Keywords:Moon, 3D spherical shell, mantle convection, size of the core, flow pattern
Clarifying the effects of three-dimensional spherical geometry on mantle convection is a major issue of mantle dynamics in terrestrial planets. We study in detail the nature of thermal convection of a variable viscosity fluid in the basally heated spherical mantle of small planets with a small core, keeping in mind the application of our numerical models to the Moon. Spherical geometry affects mantle convection mildly when the ratio of the core-radius to the planetary radius rCMB takes an Earth-like value of 0.55, while it is thought to affect strongly when rCMB is small like Moon around 0.2. Here, we investigate the flow pattern systematically for rCMB from 0.1 to 0.6 with small to large viscosity dependence on temperature. We first estimate the critical Rayleigh number Rc for the onset of convective motion at various rCMB and the magnitude of temperature-dependence of viscosity by a linear perturbation analysis. Then, we study the convective flow pattern of thermal convection above Rc by numerical simulation. The result of our simulation is in good agreement with the linear analysis. The nature of convective flow pattern considerably changes as rCMB smaller than about 0.4. The flow pattern has smaller number of up- and down-wellings. We established regime diagrams of convection pattern in relation to the Rayleigh number and the temperature dependence of viscosity, for various value of rCMB. Stronger temperature dependence of viscosity is necessary for realizing the stagnant-lid regime of convection for smaller rCMB. It is due to the relatively smaller volume of high temperature region near the CMB. The horizontally averaged temperature at mid mantle remains low despite the strong temperature variation of viscosity when rCMB is small.