Revision 1

Accepted · first revision · record

Title: What selects the angle and wavelength of transitional turbulent bands?
Plain: 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: 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.
Settled by: A reduced theory derived from the Navier-Stokes equations predicting angle and wavelength within 10 percent across Re, checked by DNS in large domains.
Kind: phenomenon
Answer type: mechanism
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: 2002