Green's function method for axisymmetric flows: analysis of the Taylor-Couette flow

A numerical method for the solution of the Navier-Stokes equations in rotationally symmetric flow problems is presented. The numerical procedure is based on a boundary integral equation formulation with the fundamental solution of the Stokes' equation accounting for the rotational symmetry. The proposed methodology has been applied to the study of the Taylor-Couette flow between two concentric rotating cylinders of infinite axial length. A comparison with the available theoretical, experimental or numerical findings is performed to evaluate the accuracy of the present results. As predicted by the analytical theory and confirmed by the experiments, multiple solutions that are found for Reynolds numbers higher than the critical value, indicate the proposed methodology as a useful tool to get physical insight on the instabilities occurring in the solution of the Navier-Stokes equations. © 1990 Springer-Verlag.