Mean-field methods in mantle convection.

The use of the single-mode, mean field method as a simple tool in understanding the physics of mantle convection is investigated. We present here a summary of steady-state results derived from both the incompressible (Boussinesq) and the compressible (anelastic) set of equations for cartesian geometry. Several new findings have resulted from the mean-field method. Of foremost geophysical interest are 1) the strong non-linear coupling between the adiabatic heating parameters and the creep parameters, particularly the activation volume, 2) the constraint on the amount of internal heating in the mantle from consideration of melting temperatures in variable viscosity convection and 3) the important role played by dissipative heating in compressible convection with temperature and pressure dependent viscosity. -from Authors