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Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks

Published online by Cambridge University Press:  26 April 2006

John R. Lister
John R. Lister
Affiliation:
Research School of Earth Sciences, Australian National University, PO Box 4. Canberra 2601, ACT, Australia Present address: Institute of Theoretical Geophysics and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK.
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Abstract

Buoyancy-driven flows resulting from the introduction of fluid of one density into a crack embedded in an elastic solid of different density are analysed. Scaling arguments are used to determine the regimes in which different combinations of the buoyancy force, elastic stress, viscous pressure drop and material toughness provide the dominant pressure balance in the flow. The nonlinear equations governing the shape and rate of spread of the propagating crack are formulated for the cases of vertical propagation of buoyant fluid released into a solid of greater density and of lateral propagation of fluid released at an interface between an upper layer of lesser density and a lower layer of greater density. Similarity solutions of these equations are derived under the assumption that the volume of fluid is given by Qtα, where Q and α are constants. Both laminar and turbulent flows are considered.

Fluid fracture is an important mechanism for the transport of molten rock from the region of production in the Earth's mantle to surface eruptions or near-surface emplacement. The theoretical solutions provide simple models which describe the relation between the elastic and fluid-mechanical phenomena involved in the vertical transport of melt through the Earth's lithosphere and in the lateral intrusion of melt at a neutral-buoyancy level close to the Earth's surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 213 - 239
Copyright
© 1990 Cambridge University Press

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References

Aki, K., Fehler, M. & Das, S. 1977 Source mechanisms of volcanic tremor: fluid-driven crack models and their application to the 1963 Kilauea eruption. J. Volcanol. Geotherm. Res. 2, 259–287.Google Scholar
Anderson, O. L. & Grew, P. C. 1977 Stress corrosion theory of crack propagation with applications to geophysics. Rev. Geophys. Space Phys. 15, 77–103.Google Scholar
Bruce, P. M. & Huppert, H. E. 1989 Thermal controls of basaltic fissure eruptions. Nature 342, 665–667.Google Scholar
Bruce, P. M. & Huppert, H. E. 1990 Solidification and melting in dykes by the laminar flow of basaltic magma. In Magma Transport and Storage (ed. M. P. Ryan). Wiley.
Carmichael, I. S. E., Nicholls, J., Spera, F. J., Wood, B. J. & Nelson, S. A. 1977 High temperature properties of silicate liquids: applications to the equilibration and ascent of basic magma. Phil. Trans. R. Soc. Lond. A 286, 373–431.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. (eds.) 1954 Tables of Integral Transforms. McGraw Hill.
Fiske, R. S. & Jackson, E. D. 1972 Orientation and growth of Hawaiian volcanic rifts: the effect of regional structure and gravitational stresses. Proc. R. Soc. Lond. A 329, 299–326.Google Scholar
Hirs, G. G. 1974 A systematic study of turbulent film flow. J. Lubric. Tech. 96, 118–126.Google Scholar
Huppert, H. E. 1982a The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Huppert, H. E. 1982b Flow and instability of a viscous current down a slope. Nature 300, 427–429.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1985 Cooling and contamination of mafic and ultramafic magma during ascent through continental crust. Earth Planet. Sci. Lett. 74, 371–386.Google Scholar
Huppert, H. E., Sparks, R. S. J., Turner, J. S. & Arndt, N. T. 1984 Emplacement and cooling of komatiite lavas. Nature 309, 19–22.Google Scholar
Irwin, G. R. 1958 Fracture. In Handbuch der Physics VI (ed. S. Flügge), pp. 551–255. Springer.
Lister, J. R. 1990a Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors. J. Fluid Mech. 210, 263–280.Google Scholar
Lister, J. R. 1990b Fluid-mechanical models of crack propagation and their application to magma-transport in dykes. J. Geophys. Res. (in preparation).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.Google Scholar
Maaloe, S. 1987 The generation and shape of feeder dykes from mantle sources. Contrib. Min. Petrol. 96, 47–55.Google Scholar
MacDonald, R., Wilson, L., Thorpe, R. S. & Martin, A. 1988 Emplacement of the Cleveland Dyke: evidence from geochemistry, mineralogy and physical modelling. J. Petrol. 29, 559–583.Google Scholar
Muskhelishvili, N. I. 1975 Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff.
Pasteris, J. D. 1984 Kimberlites: complex mantle salts. Ann. Rev. Earth Planet. Sci. 12, 133–153.Google Scholar
Pollard, D. D. 1987 Elementary fracture mechanics applied to the structural interpretation of dykes. In Mafic Dyke Swarms (ed. H. C. Halls & W. H. Fahrig). Geol. Soc. Canada Special Paper 34.
Pollard, D. D. & Holzhausen, G. 1979 On the mechanical interaction between a fluid-filled fracture and the Earth's surface. Tectonophys. 53, 27–57.Google Scholar
Pollard, D. D. & Muller, O. H. 1976 The effects of gradients in regional stress and magma pressure on the form of sheet intrusions in cross-section. J. Geophys. Res. 91, 975–984.Google Scholar
Reches, Z. & Fink, J. 1988 The mechanism of intrusion of the Inyo Dike, Long Valley Caldera, California. J. Geophys. Res. 93, 4321–4334.Google Scholar
Rubin, A. M. & Pollard, D. D. 1987 Origins of blade-like dikes in volcanic rift zones. US Geol. Survey Professional Paper 1350.
Ryan, M. P. 1987 Neutral buoyancy and the mechanical evolution of magmatic systems. In Magmatic Processes: Physicochemical Principles (ed. B. O. Mysen). pp. 259–255. Geochem. Soc. Special Publication 1.
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill.
Shaw, H. R. 1980 The fracture mechanisms of magma transport from the mantle to the surface. In Physics of Magmatic Processes (ed. R. B. Hargreaves), pp. 201–255. Princeton.
Smith, P. C. 1973 A similarity solution for slow viscous flow down an inclined plane. J. Fluid Mech. 58, 275–288.Google Scholar
Spence, D. A. & Sharp, P. W. 1985 Self-similar solutions for elastohydrodynamic cavity flow. Proc. R. Soc. Lond. A 400, 289–313.Google Scholar
Spence, D. A. & Turcotte, D. L. 1989 Buoyancy-driven magma fracture: a mechanism for ascent through the lithosphere and the emplacement of diamonds. J. Geophys. Res. (submitted).Google Scholar
Spera, F. 1980 Aspects of magma transport. In Physics of Magmatic Processes (ed. R. B. Hargreaves), pp. 265–255. Princeton.
Swanson, D. A., Wright, T. L. & Helz, R. T. 1975 Linear vent systems and estimated rates of magma production for the Yakima basalt on the Columbia Plateau. Am. J. Sci. 275, 877–905.Google Scholar
Walker, G. P. L. 1989 Gravitational (density) controls on volcanism, magma chambers and intrusions. Austral. J. Earth Sci. 36, 149–165.Google Scholar
Weertman, J. 1971 The theory of water-filled crevasses in glaciers applied to vertical magma transport beneath oceanic ridges. J. Geophys. Res. 76, 1171–1183.Google Scholar