Turbulence in Earth's core generates large topographic torques on the mantle

Seismic and geodynamic studies indicate that the boundary between the Earth's liquid outer core and solid mantle is not spherical, but is likely characterized by topography in the form of inverted mountains and valleys that have typical amplitudes of several kilometers. One of the dynamical consequences of these deformations is that turbulent flow in the core can exert pressure torques on the mantle, thereby resulting in a transfer of angular momentum between the outer core and the mantle. Understanding this transfer of angular momentum is important for explaining variations in the Earth's rotation rate, or length of day. Whether kilometer-sized topography can explain observed variations in length of day is a longstanding question in geophysics. Here we use a suite of state-of-the-art numerical simulations of hydrodynamic convection in a rotating spherical shell with boundary topography to show that topographic torques exhibit a linear dependence on topographic amplitude and approach a quadratic dependence on flow speeds. This observation is explained with the asymptotic theory of rapidly rotating convection. These results imply that topographic torques are of sufficient magnitude to explain length of day variations.