An asymptotic investigation into the stabilization effect of suction in the rotating-disk boundary layer flow

Abstract

The suction effects in the three-dimensional boundary layer flow due to a rotating disk are analyzed from the linear stability point of view making use of the asymptotic structure of the suction mean velocity profiles of the boundary layer. The primary interest of the current work is in giving an explanation to the well-known stabilization influence of the suction from an easy to implement asymptotic means. As a consequence of the analysis, the shapes of the linear amplitude functions are derived analytically. There also results a dispersion relation for the eigenvalues existing in the limit of large suction. A comparison is then made between the perturbations obtained from the present work and also from the direct numerical solution of the linear stability equations. The asymptotic approach pursued provides a good indication as to why the large suction in the specific three-dimensional boundary layer should act in favor of the stabilization of the flow by strongly damping the external disturbances received into the suction boundary layer.