase viscous gravity currents

Published online by Cambridge University Press:  10 July 2009

CHLOÉ MICHAUT  and
DAVID BERCOVICI
CHLOÉ MICHAUT*
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520-8109, USA
DAVID BERCOVICI
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520-8109, USA
*
†Present address: Institut de Physique du Globe de Paris, Université Paris VII Denis-Diderot, 4, Avenue de Neptune, 94100 St-Maur des Fossés, France. E-mail address for correspondence: [email protected]
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Abstract

Two-phase viscous gravity current theory has numerous applications in the natural sciences, from small-scale lava, sedimentary and glacial flows, to large-scale flows of partially molten mantle. We develop the general equations for two-phase viscous gravity currents composed of a high viscosity matrix and low viscosity fluid for both constant volume and constant flux conditions. A loss of fluid phase is taken into account at the current's upper boundary and corresponds to the degassing of a lava flow or loss of water in sedimentary flows. As the current spreads, its surface increases and fluid loss is facilitated, which modifies the mixture density and viscosity and thus the current's shape; hence spreading of the flow affects fluid loss and vice-versa. Our results show that two-phase gravity currents retain and transport the fluid out to large distances, but the fluid is almost entirely lost within a region of finite radius. This ‘loss radius’ depends on the flow's volume or flux, fluid and matrix properties as well as on the size of fluid parcels or matrix permeability. Application to lava flows shows that degassing occurs over a large area, which affects gas release and transport in the atmosphere.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 299 - 329
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Baines, P. G. & Sparks, R. S. J. 2005 Dynamics of giant volcanic ash clouds from supervolcanic eruptions. Geophys. Res. Lett. 32, L24808. DOI:10.1029/2005GL024597.CrossRefGoogle Scholar
Bercovici, D. & Lin, J. 1994 A theoretical model of cooling viscous gravity currents with temperature-dependent viscosity. Geophys. Res. Lett. 21, 1177–1180.CrossRefGoogle Scholar
Bercovici, D. & Lin, J. 1996 A gravity current model of cooling mantle plume heads with temperature-dependent buoyancy and viscosity. J. Geophys. Res. 101, 3291–3309.CrossRefGoogle Scholar
Bercovici, D. & Ricard, Y. 2003 Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation. Geophys. J. Intl 152, 581–596.CrossRefGoogle Scholar
Bercovici, D., Ricard, Y. & Schubert, G. 2001 a A two-phase model for compaction and damage. 1. General theory. J. Geophys. Res. 106, 8887–8906.CrossRefGoogle Scholar
Bercovici, D., Ricard, Y. & Schubert, G. 2001 b A two-phase model for compaction and damage. 3. Applications to shear localization and plate boundary formation. J. Geophys. Res. 106, 8925–8940.CrossRefGoogle Scholar
Bonnecaze, R. T., Hallworth, M. A., Huppert, H. E. & Hogg, A. J. 1998 Axisymmetric particle-driven gravity currents. J. Fluid Mech. 359, 109–142.Google Scholar
Bonnecaze, R. T., Huppert, H. E. & Lister, J. R. 1993 Particle-driven gravity currents. J. Fluid Mech. 250, 339–369.CrossRefGoogle Scholar
Courant, R., Friedrichs, K. & Lewy, H. March 1967 On the partial difference equations of mathematical physics. IBM J. Res. Develop. 11 (2), 215–234.CrossRefGoogle Scholar
Crisp, J. & Baloga, S. 1990 A model for lava flows with two thermal components. J. Geophys. Res. 95, 1255–1270.CrossRefGoogle Scholar
Eichelberger, J. C., Carrigan, C. R., Westrich, H. R. & Price, R. H. 1986 Non-explosive silicic volcanism. Nature 323, 598–602.CrossRefGoogle Scholar
Fink, J. H. & Griffiths, R. W. 1990 Radial spreading of viscous gravity currents with solidifying crust. J. Fluid Mech. 221, 485–509.CrossRefGoogle Scholar
Fowler, A. C. 1984 On the transport of moisture in polythermal glaciers. Geophys. Astrophys. Fluid Dyn. 28, 99–140.CrossRefGoogle Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics, International Geophysics Series, vol. 30. Academic Press.Google Scholar
Griffiths, R. W. & Fink, J. H. 1992 The morphology of lava flows in planetary environments: predictions from analog experiments. J. Geophys. Res. 97, 19739–19748.CrossRefGoogle Scholar
Griffiths, R. W. & Fink, J. H. 1993 Effects of surface cooling on the spreading of lava flows and domes. J. Fluid Mech. 252, 667–702.CrossRefGoogle Scholar
