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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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