Recirculation within a fluid sphere at moderate Reynolds numbers

Abstract

Motion of a single fluid sphere is described by two theories, each characterized by different levels of Hill's vortex circulation within the sphere. An existing experimental data set giving measurements of vertical velocity along the major axis of the sphere is re-examined. Contrary to published discussions of that experiment, we find that the theory of Parlange agrees better with the laboratory data than that of Harper & Moore. This agreement supports the key difference between the two theories, i.e. that the fluid within the sphere is unlikely to have a singular (infinite) velocity as it moves upwards towards the stagnation region at the top of the sphere.