Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.