Abstract
This paper examines the conditions under which Squire's Theorem on the stability of parallel flows is valid for Rivlin-Ericksen fluids. Although the theorem is not applicable in general, it is valid for a non-trivial class of viscoelastic fluids, for which a physical interpretation is given. Those slightly viscoelastic fluids which do not belong to this class are found to satisfy a modified form of Squire's Theorem. It is shown that the effects of viscoelasticity on in-plane and out-of-plane disturbances may be quite different: one may lead to stabilization and the other to destabilization. A method of solution which has been used for in-plane analyses may also be applied to three-dimensional analyses.
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