Effects of partial slip on the local-global linear stability of the infinite rotating disk boundary layer

Abstract

A numerical investigation is undertaken on the effect of small-scale surface roughness on the local absolute and global stability of the flow due to a rotating disk. Surface roughness is modeled via the imposition of the partial-slip wall boundary condition, with radial and concentric anisotropic roughnesses and isotropic roughness considered. The effect of the partial-slip parameters on the neutral characteristics for absolute instability is presented, while the azimuthal mode numbers required for global linear instability to occur are determined for the genuine inhomogeneous base flow. Predictions for the threshold values for the azimuthal mode numbers needed for globally unstable behavior are also computed by coupling solutions of the Ginzburg–Landau equation with the local linear stability properties obtained using the homogeneous flow approximation. These are found to be in excellent agreement with the exact values realized from the numerical simulations. In general, surface roughness is demonstrated to stabilize the absolute instability and the global linear instabilities.