How does purely elastic turbulence arise in straight channels and pipes?
In plain words
Polymer solutions can become chaotic even when flowing too slowly for ordinary turbulence, because stretched molecules store and release elastic energy. In curved flows the cause is known, but in straight pipes and channels it is still debated.
Precise statement
Dilute polymer solution (viscosity ratio $\beta = \eta_s/(\eta_s + \eta_p)$, relaxation time $\lambda$) in pressure-driven channel or pipe flow at $\mathrm{Re} \to 0$, where Oldroyd-B pipe flow is linearly stable and channel flow is unstable only for $\beta > \text{about }0.99$ at Wi of order $10^3$. Determine the mechanism that sustains chaotic flow above a threshold Weissenberg number $\mathrm{Wi}_c = \lambda U/d$: subcritical finite-amplitude coherent states, or a center-mode linear instability enabled by shear thinning and finite polymer extensibility, and give $\mathrm{Wi}_c$ as a function of $\beta$ and model parameters.
What would settle it
Experiments with characterized polymer rheology at $\mathrm{Re} < 10^{-2}$ matched quantitatively by simulations of the same constitutive model, identifying the onset mechanism and $\mathrm{Wi}_c$.
Status in the literature
Unverified note
Channel DNS with the simplified Phan-Thien-Tanner model show subcritical purely elastic turbulence (Lellep, Linkmann, Morozov, PNAS 2024); 2026 pipe experiments find elastic turbulence at Re four orders of magnitude below predicted instability thresholds (Kamil and Hof, arXiv:2609.16492).