Influence of three-dimensional wall roughness on the transition of a finite Stokes layer

A finite Stokes layer with a large half-width over three-dimensional wall roughness is numerically simulated by solving the perturbation equations. Simulations are conducted for different parameters that affect the shape of the wall roughness, e.g., streamwise wave number, spanwise wave number and the amplitude of the roughness. The calculations are performed at a Reynolds number of Rδ=600, which represents the transitional Reynolds number observed in experimental cases. The onset of the transition is shown to be highly correlated with the amplitude of pre-existing two-dimensional waves. It is found that the critical amplitude of the two-dimensional wave is approximately 1% of the velocity amplitude of the external flows. Moreover, the results indicate that the appearance of the transition is also affected by the fundamental wave numbers.