© 1981 by Oxford University Press
THE INSTABILITY OF FLOW IN THE NARROW GAP BETWEEN TWO PROLATE SPHEROIDS. PART II. ARBITRARY AXIS RATIO
( Department of Mathematics, University College London )
The flow in the narrow gap between two spheroidal surfaces, the inner of which is rotating, is examined theoretically. In Part I, the axis ratio of the spheroids was small and the analysis is extended here to arbitrary axis ratios, including the important special case of spherical boundaries. In agreement with the prediction in Part I, a band of toroidal vortices near the equator exists at a critical Taylor number greater than that for Couette flow by an amount independent of the gap-width. Although this solution has the right form, comparison with experimental results shows that the theoretical Taylor number for instability is too large. Two attempts to remove this discrepancy are tried. An alternative scaling, previously shown to be inadequate in the linear case, is shown to be still unacceptable when nonlinear terms are included. Nonaxisymmetric disturbances are examined, but these are found to have a critical Taylor number greater than that for axisymmetric disturbances. Finally, the initialvalue problem for the amplitude equation is considered, over the whole range of boundary shapes from cylinders to spheres.