An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc

An investigation of high Reynolds number stationary instabilities in the boundary layer on a rotating disc is given. It is shown that in addition to the inviscid mode at high Reynolds numbers, there is a stationary short wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wavenumber and orientation of this mode is obtained. A similar analysis is given for the inviscid mode, the expansion procedure used is capable of taking nonparallel effects into account in a self consistent manner. The results are compared to numerical calculations and experimental observations.