Modelling melting rates in upwelling mantle

Upwelling regions of the mantle can undergo partial melting as a result of decompression. Many models for the dynamics of these regions have largely ignored the actual melting process or have prescribed a uniform melting rate proportional to the upwelling velocity. This paper uses a simple model for an upwelling column to calculate the melting rate from conservation principles. The model rock comprises two chemical components, and is assumed to be in thermodynamic equilibrium. For idealized linear phase constraints the melting rate can be calculated analytically, and is found to be proportional to the average upwelling velocity of both the matrix and melt.A secondary aim is to discuss reactive instabilities; the model predicts that the one dimensional state will be linearly stable, whereas previous models have suggested that reactive infiltration instability should occur. This is argued to be a result of the ‘background’ melting rate which has not usually been fully accounted for, but which has a stabilizing effect. The model here can also be applied to a column in which some melt is already present, and in that case it does exhibit a channeling instability. It is concluded that accounting for melt production consistently in mid-ocean ridge models is important when assessing the likely modes of melt transport.

Research Highlights
► Fluid dynamical model for upwelling mantle incorporates a melting term.
► Idealized melting rate is proportional to mean vertical velocity of matrix and melt.
► Reactive channeling instability is possible but only if sufficient melt is present.
► One dimensional column appears stable — inflow conditions are important.