Asymmetric flow above a rotating disk

Abstract

In this paper we generalize the von Kármán solution for flow above a single rotating disk, to include non-axisymmetric solutions. These solutions contain an arbitrary parameter; for zero value of the parameter the asymmetric flow degenerates into the classical von Kármán solution. Thus the classical solution is never isolated when considered within the scope of the full Navier–Stokes equations; there are asymmetric solutions in every neighbourhood of the von Kármán solution. Calculations are reported here for s = 0, 0.02 and 0.06, where s represents the ratio of angular velocity of the fluid at infinity to the angular velocity of the disk. A subset of the solutions obtained here corresponds to flow induced by the rotation of a disk when the latter is placed in a fluid that is moving with a constant uniform velocity.