  The goal of the present study is: (i) to demonstrate the two-dimensional
nature of the elasto-inertial instability in elasto-inertial turbulence (EIT),
(ii) to identify the role of the bi-dimensional instability in
three-dimensional EIT flows and (iii) to establish the role of the small
elastic scales in the mechanism of self-sustained EIT. Direct numerical
simulations of FENE-P fluid flows are performed in two- and three-dimensional
channels. The Reynolds number is set to $\mathrm{Re}_\tau = 85$ which is
sub-critical for 2D flows but beyond transition for 3D ones. The polymer
properties correspond to those of typical dilute polymer solutions and two
moderate Weissenberg numbers, $\mathrm{Wi}_\tau = 40, 100$, are considered. The
simulation results show that sustained turbulence can be observed in 2D
sub-critical flows, confirming the existence of a bi-dimensional
elasto-inertial instability. The same type of instability is also observed in
3D simulations where both Newtonian and elasto-inertial turbulent structures
co-exist. Depending on the Wi number, one type of structure can dominate and
drive the flow. For large Wi values, the elasto-inertial instability tends to
prevail over the Newtonian turbulence. This statement is supported by (i) the
absence of the typical Newtonian near-wall vortices and (ii) strong
similarities between two- and three-dimensional flows when considering larger
Wi numbers. The role of the small elastic scales is investigated by introducing
global artificial diffusion in the hyperbolic transport equation for polymers.
The study results show that the introduction of large polymer diffusion in the
system strongly damps a significant part of the elastic scales that are
necessary to feed turbulence, eventually leading to the flow laminarization. A
sufficiently high Schmidt number is necessary to allow self-sustained
turbulence to settle.
