Laboratory Measurements of the Circulation Decay of Vortices Generated From a Lifting Wing

Abstract

Circulation measurements of the vortices generated behind a wing are made in both unstratified and stratified water. The circulations are measured in both the two-dimensional line vortices which evolve immediately behind the wing and in the three-dimensional ring vortices which evolve from the line vortices. The measurements show that the circulation decay of the vortices is faster in a stratified fluid than in an unstratified fluid, as expected. The circulations of the line vortices were measured in a plane perpendicular to the direction of motion of the wing. The circulations of the ring vortices were initially measured in a plane parallel to the direction of motion of the wing. Because these two measurement planes are perpendicular to each other, the circulations of ring vortices in an unstratified fluid were also measured in the plane perpendicular to the motion of the wing, that is, in the same measurement plane as the line vortices. These two sets of circulations of the ring vortices, in a plane perpendicular to the motion of the wing and in a plane parallel to the motion of the wing, are shown to be similar. For all the measurements, the circulation decay of vortex rings is shown to be about three times slower than the circulation decay of the line vortices. Finally, the circulations of the line vortices in a stratified fluid, with a Froude number of around 6, are shown to be consistent with measurements of circulations of aircraft vortices out of ground effect in an atmosphere with the same Froude number. This consistency suggests that laboratory measurements of the vortices behind lifting wings may, at least in some cases, be applicable to full-scale aircraft vortices.