Abstract
Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433-20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.
Original language | English |
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Pages (from-to) | 5-36 |
Number of pages | 32 |
Journal | Journal of Fluid Mechanics |
Volume | 852 |
Early online date | 2 Aug 2018 |
DOIs | |
Publication status | Published - 10 Oct 2018 |
Keywords
- Geophysical and geological flows
- Porous media
- Reacting multiphase flow
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David W. Rees Jones
- Applied Mathematics - Lecturer
- School of Mathematics and Statistics - Director of Teaching
Person: Academic