On slow transverse motion of a sphere through a rotating fluid

Abstract

The fluid is assumed to be inviscid and to be confined within two parallel planes, each perpendicular to the axis of rotation. A sphere is set moving, relative to the rotating fluid, in a straight line with uniform velocity and the temporal development of the flow structure examined. It is found that ultimately the flow has different properties inside and outside the cylinder [Cscr ], circumscribing the sphere and having its generators parallel to the axis of rotation. Inside [Cscr ] the fluid moves with the sphere as if solid; in early experiments of Taylor (1923) this phenomenon was observed. Outside [Cscr ] the motion is a two-dimensional potential flow past [Cscr ] as if it were solid. Then the asymmetry observed by Taylor and predicted in an earlier theory of the author for an unbounded fluid (1953) is not borne out. A partial explanation is offered.