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PublisherThe University of Arizona.
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AbstractTurbulence has long been believed to be associated with the behavior of vorticity. Ever since experiments showed clearly the presence of vortex structures in turbulent flow, concentrated efforts have tried to identify the important dynamics of three-dimensional vortex flow. In particular, conjectures abound about the importance of vortex stretching and vortex line reconnection. Numerical experiments based on ad hoc assumptions on the nature of the cores of vortex filaments have shown interesting behavior. In some cases, it has been argued that singularities develop in finite time and in other cases that the filament exhibits fractal dimensions. These inviscid calculations also show that filaments of opposite signed vorticity tend to pair up and that the local flow is two-dimensional. Consequently, we have begun a study that clarifies the behavior of a pair of counter-rotating vortices in the presence of an external strain flow that would be induced by the presence of vorticity well away from the local two-dimensional plane. So far, the results are quite interesting and depend on the nature of the strain flow. We always assume that the horizontal component of the strain pushes the filaments together. It is the other two components that then affect the results. Without any strain along the axes of the filaments, the vortex cores are pulled into parallel elliptical shapes. Eventually, the cores are so deformed that they become unstable in the same way a parallel shear flow would and the vortex structures disrupt. This phenomenon will be missed by filament codes that assume the cores remain circular. On the other hand, a strain component along the filaments increases the vorticity but keeps the core structure mostly circular. As the cores approach one another, viscous effects overcome the increase in vorticity due to stretching and the cores dissipate away.