Hallworth, M. A., Huppert, H. E. & Hogg, A. J. 1998 Effects on external flow on compositional and particle gravity currents. J. Fluid Mech. 359, 109–142.CrossRefGoogle Scholar
Hallworth, M. A., Huppert, H. E. & Sparks, R. S. J. 1987 A laboratory simulation of basaltic lava flows. Modern Geol. 11, 83–107.Google Scholar
Ho, A. M. & Cashman, K. V. 1997 Temperature constraints on the Gingko flow of the Columbia River basalt group. Geology 25, 403–406.2.3.CO;2>CrossRefGoogle Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.CrossRefGoogle Scholar
Huppert, H. E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299–322.CrossRefGoogle Scholar
Huppert, H. E., Shepherd, J. B., Sigurdsson, H. & Sparks, R. S. J. 1982 On lava dome growth, with application to the 1979 lava extrusion of the Soufrière of St Vincent. J. Volc. Geotherm. Res. 14, 199–222.CrossRefGoogle Scholar
Huppert, H. E. & Simpson, J. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.CrossRefGoogle Scholar
Jaupart, C. 1991 Effects of compressibility on the flow of lava. Bull. Volcanol. 54, 1–9.CrossRefGoogle Scholar
Johnson, A. M. & Pollard, D. D. 1973 Mechanics of growth of some laccolithic intrusions in the Henry Mountains, Utah, I. Field observations, Gilbert's model, physical properties and flow of the magma. Tectonophysics 18, 261–309.CrossRefGoogle Scholar
Klug, C. & Cashman, K. V. 1996 Permeability development in vesiculating magmas: implications for fragmentation. Bull. Volcanol. 100, 58–87.Google Scholar
Lister, J. R. & Kerr, R. C. 1989 The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface. J. Fluid Mech. 203, 215–249.CrossRefGoogle Scholar
Llewellin, E., Mader, H. M. & Wilson, S. D. R. 2002 The rheology of a bubbly liquid. Proc. R. Soc. Lond. A 458, 987–1016.CrossRefGoogle Scholar
Manga, M. 1996 Waves of bubbles in basaltic magmas and lavas. J. Geophys. Res. 101, 17457–17465.CrossRefGoogle Scholar
McKenzie, D. 1984 The generation and compaction of partially molten rock. J. Petrol. 25, 713–765.CrossRefGoogle Scholar
Nakada, S. & Motomura, Y. 1999 Petrology of the 1991–1995 eruption at Unzen: effusion pulsation and groundmass crystallization. J. Volcanol. Geoth. Res. 89, 173–196.CrossRefGoogle Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Taylor and Francis.Google Scholar
Ricard, Y., Bercovici, D. & Schubert, G. 2001 A two-phase model for compaction and damage. 2. Applications to compaction, deformation, and the role of surface tension. J. Geophys. Res. 106, 8907–8924.CrossRefGoogle Scholar
Self, S., Keszthelyi, L. & Thordarson, T. 1998 The importance of pahoehoe. Annu. Rev. Earth Planet. Sci. 110, 26–81.Google Scholar
Self, S., Widdowson, M. & Jay, T.Thordarson, A. E. 2006 Volatile fluxes during flood basalt eruptions and potential effects on the global environment: a Deccan perspective. Earth Planet. Sci. Lett. 248, 518–532.CrossRefGoogle Scholar
Sparks, R. S. J., Young, S. R., Barclay, J., Calder, E. S., Cole, P., Darroux, B., Davies, M. A., Druitt, T. H., Hartford, C., Herd, R., James, M., Lejeune, A. M., Loughlin, S., Norton, G., Skerrit, G., Stasiuk, M. V., Stevens, N. S., Toothill, J., Wadge, G. & Watts, R. 1998 Magma production and growth of the lava dome of the Soufrière Hills Volcano, Montserrat, West Indies: November 1995 to December 1997. Geophys. Res. Lett. 25, 3421–3424.CrossRefGoogle Scholar
Spiegelman, M. 1993 a Flow in deformable porous media. Part 1. Simple analysis. J. Fluid Mech. 247, 17–38.CrossRefGoogle Scholar
Spiegelman, M. 1993 b Flow in deformable porous media. Part 2. Numerical analysis – the relationship between shock waves and solitary waves. J. Fluid Mech. 247, 39–63.CrossRefGoogle Scholar
Spiegelman, M. 1993 c Physics of melt extraction: theory, implications and applications. Philos. Trans. R. Soc. Lond. Ser. A 342, 23–41.Google Scholar
Stasiuk, M. V., Jaupart, C. & Sparks, R. S. J. 1993 Influence of cooling on lava flow dynamics. Geology 21, 335–338.2.3.CO;2>CrossRefGoogle Scholar
Sumita, I., Yoshida, S., Kumazawa, M. & Hamano, Y. 1996 A model for sedimentary compaction of a viscous medium and its application to innercore growth. Geophys. J. Intl 124, 502–524.CrossRefGoogle Scholar
Thordarson, T. & Self, S. 1993 The Laki (Skatfar fires) and Grimsvotn eruptions in 1783–1785. Bull. Volcanol. 55, 233–263.CrossRefGoogle Scholar
Timmermans, M.-L. E., Lister, J. R. & Huppert, H. E. 2001 Compressible particle-driven gravity currents. J. Fluid Mech. 445, 305–325.CrossRefGoogle Scholar