A phase diagram for viscoelastic wavy-channel flow*

Viscoelastic channel flow exhibits a wealth of interesting dynamics in areas of parameter space where the corresponding Newtonian flow would be laminar. The most significant regimes – inertialess elastic turbulence and elasto-inertial turbulence – are known to be subcritical, and there is a need to identify the mechanisms by which vortical perturbations can be established in the bulk of the flow. In this work, we study the flow response to surface waviness at the lower wall, specifically the penetration depth of the vorticity perturbation. We construct a phase diagram in terms of the dimensionless roughness lengthscale and an elastic critical-layer height. The strongest vortical response is observed over long-wave distortions. For inertialess flows, the vanishing streamwise normal stress at the channel centreline creates a blocking effect whereby the rolls created by the surface waves are confined to the lower half of the channel and a large vorticity perturbation is established in a central boundary layer. In elasto-inertial flows, a resonance generates a strong vorticity response at critical layers in both halves of the channel.