Effects of roughness on nonlinear stationary vortices in rotating disk flows

Primary stability 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 Rc as determined by linear theory . Both the single mode case, where the wave vector K equals its critical Kc at the onset of stationary primary stability, and the bi-modal case, where the wave vectors Kn(n=1,2) are close to Kc for the primary stability of the flow, are considered. The analysis leads to stable solutions for particular roughness forms and magnitude, and particlul ar wave vectors Kn(n=1,2) of the surface roughness