Mantle convection as a boundary layer phenomenon

Summary. The boundary layer nature of vigorous thermal convection is explored using high resolution numerical solutions to the governing hydrodynamic equations. These solutions are obtained for a series of idealized models of the Earth’s mantle in which the viscosity is assumed to be constant. A detailed analysis of the local energy balance within the horizontal and vertical thermal boundary layers is presented in terms of which a test of the fundamental assumptions of boundary layer theory is provided. The results of this test have important geophysical consequences since the asymptotic predictions of boundary layer theory have been employed extensively in the context of thermal history modelling. Although boundary layer theory closely predicts the correct power-law behaviour of various quantities it does not determine their absolute values accurately. Vertical advection is shown to play an important role in the energy balance within horizontal boundary layers at all Rayleigh numbers. Horizontal and vertical advection dominate the energy balance within vertical plumes while horizontal diffusion plays a very minor role. When heating is partially from within the fluid, vertical advection into the upper thermal boundary layer can produce significant departures in the thermal structure from that found when heating is entirely from below. For a free upper boundary this results in a relative flattening of the variations of surface topography and heat flow across the convection cells. For a constant velocity upper boundary (similar to plate motion) the bathymetry flattens but the heat flow does not; this result agrees with marine observations. Rigidity of the thermal boundary layer below the upper surface is not included explicitly in the model, and it is not known whether the inclusion of this feature in future models would significantly alter the topographic expression. If not, the observed departure of the oceanic bathymetry from a 6 dependence at old ocean floor ages could be attributed to a small amount of internal heating in a mantle-wide convective circulation.