Direct path from turbulence to time-periodic solutions
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We look for the origin of turbulent stripes in plane-Poiseuille flow by descending slowly in Reynolds number. In domains large enough to allow for full localization, this descent ends around Re≈650, below which stripes become short-lived, decaying quickly to laminar flow. We avoid this "relaminarization barrier" within the setting of "minimal band units": working in a narrow periodic tilted domain where lifetimes of stripes are much larger, we are able to track turbulent stripes down to the onset of chaos. We find that the correlation dimension of the chaotic attractor drops rapidly with decreasing Re. Our descent ends with a stable relative periodic orbit, after which numerical continuation takes over and finds the origin: a lower branch travelling wave.