Solitary-waves in geophysical two-phase viscous media: A semi-analytical solution

To better understand the process of geofluid (melt, water) migration in the earth’s mantle, we have investigated the mathematical formulation of the two-phase theory for compaction, which implicitly accounts for a porosity dependent effective (bulk) viscosity of the two-phase mixture. Following previous studies, we have searched for solitary waves solution of permanent shape. Our results confirm analytically the existence of such solitary waves. To highlight their characteristics, a comparison of the properties of these waves with the waves produced in a two-phase mixture with constant effective (bulk) viscosity is presented. In particular, the solitary waves that are observed in porosity dependent effective viscosity simulations are steeper and their speed decreases as a function of one over the background porosity. These characteristics may have important implications for the interpretation of the geochemistry and morphology of melt-related processes. Additionally, our analytical solutions can be used for numerical benchmarking of two-phase codes.