Parameterized thermal convection in a layered region and the thermal history of the Earth

Abstract

Parameterized convective schemes for constant viscosity fluids are used to investigate the influence of layering on the relationship between the rate of heat loss from and heat supply to a number of convecting layers of different viscosity and thicknesses. Simple analytic expressions are obtained which accurately predict the behavior to a step decrease in the heat supply, and show that layering considerably increases the response time. The same arguments are applied to a planet consisting of spherical shells. They show that the response of the earth's heat loss to the decay of radioactive elements depends strongly on whether or not mantle convection extends from the core to the surface. If it does so, the surface heat flux is only about 50% greater than the heat generation rate. However if upper and lower mantle convection occurs in two separate shells, as seismological and geochemical arguments suggest, the response time is increased. The present surface heat flux is then principally controlled by the thermal structure of the earth at the time it was formed. The best estimate of the present ratio of the heat loss to heat generation is about two, and this value is consistent with the behavior of an earth model consisting of a two‐layered mantle overlying a core.