Sensitivity of mean vertical velocity w to mean dike width 2a under SP conditions for a range of dynamic viscosities (a). Turbulent and laminar flow are indicated by solid and dashed–dotted lines, respectively. Dike widths less than the critical value required for sustained flow are indicated by the “complete solidification” field. Times for N₂ magma to ascend through 1 km of SP ice are shown in (b). Corresponding volumetric flow rates Q are shown in (c) assuming the dike breadth is 1000 times its width.