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A mathematical model of magma transport in the asthenosphere

1985; Taylor & Francis; Volume: 33; Issue: 1-4 Linguagem: Inglês

10.1080/03091928508245423

1029-0419

A. C. Fowler,

Navier-Stokes equation solutions

Abstract We present a mathematical model for the flow of a partial melt through its solid phase. The model is based on the conservation laws of two-phase flow, which reduce to a generalization of porous flow in a permeable medium, when the solid matrix deforms very slowly. The continuity equation for the melt contains a source term (due to melting), which is determined by the energy equation. In addition, the melt fraction is unknown, and a new equation, representing conservation of pore space, is introduced. This equation may also be thought of as a constitutive law for the melt pressure (which is not lithostatic). The model is non-dimensionalized and simplified. Some simple solutions are considered, and it is suggested that the occurrence of high fluid pressures in the solutions may initiate fractures in the lithosphere, thus providing a starting-up mechanism for magma ascent to the surface.