Mixing and compositional stratification produced by natural convection 1. Experiments and their application to Earth's core and mantle

An extensive series of laboratory experiments is used to quantify the circu mstances under which fluids can be mixed by natural convection at high flux Rayleigh number. A compositionally buoyant fluid was injected at a fixed r ate into an overlying layer of ambient fluid from a planar, horizontally un iform source. The nature of the resulting compositional convection was foun d to depend on two key dimensionless parameters: a Reynolds number Re and t he ratio U of the ambient fluid viscosity to the input fluid viscosity. Inc reasing the Reynolds number corresponded to increasing the vigor of the con vection, while the viscosity ratio was found to determine the spacing betwe en plumes and whether buoyant fluid rose as sheets (U < 1) or axisymmetric plumes (U > 1). From measurements of the final density profile in the fluid after the experiments we quantified the extent to which buoyant liquid was mixed in terms of a thermodynamic mixing efficiency E. The mixing efficien cy was found to be high (E > 0.9) when either the Reynolds number was large (Re > 100) or the viscosity ratio was small (U < 0.2) and was found to be low (E < 0.1) when both Re < 1 and U > 200. The amount of mixing was relate d to whether ascending plumes generated a large-scale circulation in the am bient fluid. When our results are applied to the differentiation of the Ear th's core, we suggest that the convection resulting from the release of buo yant residual liquid into the liquid outer core due to crystallization at t he boundary between the inner and the outer core will probably lead to near ly complete mixing. In the dynamically very different context of the mantle , mantle plumes are predicted to ascend through the mantle and pond beneath the lithosphere, whereas convection driven by the subduction of oceanic li thosphere is expected to produce moderate to extensive mixing of the mantle . When the competing plate and plume modes of mantle convection are conside red together, we find that owing to a larger driving buoyancy flux, the pla te-scale flow will destroy any stratification at the top of the mantle prod uced by mantle plumes. Applying our results to the "stagnant lid" style of thermal convection predicted to occur in the mantles of the Moon, Mercury, Mars, Venus, and pre-Archean Earth, we expect the respective flows to produ ce minor thermal stratification at the respective core-mantle boundaries. I n part 2 of this study [Jellinek and Kerr, this issue] we apply our results to the differentiation of magma chambers and komatiite lava flows.