Stability of a chemically layered upper mantle

The possibility that the upper mantle at depths less than 670 km is chemically as well as mineralogically layered has been extensively discussed. One idea posits that sublithospheric upper mantle (d < 400 km) is dominantly harzburgitic and of low intrinsic density compared with majoritic and clinopyroxene-rich piclogite which occupies the seismic transition region at depths between 400–670 km. The gravitational stability of the ‘harzburgite over piclogite’ arrangement (light above heavy) when heated from below is investigated here in order to better understand the dynamics of mixing. The calculations neglect the effects of plates, compressibility, viscous dissipation, phase change and radiogenic heating and focus on the role played by Δρρ0, the intrinsic density difference between the layers during mixing at fixed Rayleigh number. The dimensionless parameters of this problem include the thermal Rayleigh number based on the heat flux q0 into the basal piclogitic layers (Rq = α gq0d4k κν), the ratio of chemical to thermal buoyancy Rρ = (Δρρ0)kαq0d, and the thickness ratio of the two layers Δ. Here α, g, d, κ, k, ν, Δρ, ρ0 represent the expansitivity, gravity, total depth, thermal diffusivity, thermal conductivity, kinematic viscosity, isothermal difference in density between the two layers (i.e. the intrinsic density difference) and density of the piclogitic bottom layer, respectively. A constant-viscosity Newtonian rheology is assumed for the sublithospheric upper mantle between 100–670 km. Three measures of the extent and thoroughness of mixing are used to quantify mixing; these include the variance of the compositional field, the two-point spatial correlation function for composition and the average composition within each layer. The spatial correlation enables one to define a dominant length scale characteristic of the size of the chemical anomalies (L∗). The adimensional variance, sometimes called the mixing intensity, may be used to define a mixing time. Simulations at fixed Rq but with Δρρ0 = 0, 2, 4, 8% have been carried out for periods of time equivalent to the age of the Earth. The critical Rρ that separates well-mixed states from poorly mixed ones is Rρ ≈ 15 for Rq = 2 × 105. For nominal upper-mantle parameters this implies a critical intrinsic density difference Δρρ0 ≈ 3%. The style of mixing is grossly different depending on whether Δρρ0 is less than, or greater than, the critical value. Plume penetration with rapid changes in the average size of chemical heterogeneities is the dominant mechanism at low Δρρ0 whereas for high Δρρ0 viscous entrainment and the stretching of tendrils along the layer interface is the dominant mixing style. For density ratios near the critical value, the fraction of fertile (easily fused) peridotite within the dominantly harzburgitic upper mantle above the top of the transition region varies quasiperiodically with period ≈ 0.6 Ga, roughly equal to the supercontinent cycle time. Intermittent periods of increased lower-layer transport across the top of the transition zone may correlate with spikes in the volumetric rate of magma generation due to decompression melting of ascending fertile peridotite.