An analytic approach for calculating absolutely unstable inviscid modes ofthe boundary layer on a rotating disk

An analytical treatment of inviscidly absolutely unstable modes is pursued using the long-wavelength asymptotic approach. It is shown using the invisc id Rayleigh scalings in conjunction with the linear critical layer theory t hat the rotating-disk boundary layer flow undergoes a region of absolute in stability for some small azimuthal wave numbers. The analytically calculate d branch points for the absolute instability are found to be in good agreem ent with those obtained via a numerical solution of the inviscid Rayleigh e quation.