Transition to turbulence in rough plane Couette flow

This DNS study considers transition to turbulence in plane Couette flow (pCf) with a rough stationary wall and a smooth moving wall. The roughness elements are square ribs of height $k=0.2h$ (where $h$ is the half-channel height). Two different pitch separations, $\lambda =2k$ and $10k$ , are considered, i.e. d-type and k-type roughness, respectively. The transition in both rough pCf cases takes place through a stage of alternate laminar–turbulent bands aligned in an oblique fashion. However, roughness causes a shift in the transitional Reynolds number ( $Re$ ) range. In the k-type roughness, stable bands are observed in the range $Re \in [300, 325]$ , which is a downwards shift from the transitional $Re$ range for the smooth pCf ( $Re \in [325,400]$ ). The d-type roughness, on the other hand, surprisingly shifts the transitional $Re$ range upwards to $Re \in [350,425]$ . This peculiar behaviour is associated with the ability of the ribs to shed and regenerate vorticity. Large-scale components extracted using a filtering process relate to the transition bands and flow parallel to the oblique laminar–turbulent boundaries. Counter-rotating vortices are present in the turbulent regions of the flow field, which exist in tandem with the high- and low-velocity streaks. Another interesting observation is the secondary Reynolds shear stresses, $-\overline {v^{\prime }u^{\prime }}$ and $-\overline {w^{\prime }v^{\prime }}$ , which are non-zero in the transitional regime, in contrast to the turbulent regime where they are negligible.