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Unsteady flow of a viscous fluid due to non-coaxial rotations of a disk and a fluid at infinity. (English) Zbl 0891.76087

Summary: An exact solution of the time-dependent Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a disk and a fluid at infinity. It is shown that the flow 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 flow becomes three-dimensional. An analytical solution describing the flow 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.

MSC:

76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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