TY - JOUR

T1 - Steady state double-diffusive convection in magma chambers heated from below.

AU - Clark, S.

AU - Spera, F. J.

AU - Yuen, D. A.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - 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 (Lecrit) separates steady single-cell convection from unsteady convection and conduction. For isoviscous convection at a wave number k = pi and for Le > Lecrit = 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.

AB - 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 (Lecrit) separates steady single-cell convection from unsteady convection and conduction. For isoviscous convection at a wave number k = pi and for Le > Lecrit = 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.

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M3 - Article

AN - SCOPUS:0023467940

SP - 289

EP - 305

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -