• mantle convection;
  • numerical simulation;
  • rheology

[1] 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.