Origin of very-large-scale motions in wall turbulence
In plain words
Turbulent pipe and boundary-layer flows contain very long streaks of fast and slow fluid, ten or more times longer than the pipe radius or layer thickness, carrying much of the turbulent energy. What creates and sustains them is not agreed.
Precise statement
Pipe, channel and boundary-layer flows at $\mathrm{Re}_{\tau} > 10^3$ contain streamwise-velocity structures 10 to 20 outer lengths long (very-large-scale motions, superstructures). Determine whether they are sustained by an autonomous self-sustaining cycle at large scale, by linear transient amplification of forcing from smaller scales, or by aggregation of attached eddies, using a test that discriminates among these.
What would settle it
Controlled DNS or experiments at $Re_{\tau} > 2000$ that suppress one candidate mechanism, for example by removing small scales or damping near-wall cycles, and measure the response of the large-scale energy.