Why is the two-dimensional inverse energy cascade non-intermittent?
In plain words
In three-dimensional turbulence rare violent events dominate high-order statistics, but the energy flow to large scales in flat turbulence shows no growth of such events with decreasing scale. The reason for this difference is not known.
Precise statement
In the inverse energy cascade of forced 2D Navier-Stokes turbulence, velocity-increment exponents are $\zeta_p = p/3$ within error, and increment distributions are self-similar though measurably non-Gaussian (Boffetta, Celani, Vergassola 2000). Explain the absence of anomalous scaling from the dynamics, and determine whether small deviations exist at high order or for other forcing protocols.
What would settle it
A theory predicting $\zeta_{p} = p/3$ or specific small corrections, checked against DNS at resolutions above $16384^{2}$.