Numerical investigation of layered convection in a three- dimensional shell with application to planetary mantles

[1] Stratified stable layered mantle convection in a three-dimensional (3-D) spherical shell is investigated for a range of depth of layer, intrinsic density contrast between the layers (Dr), and heating mode. Three heating modes are studied: internal heating, bottom heating across core-mantle boundary, and both combined. For each heating mode, layers were investigated centered at depths from 500 km to 2500 km in 500 km steps and with Dr from 1 to 5% in 1% steps. We did not find stable layering for Dr of 1%. Cases with no bottom heating were stable with Dr of 2%, but Dr of at least 3% were required by cases with a component of bottom heating. All cases with Dr of 4% or more were stable. We found that the stability of the layer is strongly dependent on the buoyancy ratio B (B = Dr raDT, where Dr is the chemical density increase across the boundary, r is the density in the upper layer, a is the thermal expansivity and DT is the radial temperature difference across the whole system) with a dense layer becoming unstable B 0.5. We characterize the height and length scale of the undulations and the area of the interface. Deformations of the interface are largest for cases in which interface is in the midmantle and for cases with small density contrasts. We find that the heating mode does not affect the thermal structure of the layered system, which can be explained with energy balance considerations. The amplitude of the interfacial deformation is found to be unaffected by the heating mode and can be predicted using B. Our results suggest the interfacial thermal boundary layers require large temperature contrasts; therefore the lack of evidence for thermal boundary layers in global seismology studies between 500 and 2500 km depth suggests interfaces at these depths are unlikely.