Subcritical instabilities in viscoelastic flows

The conditions under which a flow remains laminar or transitions to a turbulent state is of both fundamental scientific and practical importance. Whilst some flow instabilities arise from the base state becoming linearly unstable, the transition to turbulence in channel flow arises from a subcritical instability in which the base state remains linearly stable, but for which a finite amplitude perturbation beyond a critical size causes a transition to a chaotic state. Using techniques from dynamical systems theory it has recently been possible to identify how this critical amplitude varies with flow conditions.
The idea in this project is to apply this methodology to fluids containing polymers. These fluids show a range of instabilities during processing that experimental evidence suggests are of the same type as transition to turbulence in Newtonian flows. The aim of the project is to determine the conditions where a transition to a chaotic state takes place.