Abstract The influence of fluid elasticity on the onset and stability of axisymmetric Taylor vortices is examined for the Taylor-Couette flow of an Oldroyd-B fluid. A truncated Fourier representation of the flow field and stress leads to a six-dimensional dynamical system that generalizes the three-dimensional system for a Newtonian fluid. The stability picture and flow are drastically altered by the presence of the nonlinear (upper convective) terms in the constitutive equation. It is found that the critical Reynolds number Rec at the onset of Taylor vortices decreases with increasing fluid elasticity or normal stress effects, and is strongly influenced by fluid retardation. For weakly elastic flows, there is an exchange of stability at Re = Rec through a supercritical bifurcation similar to the one predicted by the Newtonian model. As the elasticity number exceeds a critical value, a subcrilical bifurcation emerges at Rec, similar to the one predicted by the Landau-Ginzburg’s equation.
Roger E. Khayat (Sun,) studied this question.
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