A geometrical interpretation of force on a translating body in rotational flow

Some recent results for the force on a translating rigid three-dimensional body in incompressible flow, in which the integration is over the vorticity field rather than surface pressure, are interpreted from a point of view that distinguishes changes of fluid impulse directly attributable to the vorticity field from those due to its image system in the body. An expression is first derived geometrically for a sphere in inviscid fluid; the flow is taken to consist of discrete vortex loops whose change in impulse, and that of the image system in the sphere, are calculated via their projected areas. As an example, the force on a sphere due to an infinite line vortex is calculated exactly. To generalize the geometrical derivation to bodies of any shape, a reciprocal theorem is proved concerning the impulse of the image system of a dipole. This yields the inviscid form of a result derived mathematically by Howe [J. Fluid Mech. 206, 131 (1989)]. Physical interpretations of the various terms in Howe's expression are offered, and the relationship to a very similar independent result by Chang [Proc. R. Sec. London Ser. A 437, 517 (1992)] is discussed. (C) 1996 American Institute of Physics.