Linear instability of viscoelastic pipe flow

A modal stability analysis shows that pressure-driven pipe flow of an Oldroyd-B fluid is linearly unstable to axisymmetric perturbations, in stark contrast to its Newtonian counterpart which is linearly stable at all Reynolds numbers. The dimensionless groups that govern stability are the Reynolds number being the Weissenberg number), marking a possible paradigm shift in our understanding of transition in rectilinear viscoelastic shearing flows. The predicted unstable eigenfunction should form a template in the search for novel nonlinear elasto-inertial states, and could provide an alternate route to the maximal drag-reduced state in polymer solutions. The latter has thus far been explained in terms of a viscoelastic modification of the nonlinear Newtonian coherent structures.