The stability of the boundary layer on a sphere rotating in a uniform axial flow

We consider the local convective and absolute instabilities of the boundary layer on a rotating sphere located in a uniform axial flow, extending our previous work, which considered still outer fluid. Axial flow is seen to stabilise the convective instabilities, and our predicted onset of the spiral vortices is in good agreement with existing experimental data. The vortex angle is found to increase at each latitude with increased axial flow, as does the number of vortices. Results are presented that indicate that the latitude at which “slow” vortices first replace stationary vortices is slightly increased with axial flow. The results of our absolute instability analysis show that axial flow delays the onset of absolute instability at each latitude, and the maximum absolute growth rates are found to reduce with increased axial flow. The onset of absolute instability is found to be much more sensitive to axial flow than is the onset of convective instabilities.