Multistability of elasto-inertal two-dimensional channel flow*

Elasto-inertial turbulence (EIT) is a recently discovered, chaotic flow state observed in dilute polymer solutions. The dynamical origin of EIT has been hypothesised to be linked to a centre-mode instability [Garg et al. PRL 121, 2018], which gives rise to an arrowhead-shaped travelling wave. Two-dimensional direct numerical simulations (DNS) have shown evidence of various dynamical regimes, including stable arrowheads, chaotic arrowheads and full elasto-inertial chaos [Samanta et al. PNAS 110, 2013; Dubief et al. PRF 7, 2022], with the preferred dynamics appearing to depend in a non-trivial way on the flow parameters. In this talk we show that these regimes do not succeed each other (e.g. in bifurcations as the Weissenberg number is varied) but rather coexist in parameter space. In fact, two-dimensional viscoelastic channel flow is a multistable system with up to four different coexisting attractors: the laminar state, a steady arrowhead, a chaotic arrowed and EIT. We use DNS to explore the effect of Weissenberg and Reynolds numbers, polymer concentration and finite extensibility (using the FENE-P model) on the existence of the four attractors.