STEADY SOLUTIONS FOR FEEDER DYKES IN A DENSITY-STRATIFIED LITHOSPHERE

The propagation of dykes in the lithosphere is described physically as a fluid-driven fracture process in a brittle elastic solid. From this description, mathematical solutions to the coupled equations of fluid mechanics, fracture mechanics and elasticity are used to provide simple quantitative models for steady flow (i.e. constant flow-rate) in a feeder dyke through a density-stratified lithosphere. Conditions for fracture at the dyke margins and elastic deformation of the dyke walls to be significant are derived and evaluated. The solutions demonstrate the importance of fracture, elasticity and viscous pressure drop in determining the dyke's dimensions and of the role of the level of neutral buoyancy (LNB) in determining the height of ascent. Below the LNB, vertical flow is driven by a dominant pressure balance between the local buoyancy and the local viscous pressure drop. The width and lateral extent of a dyke increase towards the LNB, and there is a transition from vertical flow to lateral flow directed along the LNB.