A mathematical model of magma transport in the asthenosphere
A mathematical model of magma transport in the asthenosphere
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软流圈中岩浆输送的数学模型
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
A. Fowler
中科院分区：
文献类型：
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作者：
A. Fowler
摘要本文提出了一个部分熔体通过其固相流动的数学模型。该模型基于两相流守恒定律，当固体基质变形非常缓慢时，两相流守恒定律可归结为可渗透介质中多孔介质流动的一般化。熔体的连续性方程包含一个源项（由于熔化），它由能量方程确定。此外，熔体分数是未知的，并介绍了一个新的方程，代表孔隙空间守恒。该方程也可以被认为是熔体压力的本构律（其不是岩石静力学的）。该模型是无量纲化和简化的。一些简单的解决方案被认为是，它被认为是在解决方案中的高流体压力的发生可能会启动在岩石圈的裂缝，从而提供了一个启动机制，岩浆上升到表面。
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.