A model equation for axisymmetric stability of small-gap parallel-plate ows

We consider a model equation derived in [18] for the linear stability of a torsional ow of an Oldroyd-B uid in a parallel-plate device. Axisymmetry, small gap and zero Reynolds numbers are assumed. The equation is not separable in the radial and vertical variables. The advantage is that its eigenmodes depend only on the aspect ratio. Once evaluated, the eigenmodes are used to calculate the onset conditions for any retardation parameter and Deborah number. The onset conditions and streamfunction contours are compared with the normal-mode analysis of [14] which assumed radially localized disturbances, and the computational results on the full equations [1]. Two facets of the model equation are discussed; rst, how well the onset conditions and eigenmodes compare with those of the case where the radially localized assumption is made, and secondly, how they approximate those of the full equations.