Stability of flow over a rotating disk

The perturbation equations that characterize laminar flow stability over a rotating infinite disk are derived by strict order-of-magnitude analysis. The effect of the axial velocity component on flow conditions at criticality is shown to be nonnegligible, and the variation of the basic flow velocity along planes parallel to the disk is recognized. The strategy used for the numerical solution of the stability equations is Galerkin's method with B-spline discretization. Compared with the Poiseuille solutions of Orszag (1971), the method is shown to perform well without placing undue demands on computing capability. It is found that critical values of Reynolds number, wavelength, vortex orientation, and number of spiral vortices calculated by the present method compare favorably with the experimental data of Kobayashi et al. (1980).