Stratification of the outer core at the core-mantle boundary

Abstract

The thermal regime of the core is controlled by the heat flux taken by the mantle across the core-mantle boundary (CMB) and its ratio Nu, the Nusselt number, to the conductive heat flux along the core adiabat. If Nu > 1, then compositional convection from the inner-core boundary (ICB) will be augmented by thermal convection from the CMB, and the outer core will be well-mixed and unstratified. If Nu < 1, as some recent estimates suggest, there is a competition between a stabilising thermal buoyancy flux from the CMB and the convective compositional buoyancy flux from the ICB. An entirely analogous competition arises if light elements diffuse from the mantle into the core. A fundamental question is whether such a stabilising buoyancy flux can stratify a layer at the CMB and, if so, how thick the layer would be. A simple spherically averaged fluid-mechanical and thermodynamic model is derived and used to examine the possibilities. Previous suggestions that compositional convection is sufficiently vigorous to maintain a well-mixed state require active entrainment downwards of buoyant fluid, which is doubtful if inertial effects are negligible. It is suggested instead that a stratified layer accumulates below the CMB, which is not incorporated into the underlying convection zone, though it may be mixed slowly by double-diffusive ‘salt-fingering.’ The thickness of the layer is calculated theoretically as a function of the controlling fluxes of heat and composition across the CMB. In the thermal case, the layer thickness adjusts rapidly to reflect the current value of Nu and is largely independent of the cooling history. The layer thickness is of order 100 km for Nu = 0.9, with a buoyancy frequency less than 10 −4 s −1. The compositional case typically gives a thinner but more strongly stratified layer and adjusts more slowly. Seismic, geomagnetic and length-of-day evidence for such layers is assessed.