Abstract
We give a brief review of the asymptotic theory of slender vortex filaments to emphasize (1) the choices of scalings, small parameters and the distinguished limit, (2) the consistency conditions, (3) the optimum similar and nonsimilar viscous vortical core structures, and (4) their applications to complement experimental investigations. We present highlights of several extensions of the asymptotic theory: analyses for core structures with axial variation, for the interaction of filaments with a solid body and sound generation, and for a filament in a background rotational flow. We then outline the vortical flow problems currently under investigation. (Author)