Interfacial turbulent mixing in stratified magma reservoirs

We analyse the interfacial turbulent mixing of molten magmas in a two-layer stratified convecting magma chamber. We examine situations where convection is driven by the heat and/or compositional flux associated with the melting of a solid boundary. The model applies to the case in which the Rayleigh number is sufficiently large that the effect of a viscosity difference on turbulent entrainment is negligible and so the model predictions represent an upper bound for interfacial mixing. Our results suggest that the extent of mixing induced by the thermal buoyancy flux is relatively small. However, the compositional buoyancy fluxes associated with phase change may be much larger and the mixing they induce may significantly affect the evolution of the reservoir. Our analysis of the melting of the floor of a two-layer stratified magma chamber shows that turbulent mixing at the interface between the two magmas may suppress the melting, and decrease the final amount of melt produced when the system reaches thermal equilibrium. It is also shown that, although floor melting tends to decrease the density of the lower layer of magma, somewhat counterintuitively, turbulent interfacial mixing with the overlying layer of smaller density may inhibit large scale overturn and preserve the stratified state of the chamber. In the case in which both the floor and roof of a chamber melt, turbulent mixing at the interface between the newly formed light melt at the roof and the lower layer of dense magma induces a shift of the melting process from the floor to the roof. For typical parameter values in a basaltic magma chamber, we estimate that under conditions of very large Rayleigh number, the amount of crustal melt produced al the roof may be as high as 50% of that produced at the floor.