Mantle convection with longest‐wavelength thermal heterogeneity in a 3‐D spherical model: Degree one or two?

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Abstract
The formation of longest‐wavelength mantle convection in the sluggish‐lid regime is investigated using a three‐dimensional spherical model. The bottom Rayleigh number is fixed at 107. Considering temperature‐dependent rheology, degree‐one dominant thermal convection occurs for both purely basal heating and mixed (i.e., basal and internal) heating modes. For the purely basal heating mode, degree‐one convection occurs when the viscosity contrast due to temperature‐dependent rheology is 103–104 in both Boussinesq and extended‐Boussinesq fluids. However, with extended‐Boussinesq fluid, degree‐one convection may only occur in the basal heating mode: In the mixed heating mode, degree‐one convection shifts to one with high‐degree modes, presumably because of enhanced viscous dissipation in the highly viscous lid over up/downwelling plumes. The geophysically relevant degree‐two convection with sheet‐like downwellings is not observed in this study. The inclusion of visco‐plastic rheology in the top part of the mantle breaks down degree‐one convection.

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