The origin of turbulent stripes in channel flow

In plane Poiseuille flow turbulence first appears in the form of of oblique stripes that are separated by laminar regions. In experiments we find that stripes at low Reynolds numbers have an orientation of 45 degrees with respect to the streamwise direction. As shown, stripe patterns are statistically sustained even at Re as low as 675 which is considerably lower than a recent estimate for the onset of turbulence (Re = 830). Below Re~650 however stripes quickly decay and cannot be tracked to lower Re. Inspired by the experiments we perform direct numerical simulations in a rectangular domain tilted by 45 degrees (i.e. the preferred stripe angle) with respect to the streamwise direction. We find that in this case the turbulent stripes can be tracked to much lower Re, all the way to their origin. The turbulent flow in this limit turns into a localized non-turbulent stripe, which more precisely is a periodic orbit solution of the Navier Stokes equations. This stripe solution can be regarded as the precursor of turbulence and we investigate how turbulence develops from it. A notable feature is that a small increase in Re suffices to give rise to chaos and that subsequently the attractor dimension increases at an unprecedented rate.