High Weissenberg asymptotics of the centre-mode instability in viscoelastic channel flow*

Simple (Newtonian) fluids exhibit fascinating new phenomena when small amounts of long-chain polymers are added to them. However, until the work of Garg et al. (Phys. Rev Lett. 121, 024502, 2018), the rectilinear flow of  polymer-enriched Newtonian solvents was believed only to be linearly unstable if the corresponding Newtonian flow was. That is, there was no elastically-generated  linear instability without curved streamlines. Garg et al., however, found a centre-mode instability in pipe flow which was later confirmed also to exist in channel flow by Khalid et al. (J. Fluid Mech. 915, A43, 2021) at large Weissenberg numbers (Wi) and finite Reynolds numbers (Re). By studying the ultra-dilute limit (β → 1), this instability could be tracked down to  Re = 0 in channel flow (Khalid et al., Phys. Rev. Lett. 127, 134502, 2021). We will discuss the asymptotics of the instability  in the distinquished limit Wi → ∞, β → 1 such that Wi(1-β) = O(1) and  Re = 0  in the hope of revealing the fundamental mechanism for this interesting new elastic instability.