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This is not a review paper. It is, rather, a collection of thoughts on the role of asymptotics in a variety of fields, most of which are related to mechanics but are not restricted to fluids. The emphasis is more on the achievements of asymptotics, than on the description of the methods used to achieve these. The topics have been chosen so as to illustrate the versatility of asymptotic methods concerning...
The purpose of this paper is to develop an asymptotic theory for the core of a tightly winded rolled vortex sheet, when winding arises around a line. The physical picture replaces the core by a region of distributed vorticity, the so-called vortex filament. The (pseudo) mathematical picture relies on an algorithm which allows to relate (in a quite convincing but non rigorous way) a flow with vorticity...