RHEOLOGY OF THE EARTH'S MANTLE AND INSTABILITY OF CONVECTIVE FLOWB. I. Birger
A nonlinear integral rheological model is proposed to describe the rheology of the earth's mantle. For constant stress the model behaves like a power law non-Newtonian fluid. However, the model differs significantly if stress changes with time, because it has a memory, in contrast with the power law fluid model. The proposed model is applied to linear stability analysis of large-scale convective circulation in the mantle. The Lorenz equations, a three-mode spatial Fourier expansion of the non-linear thermal convection equations, are generalized for non-Newtonian fluid models. In the proposed rheological model, the instability of the lower thermal boundary layer of a whole mantle convective circulation is oscillatory. The period of the boundary layer convective oscillation is about $6\times 10^7$ years.