FLOW BETWEEN ECCENTRIC ROTATING CYLINDERS - BIFURCATION AND STABILITY

The effect of cylinder eccentricity on Couette-Taylor transition is investigated here for flow between infinite rotating cylinders. The method of analysis is Fourier expansion of the conservation equations in the axial direction, followed by projection onto a polynomial subspace. Critical points of the solution, which are characterized by singularity of the Jacobian matrix, are located via parametric continuation. This computational scheme permits an extension of the DiPrima and Stuart results to higher values of the eccentricity ratio; it also makes it possible to move far from the critical point into the supercritical Reynolds number regime. The first bifurcation from Couette flow is found to be supercritical, while supercritical flow is shown to consist of regions of plane motion with recirculation, separating toroidal vortex regions. The domain of recirculating flow is asymmetric with respect to the fine of centers, and on increasing the supercritical Reynolds number its axial dimension decreases while its radial dimension, in the plane separating the vortex cells, increases. The results established here for critical Reynolds number agree well with those of DiPrima and Stuart at eccentricities where their small perturbation solution is applicable, and there is good agreement with the experimental data of Vohr. The torque calculations compare favorably with the experimental data of Donnelly and Simon for the concentric case and with the data of Castle and Mobbs for non-zero eccentricity.