The linear stability of the flow due to a rotating disc with surface roughness
is considered. The aim is to determine whether surface roughness can lead to
drag reduction in three-dimensional boundary layers, and thus have an effect on
the transition process from a laminar flow to a turbulent flow. The surface
roughness is taken into account by considering partial-slip boundary conditions.
The basic steady flow is obtained as an exact solution of the Navier-Stokes
equations. The linear stability of this flow for perturbations corresponding to
stationary crossflow vortices is considered for the inviscid Type I
instabilities. An asymptotic study is presented for large Reynolds number, with
significant differences from the no-slip case. The solutions for the disturbed
flow are determined in the appropriate asymptotic regimes. Predictions for the
neutral wavenumbers and orientations of the crossflow vortices are obtained.
Solutions are presented for anisotropic roughness and for isotropic roughness.
Conclusions are drawn as to the significance of the results in relation to drag