Steady state double-diffusive convection in magma chambers heated from below.

In order to deduce the vertical structure of doubly-diffusive convection cells in magma chambers, solutions to the horizontally-averaged conservation equations governing the distribution of T, composition and velocity in a two component (rhyolite-basalt) Newtonian melt were obtained. Boundary conditions were chosen to model a chamber with a hot, dense (basaltic) base, overlain by cooler more silicic magma, where the influences of sidewall cooling, crystallization and melting are not considered. Steady-state solutions were obtained for values of the various parameters involved in the range appropriate to magma chambers and include the effects of a strongly T-dependent viscosity. Calculations show that a critical Lewis number (Le_crit) separates steady single-cell convection from unsteady convection and conduction. For isoviscous convection at a wave number k = pi and for Le > Le_crit = 6.7Ra^-0.12Rrho ^1.67, single-layer convection cells characterized by thin chemical and thermal boundary layers and well-mixed interiors develop. Magma chambers lie above this critical Lewis number and, therefore, steady-state model magma chambers exhibit single cell convection. Calculated heat flow values in the range 2000-20 000 mW/m² compare favourably with measurements in active geothermal areas. Redistribution times for major elements by advective-diffusive transport are in the range 10⁵-10⁶ years. Crystal settling is restricted to the chamber margins where convective velocities are much smaller. It is suggested that effects of intertia can cause differences in the dynamic behaviour of double-diffusive convection.-J.M.H.