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Title: Is the velocity spectrum of elastic turbulence universal?
Plain: The chaotic flow of polymer solutions has an energy spectrum that falls off steeply toward small eddies. Whether its slope is the same in all flows is unknown.
Precise: In elastic turbulence at $\mathrm{Re} \to 0$ the velocity spectrum is $E(k) \sim k^{-\alpha}$; theory requires $\alpha > 3$ for a smooth velocity field (Fouxon and Lebedev 2003), experiments in curvilinear flows report $\alpha$ of about 3.3 to 3.6 (approximately), and channel DNS give $\alpha \sim 4$. Determine whether $\alpha$ has a universal value as $\mathrm{Wi} \to \infty$ and, if so, compute it.
Settled by: A theory predicting $\alpha$, confirmed by spectra over at least a decade in $k$ in two different geometries at matched Wi.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: 2024 channel simulations report $k^{-4}$.
Posed since: 2003