STABILITY OF THERMAL CONVECTION IN THE EARTH IN THE CASE OF A CONTACT BOUNDARY BETWEEN THE UPPER AND LOWER MANTLE

Abstract

The generally accepted belief that the presence of a contact or chemical boundary between the upper and lower mantle gives rise to two-tier convection is entirely based on the work of Richter and Johnson, who analyzed the thermal-convection stability in a system consisting of two layers of equal thickness. We have demonstrated that when small density discontinuities occurred at the contact boundary, the critical Raleigh numbers for the occurrence of the first three instability modes increase more rapidly with density differences at the boundary than does the critical Rayleigh number associated with the fourth instability mode (with four stacked cells). The fourth mode becomes more stable than the first three when the density difference reaches a specific value. But this value is not the same as the upper limit that is imposed on this difference by the perturbation theory that we used in our earlier paper, and so we return to this subject herein.