On the non-parallel instability of the rotating-sphere boundary layer

We present a new solution for the steady boundary-layer flow over the rotating sphere that also accounts for the eruption of the boundary layer at the equator and other higher-order viscous effects. Non-parallel corrections to the local type I and type II convective instability modes of this flow are also computed as a function of spin rate. Our instability results are associated with the previously observed spiral vortices and remarkable agreement between our predictions of the number of vortices and experimental observations is found. Vortices travelling at 70 %–80 % of the local surface speed are found to be the most amplified for sufficient spin rates, also consistent with prior experimental observations.