Turbulent Dissipation in the Boundary Layer of Precession Driven Flow in a Sphere

The energy dissipation in the fluid flow near the boundary separating the core and the mantle (i.e. the CMB) of a planet or moon with a fluid interior is a crucial parameter to understand its rotational dynamics. This boundary layer is typically very small compared to the core radius, and can become turbulent under certain conditions, which presents a challenge for global scale simulations of the flow in the fluid core. Here we construct a local Cartesian model to study the boundary layer of a precessing planet or moon. The solutions we derive in the laminar regime, i.e. where the Reynolds number Re is small and the non-linear term is neglected, are consistent with previous studies. This gives us confidence to push the model further into the turbulent regime. We solve numerically the governing equations, i.e., the Navier-Stokes equation and the continuity equation for an incompressible fluid in a rotating frame. We observe that, when the flow is turbulent, the boundary layer dissipation is increased, compared to its laminar counterpart, as expected. Moreover, we found that the velocity profile agrees with the law of the wall, a theory developed to study turbulent flow near a solid boundary. Based on our numerical results, we further construct a turbulence model using similarity theory. Last but not least, due to chemical interaction on the planetary core-mantle boundary, small-scale topography or surface roughness might exist. To investigate this topographic effect, we impose a sinusoidal topography in our local model. Preliminary results show further increase of the dissipation. Our results may provide valuable insight into the boundary layer dissipation near the CMB for both the Earth and the moon.