Effect of concentric surface roughness on traveling disturbances in the rotating disk boundary layer

The linear stability of the rotating disk boundary layer with surface roughness is investigated, building upon the earlier work by Harris [“Stability of the flow over a rough rotating disk,” Ph.D. thesis (University of Warwick, 2013)] and Garrett et al. [“On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness,” Phys. Fluids 28, 014104 (2016)]. The study employs the Yoon et al. [“Flow and heat transfer over a rotating disk with surface roughness,” Int. J. Heat Fluid Flow 28, 262–267 (2007)] approach for modeling concentric surface roughness, where the roughness is defined as a function of the radial direction coupled with a spatial-averaging of the base flow. Neutral stability curves and critical conditions for linear instability are computed for varying roughness factors and for traveling wave disturbances with temporal frequencies ω¯∈[−10,10]. The results demonstrate that surface roughness stabilizes the type-I crossflow instability and destabilizes the type-II Coriolis instability. Finally, a high-Reynolds number asymptotic analysis is undertaken for the upper branch of the neutral stability curve associated with the crossflow instability.