Nonlinear stability analysis of viscoelastic Taylor-Couette flow in the presence of viscous heating

Recently, based on a linear stability analysis we demonstrated the existence of a new thermoelastic mode of instability in the viscoelastic Taylor-Couette flow [Al-Mubaiyedh et al., Phys. Fluids 11, 3217 (1999); J. Rheol. 44, 1121 (2000)]. In this work, we use direct time-dependent simulations to examine the nonlinear evolution of finite amplitude disturbances arising as a result of this new mode of instability in the postcritical regime of purely elastic (i.e., Re=0), nonisothermal Taylor-Couette flow. Based on these simulations, it is shown that over a wide range of parameter space that includes the experimental conditions of White and Muller [Phys. Rev. Lett. 84, 5130 (2000)], the primary bifurcation is supercritical and leads to a stationary and axisymmetric toroidal flow pattern. Moreover, the onset time associated with the evolution of finite amplitude disturbances to the final state is comparable to the thermal diffusion time. These simulations are consistent with the experimental findings.