Effects of roughness on nonlinear stationary vortices in rotating disk flows

Primary instability of rotating disk boundary layer flow over a rough surface for stationary modes was investigated by using the weakly nonlinear theory where the Reynolds number R is close to its critical value R_c as determined by linear theory. Both the single mode case, where the wave vector K equals its critical K_c at the onset of stationary primary instability, and the bimodal case, where the wave vectors K_n (n = 1, 2) are close to K_c for the primary instability of the flow, are considered. The analysis leads to stable solutions for particular roughness forms and magnitude, and particular wave vectors ?K_n (n = 1, 2) of the surface roughness.