Is active turbulence described by universal statistical laws
In plain words
Dense bacteria and gels of motor proteins produce chaotic swirling flows even though their inertia is negligible (Reynolds number near zero). Whether these flows obey universal statistical laws, as ordinary turbulence does, is unknown.
Precise statement
For active nematics and polar active fluids (active nematohydrodynamics, Toner-Tu-Swift-Hohenberg model), determine whether the kinetic-energy spectrum $E(k)$ at scales larger than the active length $\ell_a$ shows power laws independent of parameters and boundary conditions, and whether there is a scale-to-scale energy flux. An answer gives the exponents and their range of validity, and agreement with microtubule-kinesin and bacterial-suspension experiments.
What would settle it
A closed theory predicting E(k) and energy fluxes that agrees with simulations of several models and with spectra measured in at least two experimental systems.
Status in the literature
Some active-nematic theories predict universal large-scale spectral scaling (2020), while other models and experiments report parameter-dependent exponents.