Abstract
Abstract. In source regions of magmatic systems the temperature is above solidus, and melt ascent is assumed to occur predominantly by two-phase flow, which includes a fluid phase (melt) and a porous deformable matrix. Since McKenzie (1984) introduced equations for two-phase flow, numerous solutions have been studied, one of which predicts the emergence of solitary porosity waves. By now most analytical and numerical solutions for these waves used strongly simplified models for the shear- and bulk viscosity of the matrix, significantly overestimating the viscosity or completely neglecting the porosity dependence of the bulk viscosity. Schmeling et al. (2012) suggested viscosity laws in which the viscosity decreases very rapidly for small melt fractions. They are incorporated into a 2-D finite difference mantle convection code with two-phase flow (FDCON) to study the ascent of solitary porosity waves. The models show that, starting with a Gaussian-shaped wave, they rapidly evolve into a solitary wave with similar shape and a certain amplitude. Despite the strongly weaker rheologies compared to previous viscosity laws, the effects on dispersion curves and wave shape are only moderate as long as the background porosity is fairly small. The models are still in good agreement with semi-analytic solutions which neglect the shear stress term in the melt segregation equation. However, for higher background porosities and wave amplitudes associated with a viscosity decrease of 50 % or more, the phase velocity and the width of the waves are significantly decreased. Our models show that melt ascent by solitary waves is still a viable mechanism even for more realistic matrix viscosities.
Highlights
Magmatic phenomena such as volcanic eruptions on the earth’s surface show, among others, that melt is able to ascend from partially molten regions in the earth’s mantle
Within supersolidus source regions at low melt fractions, melt is assumed to slowly percolate by two-phase porous flow within a deforming matrix (McKenzie, 1984; Schmeling, 2000; Bercovici et al, 2001), followed by melt accumulation within rising high-porosity waves (Scott and Stevenson, 1984; Spiegelman, 1993; Wiggins and Spiegelman, 1995; Richard et al, 2012) or focusing into channels which can possibly penetrate into subsolidus regions
For the mixed geometry the velocity and half width variations are minor again. These results show that as long as melt tubes represent a significant portion of the total melt volume, they control the porosity wave dynamics and keep the porosity wave properties rather fixed
Summary
Magmatic phenomena such as volcanic eruptions on the earth’s surface show, among others, that melt is able to ascend from partially molten regions in the earth’s mantle. Within supersolidus source regions at low melt fractions, melt is assumed to slowly percolate by two-phase porous flow within a deforming matrix (McKenzie, 1984; Schmeling, 2000; Bercovici et al, 2001), followed by melt accumulation within rising high-porosity waves (Scott and Stevenson, 1984; Spiegelman, 1993; Wiggins and Spiegelman, 1995; Richard et al, 2012) or focusing into channels which can possibly penetrate into subsolidus regions. An essential parameter controlling the width and phase velocity of porosity waves is the effective shear and bulk matrix viscosity (Simpson and Spiegelman, 2011; Richard et al, 2012).
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