Steady-state Mantle-Melt Interactions in One Dimension: II. Thermal Interactions and Irreversible Terms

Progress in development of thermodynamically based models ofsilicate equilibria with explicit entropy budgets has motivateda reexamination of the conclusion of McKenzie (Journal of Petrology25, 713–765, 1984) that isentropic upwelling sufficesas a model of mantle melting. An entropy budget equation forfractional melting with melt migration in an upwelling two-phasecontinuum is presented. The energetically self-consistent meltproduction model predicted by MELTS is used to evaluate numericallythe magnitudes of differences between fractional melting (withmelt migration) and equilibrium melting (without relative movement)that can be bounded in one dimension: chemical advection byout-of-equilibrium melt; thermal disequilibrium between migratingliquid and residue; frictional dissipation of gravitationalpotential; dissipation as a result of solid compaction. Likethe familiar isobaric case in which fractional melting is significantlyless productive than equilibrium melting, chemical isolationof the escaping melts from the residue reduces the oceanic crustalthickness by