The Structure and Dynamics of Vortex Filaments

Recent concern over the hazard presented by the trailing vortices produced by large aircraft has stimulated research into one of the oldest subjects in fluid mechanics: the study of flows with concentrated vorticity in free motion. Since these vortices can be strong and persistent enough to pose a safety hazard to other aircraft, it is clearly desirable to be able to predict the structure, position, and persistence of such vortices as well as to understand the mechanisms by which vortex wakes are dissipated. Under most conditions, trailing vortices undergo a natural sinusoidal instability that eventually causes them to touch and break into a series of crude vortex rings. This process destroys the initial wake structure more rapidly than viscous or turbulent decay of the individual filaments. The character and potential hazard of the residual wake structure after the completion of the sinusoidal instability are still not well understood. It is apparent, however, that the motion, structure, and stability of flows with concentrated vorticity is of great practical interest and leads to an examination of many fundamental problems in fluid mechanics. The first organized attempt to compile what was known about the behavior of aircraft vortices, the process of generation and resulting structure, the hazard created by wake turbulence, and the possibilities for detection, avoidance, or destruction of wake vortices can be found in the proceedings of the conference on "Aircraft Wake Turbulence and Its Detection," edited by Olsen, GGldburg & Rogers (1971). Wc do not attempt a review of all of the technical activities in the field of aircraft wake turbulence; we arc here specifically interested in the fluid mechanics of trailing vortices and vortex rings as well as in the more general problem of the structure, motion, and stability of free vortices: compact regions of concentrated vorticity in free motion in a surrounding fluid that is either homogeneous and at rest or with weak background vorticity or stratification. In a very basic sense, the study of the motion of an incompressible homogeneous