STABILITY OF THE BOUNDARY-LAYER ON A SPHERE ROTATING IN STILL FLUID

A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear s tability analysis. A set of perturbation equations governing the insta bility of the flow field is derived assuming the perturbations to be c onsisting of spiral vortices. It is shown that the critical Reynolds n umbers obtained in the present analytical study are close to those obs erved in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere, wh ile the streamline-curvature instability overtakes near the equator.