Rotating convection in a dimpled sphere

Rotating convection in a spherical geometry is commonly used as a model for understanding geophysical and astrophysical fluid systems. However, real systems likely deviate from spherical symmetry. The boundary between Earth’s liquid core and mantle, for instance, is thought to be characterized by inverted mountains that protrude into the core. This non-axisymmetric topography dynamically couples the core and mantle and leads to angular momentum transport between the two systems. Here, we study rotating convection in a spherical shell with a small deformation on the outer boundary—a dimple—which breaks the axial symmetry about the rotation axis. A suite of numerical simulations are used to investigate the influence of topography on the convective dynamics, as well as the scaling behavior of the pressure torques. The simulations show that the torque scales linearly with the topographic amplitude, which can be explained by simple scaling arguments. When extrapolated to the conditions of the outer core, these results suggest that topographic coupling at the core mantle boundary is likely important in explaining the observed variations in Earth’s length of day.