Some Aspects of Thermal Convection Theory for the Earth's Mantle

A serious obstacle to developing a theory of the Earth's thermal history, allowing for the possibility of convection, is the non-linearity of the convection equations. In particular, the non-linearity arising from viscosity variation with temperature is very marked. Instead of treating viscosity either as an adjustable parameter or assigning it some value derived from indirect observation, one would like to know what value it would assume from a consideration of convection theory itself, since this might largely determine the course of thermal history. Although an analytical approach to this is impossible, if one uses a reasonable hypothesis derived from Bénard cell experiments, an answer to this problem for the Upper Mantle can be suggested.