LOW-DIMENSIONAL APPROACH TO NONLINEAR OVERSTABILITY IN THE TAYLOR-COUETTE FLOW OF PURELY ELASTIC FLUIDS

The finite amplitude purely elastic overstability, for axisymmetric Ta ylor-vortex flow of highly elastic fluids in the narrow-gap limit, is accurately predicted using the Galerkin projection method. A judicious mode selection is carried our to include the dominant normal stress t erms. The resulting twenty-mode dynamical system is capable of capturi ng the nonlinear behavior observed in the experiment of Muller et al. under conditions of negligible inertia. The model predicts, as experim ent suggests, the onset of overstability, the growth of oscillation am plitude of flow, and the emergence of higher harmonics in the power sp ectrum as fluid elasticity increases beyond a critical level.