Streak instability in viscoelastic Couette flow

The secondary instability of nonlinear streaks and transition to turbulence in viscoelastic Couette flow are studied using direct numerical simulations. Viscoelasticity is modeled using the FENE-P constitutive equations. Both the polymer concentration beta and Weissenberg number Wi are varied in order to assess their effects on transition at moderate Reynolds number. The base streaks are obtained from nonlinear simulations of the Couette flow response to a streamwise vortex. We select the initial amplitude of the vortex which yields a desired maximum amplitude of the nonlinear streaks during their temporal evolution. The development of streaks in both Newtonian and non-Newtonian flows is primarily due to the action of streamwise vorticity onto the mean shear. In the viscoelastic case, it is also affected by the polymer torque, which opposes the vorticity and becomes more pronounced at large Weissenberg number. Streaks with the same maximum streamwise velocity perturbation can therefore have different total kinetic energy at higher Weissenberg number. At every streak amplitude of interest, harmonic forcing is introduced along the transverse direction to trigger the secondary instability and breakdown to turbulence. We demonstrate that the critical amplitude of the forcing, A(d), increases at large Weissenberg number. The degree of stabilization due to elasticity depends on the initial streak intensity, A(s),(in). For weak streaks the critical amplitude for secondary instability is more sensitive to Wi than for strong ones. This is explained by the existence of two different mechanisms that can trigger transition to turbulence. The perturbation to weak streaks is initially stabilized by the polymer torque which acts to oppose the amplification of wall-normal vorticity and, as a result, delays breakdown to turbulence. The secondary instability of strong streaks, on the other hand, is more immune to this stabilizing influence of the polymer.