  Plane Couette flow of visco-elastic fluids is shown to exhibit a purely
elastic subcritical instability in spite of being linearly stable. The
mechanism of this instability is proposed and the nonlinear stability analysis
of plane Couette flow of the Upper-Convected Maxwell fluid is presented. It is
found that above the critical Weissenberg number, a small finite-size
perturbation is sufficient to create a secondary flow, and the threshold value
for the amplitude of the perturbation decreases as the Weissenberg number
increases. The results suggest a scenario for weakly turbulent visco-elastic
flow which is similar to the one for Newtonian fluids as a function of Reynolds
number.

Soft Condensed Matter;Materials Science;Fluid Dynamics