Numerical investigation of 2D convection with extremely large viscosity variations

Previous experimental studies of convection in fluids with temperature‐dependent viscosity reached viscosity contrasts of the order of 105. Although this value seems large, it still might not be large enough for understanding convection in the interiors of Earth and other planets whose viscosity is a much stronger function of temperature. The reason is that, according to theory, above 104–105 viscosity contrasts, convection must undergo a major transition—to stagnant lid convection. This is an asymptotic regime in which a stagnant lid is formed on the top of the layer and convection is driven by the intrinsic, rheological, temperature scale, rather than by the entire temperature drop in the layer. A finite element multigrid scheme appropriate for large viscosity variations is employed and convection with up to 1014 viscosity contrasts has been systematically investigated in a 2D square cell with free‐slip boundaries. We reached the asymptotic regime in the limit of large viscosity contrasts and obtained scaling relations which are found to be in good agreement with theoretical predictions.