Stability of Flow between Eccentric Rotating Cylinders

Abstract

The linear stability of two-dimensional steady flows between two long, eccentric, rotating circular cylinders is studied numerically under the condition that the inner cylinder rotates uniformly while the outer one is at rest. By using the pseudospectral method it is found that the critical Reynolds number increases with the eccentricity ε . The critical axial wave number is found to remain nearly constant for small ε and to increase with larger ε . The eigenfunctions are distributed in the region from the position of the maximum gap to 180° downstream of that position. The Taylor-vortexlike three-dimensional steady flows are computed for several supercritical Reynolds numbers. The torques acting on the cylinders and the position of maximum vortex activity are calculated.