ONSET OF TAYLOR VORTICES AND CHAOS IN VISCOELASTIC FLUIDS

The influence of fluid elasticity on the onset and stability of axisym metric Taylor vortices is examined for the Taylor-Couette flow of an O ldroyd-B fluid. A truncated Fourier representation of the how field an d stress leads to a six-dimensional dynamical system that generalizes the three-dimensional system for a Newtonian fluid. The coherence of t he model is established through comparison with existing linear stabil ity analyses and finite-element calculations of the nonlinear dynamics of the transition to time-periodic (finite-amplitude) flow. The stabi lity picture and flow are drastically altered by the presence of the n onlinear (upper convective) terms in the constitutive equation. It is found that the critical Reynolds number Re-c at the onset of Taylor vo rtices decreases with increasing fluid elasticity or normal stress eff ects, and; is strongly influenced by fluid retardation. For weakly ela stic flows, there is an exchange of stability at Re=Re-c through a sup ercritical bifurcation, similar to the one predicted by the Newtonian model. As the elasticity number exceeds a critical value, a subcritica l bifurcation emerges at Re, similar to the one predicted by the Landa u-Ginzburg equation. More importantly, it is shown that, if fluid elas ticity is adequately accounted for, any small but nonvanishing amount of fluid elasticity can lead to the onset of chaos usually observed in experiments on the Taylor-Couette flow of supposedly Newtonian fluids . This is in sharp contrast to the Newtonian model, which does not pre dict the destabilization of the Taylor vortices, and therefore cannot account for the onset of periodic and chaotic motion. (C) 1995 America n Institute of Physics.