Effects of Internal Melting and Buoyancy on Melt Band Evolution: Implications for Mid-Ocean Ridge Melt Transport

Abstract

This study analyses a two-phase porous medium whose permeability and solid viscosity are dependent on porosity. It has been established experimentally and numerically that when such a medium is subjected to shear, the porosity rearranges into stripes of high and low porosity known as melt bands (Holtzman et al. 2003; Katz et al. 2006; Butler 2009). This study uses linear theory and numerical simulations to analyze the formation of melt bands with ongoing melting and buoyancy forces. This is the first study to use analytical methods to isolate the effects of internal melting on melt bands. This study first looks at a square geometry with a simple shear stress regime to look at the effects different parameters have on the bands. The second model is used to validate the results of the first model as an analogue for the movement under the Mid-Ocean Ridge by implementing a more complex geometry based on the stream function from Spiegelman and McKenzie (1987). Both numerical and analytical results for the square geometry showed that the internal melting and strain-rate exponent, which increases the viscosity’s dependence on strain rate, both decrease the growth of the bands. The results showed that internal melting increases the effects of the strain-rate exponent on the angle of maximum growth (deviating it symmetrically about 45 degrees), but the effect is small. While buoyancy was shown to cause oscillations which are dampened by the addition of internal melting, the growth of bands is not affected. The presence of ongoing melting when bulk viscosity is constant decreases the growth rate and therefore decreases the expected magnitude of the melt bands. However, when bulk viscosity is dependent on porosity and strain-rate, the internal melting has a marginal effect on the formation of the bands. This means that the melt bands in the upper mantle may still be a viable solution for: channeling melt towards mid-ocean ridges, acting to induce seismic anisotropy, and acting as pathways of enhanced electrical conductivity.