Transverse turbulent bands in rough plane Couette flow

In most subcritical planar shear flows, the transitional regime features oblique large-scale laminar-turbulent patterns. So far, such laminar-turbulent patterns have only been investigated in flows over perfectly smooth walls and little attention has been devoted to cases with rough surfaces as found in most practical engineering, urban applications, and in nature. In this study, we investigate laminar-turbulent patterns in plane Couette flow with one rough wall by means of direct numerical simulation, as a function of the Reynolds number and of the roughness height. The roughness is modeled using a force term in the Navier-Stokes equations. The focus of this study is on a new regime featuring non-oblique turbulent bands transverse to the motion of the walls, and separated by arbitrary long laminar gaps. This regime is found when the wall is sufficiently rough. This transverse turbulent band occurs at Reynolds numbers just below the onset of self-sustained turbulence found in the smooth wall case. The localized turbulence patches have a streamwise extent as large as 50-180 gap widths, decreasing with decreasing Reynolds number. The turbulent fraction as well as the band width show a linear relationship with the Reynolds number.