SUBCRITICAL INSTABILITIES IN PLANE COUETTE FLOW OF VISCO-ELASTIC FLUIDS

Abstract A non-linear stability analysis of plane Couette flow of the Upper-Convected Maxwell model is performed. The amplitude equation describing time-evolution of a finite-size perturbation is derived. It is shown that above the critical Weissenberg number, a perturbation in the form of an eigenfunction of the linearized equations of motion becomes subcritically unstable, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. Keywords: Visco-elastic flows, subcritical instabilities, amplitude equatio