Mixing in vigorous, time‐dependent three‐dimensional convection and application to Earth's mantle

Abstract

An understanding of the mechanism of mixing in highly viscous convecting fluids is of crucial importance in explaining the observed geochemically heterogeneous nature of Earth's mantle. Using constant viscosity numerical experiments, we describe the mixing mechanism of time‐dependent Rayleigh‐Bénard convection with an infinite Prandtl number in a three‐dimensional (3‐D) rectangular container. Mixing is observed by following the positions of passive tracers advected by the flow. The major mixing mechanisms may be described in terms of the within‐cell mixing and the cross‐cell mixing. The flow structure in which tracers move on toroidal surfaces, that was previously observed in steady state 3‐D convection systems is perturbed by boundary layer instabilities in the time‐dependent experiments. This flow structure allows a very efficient exchange of mass between the boundary layers and the core of the convection cell even in the absence of time dependence. We compare this result with calculations carried out in two spatial dimensions. In similar two‐dimensional (2‐D) experiments, exchange of mass between boundary layers and core of the convection cell is entirely effected by the boundary layer instabilities. Mixing between neighboring cells appears much slower in three dimensions than in similar 2‐D experiments, perhaps because the 3‐D cell structure is more stable relative to the boundary layer instabilities. The inferred mixing rates are observed to be relatively insensitive to initial tracer location, but the timescale for mixing, t m , decreases with increasing Rayleigh number ( t m goes approximately as Ra (−3/2) ). The timescale of mixing is an important constraint on the large scale structure of Earth, because large‐scale geochemical heterogeneities persist to the present day, implying that the mantle is not well mixed.