Stability analysis of boundary layer on a sphere rotating in still fluid

Theoretical study of three-dimensional boundary layer transition on a sphere rotating in still fluid has been carried out by a linear stability analysis. It is shown that the neutral stability curve shifts toward the lower Reynolds number and the lower spiral vortex number, either closer to the equator or with the decrease in the vortex angle. The critical Reynolds numbers obtained in the analysis are close to but smaller than the experimental results. The rotational speed ratio between the spiral vortices and the surface agrees with the experiments. It is also shown that the critical Reynolds number becomes insensitive to the vortex angle near the equator. On the other hand, the critical wave number of spiral vortices becomes larger with the increase in the vortex angle and decreases near the equator. Computation including the streamline-curvature effects in general gives the critical Reynolds numbers closer to the experiments.