Computations of the axisymmetric flow between rotating cylinders

Abstract

We study Taylor vortex flows by solving the steady axisymmetric Navier-Stokes. equations in the primitive variables (u, v, w, p). Fourier expansions in z, the axial direction, and centered finite differences in r, the radial direction, are used. The resulting discretized equations are solved using the pseudoarclength continuation methods of Keller (in "Applications of Bifurcation Theory" (P. Rabinowitz, Ed.), pp. 359–384, Academic Press, New York, 1977.), which are designed to detect bifurcations. In this way we accurately determine the first branch of Taylor vortex solutions bifurcating from Couette flow for both a wide and a narrow gap. Agreement with experiments is extremely good for the wide gap case and solutions are obtained for a larger range of Reynolds numbers than previously reported.

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