Scaling laws for time-dependent stagnant lid convection in a spherical shell

Systematic numerical simulations of time dependent, stagnant lid convection in an internally heated spherical shell are performed in order to obtain scaling relationships for various convective parameters. Convection beneath the lid is time-dependent and characterized by passive upwellings and cold sheet-like downwellings. The heat flux scaling relationship agrees with results from experiment, two-dimensional numerical simulations, and boundary layer stability analysis. Without a mobile lithosphere, low heat transport efficiency and extensive melting during evolution of the terrestrial planets, which are predicted by two-dimensional studies, also apply in fully three-dimensional spherical shell geometry. The scaling relationships for convection induced stresses in the lid are also very similar to those obtained in two dimensions. This supports the idea that initiation of subduction in the stagnant lid convection regime requires a very weak lithosphere.