Journal of Fluid Mechanics

The flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid

D. W.  Moore a1, P. G.  Saffman a2 and T.  Maxworthy a3
a1 Imperial College, London S.W.7
a2 California Institute of Technology, Pasadena, California
a3 University of Southern California, Los Angeles, California

Article author query
moore dw   [Google Scholar] 
saffman pg   [Google Scholar] 
maxworthy t   [Google Scholar] 


A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophie flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.

(Published Online March 29 2006)
(Received April 3 1969)