  Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional
chaotic flow state observed in dilute polymer solutions. It has been
hypothesised that the dynamical origins of EIT are linked to a center-mode
instability, whose nonlinear evolution leads to a travelling wave with an
'arrowhead' structure in the polymer conformation, a structure also observed
instantaneously in simulations of EIT. In this work we conduct a suite of
two-dimensional direct numerical simulations spanning a wide range of polymeric
flow parameters to examine the possible dynamical connection between the
arrowhead and EIT. Our calculations reveal (up to) four co-existent attractors:
the laminar state and a steady arrowhead, along with EIT and a 'chaotic
arrowhead'. The steady arrowhead is stable for all parameters considered here,
while the final pair of (chaotic) flow states are visually very similar and can
be distinguished only by the presence of a weak polymer arrowhead structure in
the 'chaotic arrowhead' regime. Analysis of energy transfers between the flow
and the polymer indicates that both chaotic regimes are maintained by an
identical near-wall mechanism and that the weak arrowhead does not play a role.
Our results suggest that the arrowhead is a benign flow structure that is
disconnected from the self-sustaining mechanics of EIT.
