A solution is obtained for steady, cellular convection when the Rayleigh number and the Prandtl number are large. The core of each two-dimensional cell contains a highly viscous, isothermal flow. Adjacent to the horizontal boundaries are thin thermal boundary layers. On the vertical boundaries between cells thin thermal plumes drive the viscous flow. The non-dimensional velocities and heat transfer between the horizontal boundaries are found to be functions only of the Rayleigh number. The theory is used to test the hypothesis of large scale convective cells in the earth's mantle. Using accepted values of the Rayleigh number for the earth's mantle the theory predicts the generally accepted velocity associated with continental drift. The theory also predicts values for the heat flux to the earth's surface which are in good agreement with measurements carried out on the ocean floors.

No abstract

Partial melting processes at mid-ocean ridges generate oceanic lithosphere which is chemically and mineralogically zoned. Basaltic oceanic crust overlies a 20-30 km thick zone of depleted upper mantle. This zone has undergone partial melting and is largely free of the high density phase, garnet, has a higher MgO/FeO ratio, and in consequence has a lower density (,~p = 0.06 gm/cm3), than the undepleted mantle of the lower lithosphere. The lithosphere does not become gravitationally unstable upon the asthenosphere for 40-5 ° Ma, when increased density resulting from thermal contraction has offset the compositional buoyancy of the depleted zone and crust. During subduction the basaltic crust inverts to eclogite and the net compositional buoyancy of the lithosphere is eliminated. However, as the subducted lithosphere is heated it becomes less rigid and density differences both between different parts of the descending lithosphere and the surrounding mantle become important. The dense eclogite layer sinks through the underlying depleted zone at a rate determined by the temperaturedependent rheology. With further heating the depleted zone becomes less dense than the overlying undepleted mantle and will diapirically rise some 30o-400 km behind the trench depending upon the angle and rate of subduction and the age of the subducted plate. Such diapirs are able to intitiate behind-arc spreading. In a continental setting the diapirs could both heat the lithosphere and produce exceptional elevation. i. I n t r o d u c t i o nIT IS NOW generally accepted that oceanic lithosphere forms by the cooling of divergent horizontal mantle flows away from ocean ridges. Because this boundary layer is cold it has two important properties" (I) it is relatively strong and is therefore able to act as a stress guide and to exhibit the large scale mechanical properties now associated with tectonic plates; (2) it is slightly more dense than the w a r m e r mantle material beneath and thus rests unstably upon it and is liable to sink.In the development of thermal models for plates a simplified petrology has generally been assumed: an oceanic lithosphere comprising a crust which was predominantly basaltic, variously hydrated, veneered with oceanic sediment, and underlain by chemically homogenous uhramafic upper mantle (e.g. Forsyth & Press 197 I).I n this paper we take a different view and show that the production of basalt beneath a mid-ocean ridge gives rise to a chemical and mineralogical layering within the lithosphere, and to density variations which are of similar size but of opposite sign, to those which result from cooling and thermal contraction.We examine the nature and magnitude of these density variations and consider their implications first for the initiation of subduction, and then for the subsequent behaviour of the subducted plate.aTl geol.

No abstract

No abstract