© 1953 by Oxford University Press
ON THE SLOW MOTION OF AN ELLIPSOID IN A ROTATING FLUID
( Dept. of Mathematics, University of Bristol )
In the first PARTof this paper we consider the perturbation in the volocity of an inviscid fluid, rotating about an axis with angular velocity 
, which arises from the slow motion, relative to the fluid, of an ellipsoid having one of its axes parallel to the axis of rotation Oz of the fluid. Formulae in the form of Bromwich integrals are found, giving the perturbation at any time, and in the second PARTwe use them to find the ultimate velocity distribution when the ellipsoid is moving with uniform velocity. This velocity is steady in general and markedly different according as we consider points inside or outside the cylinder C, which circumscribes the ellipsoid and has its generators parallel to Oz. If the ellipsoid moves parallel to Oz, then inside C the fluid is pushed along in front of the sphere as though solid, in agreement with experiment, while outside C there is a shearing motion parallel to Oz. If the ellipsoid moves in a plane at right angles to Oz, then inside C the stream-lines lie on congruent ellipsoids, while outside C they lie on planes perpendicular to Oz but their pattern there is rather complicated (see Fig. 2). The agreement with experiment is not so good as before, but an explanation of the discrepancy is easily formulated. Exceptions to this general picture occur on C, on the ellipsoid, and, in certain circumstances, on the axis of C. Finally on C the velocity becomes infinite according to the linearized theory, and in Appendix C we indicate how viscosity would modify the flow there.