Unsteady flow of a viscous fluid due to non-coaxial rotations of a disk and a fluid at infinity

An exact solution of the time-dependent Navier-Stokes equations is obtained for the how due to non-coaxial rotations of a disk and a fluid at infinity. It is shown that the how can be two-dimensional if a convenient initial condition is specified, although, when the disk and the fluid at infinity are impulsively started from rest, the how becomes three-dimensional. An analytical solution describing the dow at small and large times after the start is obtained by the Laplace transform method. The velocity field is given in terms of the tabulated functions. (C) 1997 Elsevier Science Ltd.