Abstract
Instability of the flow on a rotating disk is governed by linearized disturbance equations of the partial differential with respect to the radial distance from the rotation axis and the normal distance from the disk surface. Applying uniform suction from the surface brings a small parameter associated with displacement thickness of the circumferential velocity profile into a dimensionless form of the equation system. Two kinds of series solutions expanded by the powers of this parameter are obtained to describe the cross-flow and centrifugal instabilities of the flow having a twisted velocity profile. The leading terms of the series solutions are determined from two eigenvalue problems of slightly different ordinary differential equations, and the superposition of those equations leads to an eigenvalue problem applicable to multiple-instability characteristics of such three-dimensional boundary layers.
