Are elasto-inertial and purely elastic turbulence the same state?
In plain words
Polymer solutions show chaotic flow both at moderate speeds, where inertia helps, and at vanishing speeds, from elasticity alone. Whether these are two forms of one state is unknown.
Precise statement
In the $(\mathrm{Re}, \mathrm{Wi}, \beta)$ parameter space of channel or pipe flow of FENE-P or simplified Phan-Thien-Tanner fluids, is there a continuous path from elasto-inertial turbulence at $\mathrm{Re} \sim 10^{3}$ to purely elastic turbulence at $\mathrm{Re} \to 0$ along which the organizing coherent structures (center-mode travelling waves, arrowhead or narwhal states) persist? Answer: yes or no, with the path or the boundary that separates the two.
What would settle it
Numerical continuation of coherent states and chaotic attractors across the full Re range for one constitutive model, checked against experiments with matched rheology.
Status in the literature
Unverified note
Linear-stability continuation (Khalid, Shankar, Subramanian 2021) and 2024 simulations support a link; 2026 pipe experiments find a change in threshold scaling where inertia vanishes.