What selects the angle and wavelength of transitional turbulent bands?
In plain words
In flows between parallel plates near the onset of turbulence, turbulent and smooth regions arrange themselves into tilted stripes with a definite angle and spacing. A theory that predicts these numbers from the flow equations is incomplete.
Precise statement
In plane Couette and plane Poiseuille flows near onset, laminar-turbulent bands form at angles of roughly 20 to 40 degrees to the streamwise direction with wavelengths of order $10^{2}$ half-gaps. Derive the selected angle and wavelength and their Re dependence from the Navier-Stokes equations, including the large-scale flow that accompanies the bands.
What would settle it
A reduced theory derived from the Navier-Stokes equations predicting angle and wavelength within 10 percent across Re, checked by DNS in large domains.
Status in the literature
Simulations reproduce the bands and analyses of the large-scale flow explain parts of the selection (Gome, Tuckerman, Barkley 2023); a closed derivation of the angle is lacking.