Interactions of an impulsively-generated two-dimensional vortex pair with flat plates and cylinders.

C. 'Impingement of an impulsively generated vortex pair upon small diameter cylinders and thin flat plates gives rise to a number of new interaction mechanisms. The vortex pair is generated in water by a piston. Flow is visualized using dye, and the interactions are documented by high speed video recording. Essential to all interaction mechanisms is production of vortices of opposite sense (relative to the respective incident vortices) due to the wall viscous layer; some grow rapidly to nearly the same scale as the incident vortex. Even bodies . whose characteristic length is an order of magnitude smaller than the scale of the incident vortex can drastically alter the vortex structure and trajectory. Horizontal and vertical velocity components were measured using an LDA system, allowing generation of corresponding vorti city., distributions. Vorticity is distributed throughout the vortex pair cell; maximum vorticity occurs at approximately the same location as the visualized vortex center. Comparison of the vorticity distribution with that predicted by an inviscid model exhibits strong agreement, except outside the boundary of the cell where errors in vorticity measurement can be substantial. INTRODUCTION, ^ _ Vortex rings and vortex lines embody the classical meaning of the word vortex. The vortex is the ;flow field that accompanies a concentrated, or continuous, (coherent distribution of vorticity, which, in the limit, may be concentrated at.a point or line (Yule 1978). A vortex is formed in a viscous homogeneous fluid when an impulse is given to a volume of the fluid. A localized region of vorticity is produced by viscous stresses, which cause the volume to entrain ambient fluid and, free of any boundaries, to propagate in the direction of the impulse (Manton 1976). Vortex rings.have been studied for over 100 years. Most mathematical models of the vortex motion assume an inviscid. fluid. The classical analytical works were primarily derived by Kelvin (1867), Hill (1894), Lamb (1932), Prandtl and Tietjens (1934), Sommerfeld (1950), Taylor (1953), and Batchelor (1967). The simplest model is Hill's spherical vortex: the moving fluid is taken to occupy a spherical envelope, with vorticity evenly distributed throughout. One of the more popular models has been Lamb's: the vorticity is assumed to be contained within a torus whose cross-sectional radius is much smaller than the mean radius of the torus. In reality, vortex rings are more like oblate spheroidal vortices, and their properties lie -between the extreme cases of the spherical vortex and the thin