A NUMERICAL STUDY OF FINITE TAYLOR FLOWS

We make use of Galerkin's procedure and B-spline test functions in this study of finite Taylor flows, with the intention of providing numerical evidence of multiplicity of solution at moderate to large values of the aspect ratio, where the end effects are less conspicuous. The discretized equations are solved via Newton's method, and we employ "minimal" augmentation for tracing fold curves of our two-dimensional manifold of parameters Γ = L/d and R = r1ω/ν, where Γ is the aspect ratio, ω is the rate of rotation of the inner cylinder, R is the Reynolds number, r2 and r1 are cylinder radii, d = r2 - r1 > 0 and the flow field is bounded in the axial direction by stationary planes at z = 0, L. We are able to demonstrate that the development of Taylor cells in R is a continuous process which is not dependent in any qualitative manner on the aspect ratio, for Γ </ 200. We also report 8, 10, 12, and 14 cell solutions at Γ ~ 12.6, the aspect ratio of the experiments of Benjamin and Mullin, on two solutions at Γ = 200, and project a fold line of the equilibrium manifold onto the R-Γ plane. Solutions along this particular curve display a 12A-10N-12A mutation of the flow pattern for monotonically decreasing values of Γ. © 1990.