Mantle convection and the thermal structure of the plates

Abstract

Though a simple thermal model of plate creation matches the observed bathymetry and heat flow with considerable accuracy, it only does so because a constant temperature is imposed as a lower boundary condition. A more realistic model is developed here, based on the idea that the thermal structure of the plate becomes unstable and leads to the development of small‐scale convection. Convective heat transport then supplies the heat flux needed to match the observations rather than an artificial constant temperature boundary condition. The temperature dependence of the rheology is represented in a simple manner. Below a given temperature the material is assumed to move rigidly, defining an upper mechanical boundary layer. Beneath this rigid layer, where the temperatures are greater, the material is assumed to have a constant Newtonian viscosity. The part of the viscous region where there are significant vertical temperature gradients, immediately below the mechanical boundary layer, forms a thermal boundary layer. As the plate cools, both the mechanical and thermal boundary layers increase in thickness. A local critical Rayleigh number criterion is used to test the stability of the thermal boundary layer. On this basis a convective instability is predicted, its occurrence coinciding with the breakdown of the linear dependence of the depth of the ocean floor on the square root of age. Though the small‐scale convection which develops from this instability modifies the thermal structure, the basic observational constraints are shown to be satisfied. The stability criterion is further tested in two different laboratory experiments. These experiments also illustrate a possible form for the instability, with cold dense material breaking away from the base of the plate and being replaced by hotter material from below.