Instability of fluid motion in a thin spherical layer

We study flow stability in a thin spherical layer with respect to small disturbances. It is shown that for each given layer thickness there is a sequence of critical Reynolds numbers above which the motion is unstable. In its form, the critical disturbance is reminiscent of the secondary flow which develops upon loss of stability of the basic fluid flow between rotating cylinders (Taylor problem).The author wishes to thank M. I. Shliomis for his continued interest in this study.