Thermal boundary layer convection in silicic magma chambers: effects of temperature-dependent rheology and implications for thermogravitational chemical fractionation.

Solution of the nonlinear boundary value problem describing the thermomechanical structure of a boundary layer adjacent to an isothermal cooled vertical wall in a strongly temperature dependent rheological medium is presented. The analysis and boundary conditions chosen are applicable to large Rayleigh number convection in a magma chamber. Numerical solution of the boundary layer equations by parallel shooting have been obtained for viscosity contrast up to 10¹¹. Parameterization of these results allows extrapolation to higher viscosity contrasts. The non-Arrhenius viscosity function mu = mu _alpha exp(-a(T_alpha -T), (-a(T_alpha -T), where a is the rheological parameter and T is the absolute temperature, is based on experimental data and accounts for the effects of temperature and crystallinity on magma viscosity. The calculations clearly show the importance of explicit consideration of the viscosity-temperature relationship in determining the quantitative features of boundary layer convection. An analytical approach is suggested for answering the question of whether or not such fractionated melt can maintain its integrity (i.e., not become remixed).-Authors